Three-dimensional ordered particulate structures: Method to retrieve characteristics from photonic band gap data

NASA Astrophysics Data System (ADS)

Miskevich, Alexander A.; Loiko, Valery A.

2015-01-01

A method to retrieve characteristics of ordered particulate structures, such as photonic crystals, is proposed. It is based on the solution of the inverse problem using data on the photonic band gap (PBG). The quasicrystalline approximation (QCA) of the theory of multiple scattering of waves and the transfer matrix method (TMM) are used. Retrieval of the refractive index of particles is demonstrated. Refractive indices of the artificial opal particles are estimated using the published experimental data.

A numerical procedure for solving the inverse scattering problem for stratified dielectric media

NASA Astrophysics Data System (ADS)

Vogelzang, E.; Yevick, D.; Ferwerda, H. A.

1983-05-01

In this paper the refractive index profile of a dielectric stratified medium, terminated by a perfect conductor, is calculated from the complex reflection coefficient for monochromatic plane waves, incident from different directions. The advantage of this approach is that the dispersion of the refractive index does not enter the calculations. The calculation is based on the Marchenko and Gelfand-Levitan equations taking into account the bound modes of the layer. Some illustrative numerical examples are presented.

Remote sensing of environmental particulate pollutants - Optical methods for determinations of size distribution and complex refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1978-01-01

A unifying approach, based on a generalization of Pearson's differential equation of statistical theory, is proposed for both the representation of particulate size distribution and the interpretation of radiometric measurements in terms of this parameter. A single-parameter gamma-type distribution is introduced, and it is shown that inversion can only provide the dimensionless parameter, r/ab (where r = particle radius, a = effective radius, b = effective variance), at least when the distribution vanishes at both ends. The basic inversion problem in reconstructing the particle size distribution is analyzed, and the existing methods are reviewed (with emphasis on their capabilities) and classified. A two-step strategy is proposed for simultaneously determining the complex refractive index and reconstructing the size distribution of atmospheric particulates.

TOMO3D: 3-D joint refraction and reflection traveltime tomography parallel code for active-source seismic data—synthetic test

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallarès, V.; Miniussi, A.; Ranero, C. R.

2015-10-01

We present a new 3-D traveltime tomography code (TOMO3D) for the modelling of active-source seismic data that uses the arrival times of both refracted and reflected seismic phases to derive the velocity distribution and the geometry of reflecting boundaries in the subsurface. This code is based on its popular 2-D version TOMO2D from which it inherited the methods to solve the forward and inverse problems. The traveltime calculations are done using a hybrid ray-tracing technique combining the graph and bending methods. The LSQR algorithm is used to perform the iterative regularized inversion to improve the initial velocity and depth models. In order to cope with an increased computational demand due to the incorporation of the third dimension, the forward problem solver, which takes most of the run time (˜90 per cent in the test presented here), has been parallelized with a combination of multi-processing and message passing interface standards. This parallelization distributes the ray-tracing and traveltime calculations among available computational resources. The code's performance is illustrated with a realistic synthetic example, including a checkerboard anomaly and two reflectors, which simulates the geometry of a subduction zone. The code is designed to invert for a single reflector at a time. A data-driven layer-stripping strategy is proposed for cases involving multiple reflectors, and it is tested for the successive inversion of the two reflectors. Layers are bound by consecutive reflectors, and an initial velocity model for each inversion step incorporates the results from previous steps. This strategy poses simpler inversion problems at each step, allowing the recovery of strong velocity discontinuities that would otherwise be smoothened.

Group refractive index reconstruction with broadband interferometric confocal microscopy

PubMed Central

Marks, Daniel L.; Schlachter, Simon C.; Zysk, Adam M.; Boppart, Stephen A.

2010-01-01

We propose a novel method of measuring the group refractive index of biological tissues at the micrometer scale. The technique utilizes a broadband confocal microscope embedded into a Mach–Zehnder interferometer, with which spectral interferograms are measured as the sample is translated through the focus of the beam. The method does not require phase unwrapping and is insensitive to vibrations in the sample and reference arms. High measurement stability is achieved because a single spectral interferogram contains all the information necessary to compute the optical path delay of the beam transmitted through the sample. Included are a physical framework defining the forward problem, linear solutions to the inverse problem, and simulated images of biologically relevant phantoms. PMID:18451922

tomo3d: a new 3-D joint refraction and reflection travel-time tomography code for active-source seismic data

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallares, V.; Ranero, C. R.

2012-12-01

We present the development state of tomo3d, a code for three-dimensional refraction and reflection travel-time tomography of wide-angle seismic data based on the previous two-dimensional version of the code, tomo2d. The core of both forward and inverse problems is inherited from the 2-D version. The ray tracing is performed by a hybrid method combining the graph and bending methods. The graph method finds an ordered array of discrete model nodes, which satisfies Fermat's principle, that is, whose corresponding travel time is a global minimum within the space of discrete nodal connections. The bending method is then applied to produce a more accurate ray path by using the nodes as support points for an interpolation with beta-splines. Travel time tomography is formulated as an iterative linearized inversion, and each step is solved using an LSQR algorithm. In order to avoid the singularity of the sensitivity kernel and to reduce the instability of inversion, regularization parameters are introduced in the inversion in the form of smoothing and damping constraints. Velocity models are built as 3-D meshes, and velocity values at intermediate locations are obtained by trilinear interpolation within the corresponding pseudo-cubic cell. Meshes are sheared to account for topographic relief. A floating reflector is represented by a 2-D grid, and depths at intermediate locations are calculated by bilinear interpolation within the corresponding square cell. The trade-off between the resolution of the final model and the associated computational cost is controlled by the relation between the selected forward star for the graph method (i.e. the number of nodes that each node considers as its neighbors) and the refinement of the velocity mesh. Including reflected phases is advantageous because it provides a better coverage and allows us to define the geometry of those geological interfaces with velocity contrasts sharp enough to be observed on record sections. The code also offers the possibility of including water-layer multiples in the modeling, which is useful whenever these phases can be followed to greater offsets than the primary ones. This increases the amount of information available from the data, yielding more extensive and better constrained velocity and geometry models. We will present synthetic results from benchmark tests for the forward and inverse problems, as well as from more complex inversion tests for different inversions possibilities such as one with travel times from refracted waves only (i.e. first arrivals) and one with travel-times from both refracted and reflected waves. In addition, we will show some preliminary results for the inversion of real 3-D OBS data acquired off-shore Ecuador and Colombia.

Dependence of the forward light scattering on the refractive index of particles

NASA Astrophysics Data System (ADS)

Guo, Lufang; Shen, Jianqi

2018-05-01

In particle sizing technique based on forward light scattering, the scattered light signal (SLS) is closely related to the relative refractive index (RRI) of the particles to the surrounding, especially when the particles are transparent (or weakly absorbent) and the particles are small in size. The interference between the diffraction (Diff) and the multiple internal reflections (MIR) of scattered light can lead to the oscillation of the SLS on RRI and the abnormal intervals, especially for narrowly-distributed small particle systems. This makes the inverse problem more difficult. In order to improve the inverse results, Tikhonov regularization algorithm with B-spline functions is proposed, in which the matrix element is calculated for a range of particle sizes instead using the mean particle diameter of size fractions. In this way, the influence of abnormal intervals on the inverse results can be eliminated. In addition, for measurements on narrowly distributed small particles, it is suggested to detect the SLS in a wider scattering angle to include more information.

Joint inversion of seismic refraction and resistivity data using layered models - applications to hydrogeology

NASA Astrophysics Data System (ADS)

Juhojuntti, N. G.; Kamm, J.

2010-12-01

We present a layered-model approach to joint inversion of shallow seismic refraction and resistivity (DC) data, which we believe is a seldom tested method of addressing the problem. This method has been developed as we believe that for shallow sedimentary environments (roughly <100 m depth) a model with a few layers and sharp layer boundaries better represents the subsurface than a smooth minimum-structure (grid) model. Due to the strong assumption our model parameterization implies on the subsurface, only a low number of well resolved model parameters has to be estimated, and provided that this assumptions holds our method can also be applied to other environments. We are using a least-squares inversion, with lateral smoothness constraints, allowing lateral variations in the seismic velocity and the resistivity but no vertical variations. One exception is a positive gradient in the seismic velocity in the uppermost layer in order to get diving rays (the refractions in the deeper layers are modeled as head waves). We assume no connection between seismic velocity and resistivity, and these parameters are allowed to vary individually within the layers. The layer boundaries are, however, common for both parameters. During the inversion lateral smoothing can be applied to the layer boundaries as well as to the seismic velocity and the resistivity. The number of layers is specified before the inversion, and typically we use models with three layers. Depending on the type of environment it is possible to apply smoothing either to the depth of the layer boundaries or to the thickness of the layers, although normally the former is used for shallow sedimentary environments. The smoothing parameters can be chosen independently for each layer. For the DC data we use a finite-difference algorithm to perform the forward modeling and to calculate the Jacobian matrix, while for the seismic data the corresponding entities are retrieved via ray-tracing, using components from the RAYINVR package. The modular layout of the code makes it straightforward to include other types of geophysical data, i.e. gravity. The code has been tested using synthetic examples with fairly simple 2D geometries, mainly for checking the validity of the calculations. The inversion generally converges towards the correct solution, although there could be stability problems if the starting model is too erroneous. We have also applied the code to field data from seismic refraction and multi-electrode resistivity measurements at typical sand-gravel groundwater reservoirs. The tests are promising, as the calculated depths agree fairly well with information from drilling and the velocity and resistivity values appear reasonable. Current work includes better regularization of the inversion as well as defining individual weight factors for the different datasets, as the present algorithm tends to constrain the depths mainly by using the seismic data. More complex synthetic examples will also be tested, including models addressing the seismic hidden-layer problem.

tomo3d: a new 3-D joint refraction and reflection travel-time tomography code for active-source seismic data

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallarès, V.; Ranero, C. R.

2012-04-01

We present the development state of tomo3d, a code for three-dimensional refraction and reflection travel-time tomography of wide-angle seismic data based on the previous two-dimensional version of the code, tomo2d. The core of both forward and inverse problems is inherited from the 2-D version. The ray tracing is performed by a hybrid method combining the graph and bending methods. The graph method finds an ordered array of discrete model nodes, which satisfies Fermat's principle, that is, whose corresponding travel time is a global minimum within the space of discrete nodal connections. The bending method is then applied to produce a more accurate ray path by using the nodes as support points for an interpolation with beta-splines. Travel time tomography is formulated as an iterative linearized inversion, and each step is solved using an LSQR algorithm. In order to avoid the singularity of the sensitivity kernel and to reduce the instability of inversion, regularization parameters are introduced in the inversion in the form of smoothing and damping constraints. Velocity models are built as 3-D meshes, and velocity values at intermediate locations are obtained by trilinear interpolation within the corresponding pseudo-cubic cell. Meshes are sheared to account for topographic relief. A floating reflector is represented by a 2-D grid, and depths at intermediate locations are calculated by bilinear interpolation within the corresponding square cell. The trade-off between the resolution of the final model and the associated computational cost is controlled by the relation between the selected forward star for the graph method (i.e. the number of nodes that each node considers as its neighbors) and the refinement of the velocity mesh. Including reflected phases is advantageous because it provides a better coverage and allows us to define the geometry of those geological interfaces with velocity contrasts sharp enough to be observed on record sections. The code also offers the possibility of including water-layer multiples in the modeling, whenever this phase can be followed to greater offsets than the primary phases. This increases the quantity of useful information in the data and yields more extensive and better constrained velocity and geometry models. We will present results from benchmark tests for forward and inverse problems, as well as synthetic tests comparing an inversion with refractions only and another one with both refractions and reflections.

Numerical methods for the design of gradient-index optical coatings.

PubMed

Anzengruber, Stephan W; Klann, Esther; Ramlau, Ronny; Tonova, Diana

2012-12-01

We formulate the problem of designing gradient-index optical coatings as the task of solving a system of operator equations. We use iterative numerical procedures known from the theory of inverse problems to solve it with respect to the coating refractive index profile and thickness. The mathematical derivations necessary for the application of the procedures are presented, and different numerical methods (Landweber, Newton, and Gauss-Newton methods, Tikhonov minimization with surrogate functionals) are implemented. Procedures for the transformation of the gradient coating designs into quasi-gradient ones (i.e., multilayer stacks of homogeneous layers with different refractive indices) are also developed. The design algorithms work with physically available coating materials that could be produced with the modern coating technologies.

Retrieval of the aerosol size distribution in the complex anomalous diffraction approximation

NASA Astrophysics Data System (ADS)

Franssens, Ghislain R.

This contribution reports some recently achieved results in aerosol size distribution retrieval in the complex anomalous diffraction approximation (ADA) to MIE scattering theory. This approximation is valid for spherical particles that are large compared to the wavelength and have a refractive index close to 1. The ADA kernel is compared with the exact MIE kernel. Despite being a simple approximation, the ADA seems to have some practical value for the retrieval of the larger modes of tropospheric and lower stratospheric aerosols. The ADA has the advantage over MIE theory that an analytic inversion of the associated Fredholm integral equation becomes possible. In addition, spectral inversion in the ADA can be formulated as a well-posed problem. In this way, a new inverse formula was obtained, which allows the direct computation of the size distribution as an integral over the spectral extinction function. This formula is valid for particles that both scatter and absorb light and it also takes the spectral dispersion of the refractive index into account. Some details of the numerical implementation of the inverse formula are illustrated using a modified gamma test distribution. Special attention is given to the integration of spectrally truncated discrete extinction data with errors.

Retrieving the aerosol complex refractive index using PyMieScatt: A Mie computational package with visualization capabilities

NASA Astrophysics Data System (ADS)

Sumlin, Benjamin J.; Heinson, William R.; Chakrabarty, Rajan K.

2018-01-01

The complex refractive index m = n + ik of a particle is an intrinsic property which cannot be directly measured; it must be inferred from its extrinsic properties such as the scattering and absorption cross-sections. Bohren and Huffman called this approach "describing the dragon from its tracks", since the inversion of Lorenz-Mie theory equations is intractable without the use of computers. This article describes PyMieScatt, an open-source module for Python that contains functionality for solving the inverse problem for complex m using extensive optical and physical properties as input, and calculating regions where valid solutions may exist within the error bounds of laboratory measurements. Additionally, the module has comprehensive capabilities for studying homogeneous and coated single spheres, as well as ensembles of homogeneous spheres with user-defined size distributions, making it a complete tool for studying the optical behavior of spherical particles.

The investigation of advanced remote sensing techniques for the measurement of aerosol characteristics

NASA Technical Reports Server (NTRS)

Deepak, A.; Becher, J.

1979-01-01

Advanced remote sensing techniques and inversion methods for the measurement of characteristics of aerosol and gaseous species in the atmosphere were investigated. Of particular interest were the physical and chemical properties of aerosols, such as their size distribution, number concentration, and complex refractive index, and the vertical distribution of these properties on a local as well as global scale. Remote sensing techniques for monitoring of tropospheric aerosols were developed as well as satellite monitoring of upper tropospheric and stratospheric aerosols. Computer programs were developed for solving multiple scattering and radiative transfer problems, as well as inversion/retrieval problems. A necessary aspect of these efforts was to develop models of aerosol properties.

Spectral solution of the inverse Mie problem

NASA Astrophysics Data System (ADS)

Romanov, Andrey V.; Konokhova, Anastasiya I.; Yastrebova, Ekaterina S.; Gilev, Konstantin V.; Strokotov, Dmitry I.; Chernyshev, Andrei V.; Maltsev, Valeri P.; Yurkin, Maxim A.

2017-10-01

We developed a fast method to determine size and refractive index of homogeneous spheres from the power Fourier spectrum of their light-scattering patterns (LSPs), measured with the scanning flow cytometer. Specifically, we used two spectral parameters: the location of the non-zero peak and zero-frequency amplitude, and numerically inverted the map from the space of particle characteristics (size and refractive index) to the space of spectral parameters. The latter parameters can be reliably resolved only for particle size parameter greater than 11, and the inversion is unique only in the limited range of refractive index with upper limit between 1.1 and 1.25 (relative to the medium) depending on the size parameter and particular definition of uniqueness. The developed method was tested on two experimental samples, milk fat globules and spherized red blood cells, and resulted in accuracy not worse than the reference method based on the least-square fit of the LSP with the Mie theory. Moreover, for particles with significant deviation from the spherical shape the spectral method was much closer to the Mie-fit result than the estimated uncertainty of the latter. The spectral method also showed adequate results for synthetic LSPs of spheroids with aspect ratios up to 1.4. Overall, we present a general framework, which can be used to construct an inverse algorithm for any other experimental signals.

[Research on the measurement range of particle size with total light scattering method in vis-IR region].

PubMed

Sun, Xiao-gang; Tang, Hong; Dai, Jing-min

2008-12-01

The problem of determining the particle size range in the visible-infrared region was studied using the independent model algorithm in the total scattering technique. By the analysis and comparison of the accuracy of the inversion results for different R-R distributions, the measurement range of particle size was determined. Meanwhile, the corrected extinction coefficient was used instead of the original extinction coefficient, which could determine the measurement range of particle size with higher accuracy. Simulation experiments illustrate that the particle size distribution can be retrieved very well in the range from 0. 05 to 18 microm at relative refractive index m=1.235 in the visible-infrared spectral region, and the measurement range of particle size will vary with the varied wavelength range and relative refractive index. It is feasible to use the constrained least squares inversion method in the independent model to overcome the influence of the measurement error, and the inverse results are all still satisfactory when 1% stochastic noise is added to the value of the light extinction.

Use of Ensemble Numerical Weather Prediction Data for Inversely Determining Atmospheric Refractivity in Surface Ducting Conditions

NASA Astrophysics Data System (ADS)

Greenway, D. P.; Hackett, E.

2017-12-01

Under certain atmospheric refractivity conditions, propagated electromagnetic waves (EM) can become trapped between the surface and the bottom of the atmosphere's mixed layer, which is referred to as surface duct propagation. Being able to predict the presence of these surface ducts can reap many benefits to users and developers of sensing technologies and communication systems because they significantly influence the performance of these systems. However, the ability to directly measure or model a surface ducting layer is challenging due to the high spatial resolution and large spatial coverage needed to make accurate refractivity estimates for EM propagation; thus, inverse methods have become an increasingly popular way of determining atmospheric refractivity. This study uses data from the Coupled Ocean/Atmosphere Mesoscale Prediction System developed by the Naval Research Laboratory and instrumented helicopter (helo) measurements taken during the Wallops Island Field Experiment to evaluate the use of ensemble forecasts in refractivity inversions. Helo measurements and ensemble forecasts are optimized to a parametric refractivity model, and three experiments are performed to evaluate whether incorporation of ensemble forecast data aids in more timely and accurate inverse solutions using genetic algorithms. The results suggest that using optimized ensemble members as an initial population for the genetic algorithms generally enhances the accuracy and speed of the inverse solution; however, use of the ensemble data to restrict parameter search space yields mixed results. Inaccurate results are related to parameterization of the ensemble members' refractivity profile and the subsequent extraction of the parameter ranges to limit the search space.

Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1976-01-01

The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

New infrared transmitting material via inverse vulcanization of elemental sulfur to prepare high refractive index polymers.

PubMed

Griebel, Jared J; Namnabat, Soha; Kim, Eui Tae; Himmelhuber, Roland; Moronta, Dominic H; Chung, Woo Jin; Simmonds, Adam G; Kim, Kyung-Jo; van der Laan, John; Nguyen, Ngoc A; Dereniak, Eustace L; Mackay, Michael E; Char, Kookheon; Glass, Richard S; Norwood, Robert A; Pyun, Jeffrey

2014-05-21

Polymers for IR imaging: The preparation of high refractive index polymers (n = 1.75 to 1.86) via the inverse vulcanization of elemental sulfur is reported. High quality imaging in the near (1.5 μm) and mid-IR (3-5 μm) regions using high refractive index polymeric lenses from these sulfur materials was demonstrated. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mature red blood cells: from optical model to inverse light-scattering problem.

PubMed

Gilev, Konstantin V; Yurkin, Maxim A; Chernyshova, Ekaterina S; Strokotov, Dmitry I; Chernyshev, Andrei V; Maltsev, Valeri P

2016-04-01

We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content.

Mature red blood cells: from optical model to inverse light-scattering problem

PubMed Central

Gilev, Konstantin V.; Yurkin, Maxim A.; Chernyshova, Ekaterina S.; Strokotov, Dmitry I.; Chernyshev, Andrei V.; Maltsev, Valeri P.

2016-01-01

We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content. PMID:27446656

Joint refraction and reflection travel-time tomography of multichannel and wide-angle seismic data

NASA Astrophysics Data System (ADS)

Begovic, Slaven; Meléndez, Adrià; Ranero, César; Sallarès, Valentí

2017-04-01

Both near-vertical multichannel (MCS) and wide-angle (WAS) seismic data are sensitive to same properties of sampled model, but commonly they are interpreted and modeled using different approaches. Traditional MCS images provide good information on position and geometry of reflectors especially in shallow, commonly sedimentary layers, but have limited or no refracted waves, which severely hampers the retrieval of velocity information. Compared to MCS data, conventional wide-angle seismic (WAS) travel-time tomography uses sparse data (generally stations are spaced by several kilometers). While it has refractions that allow retrieving velocity information, the data sparsity makes it difficult to define velocity and the geometry of geologic boundaries (reflectors) with the appropriate resolution, especially at the shallowest crustal levels. A well-known strategy to overcome these limitations is to combine MCS and WAS data into a common inversion strategy. However, the number of available codes that can jointly invert for both types of data is limited. We have adapted the well-known and widely-used joint refraction and reflection travel-time tomography code tomo2d (Korenaga et al, 2000), and its 3D version tomo3d (Meléndez et al, 2015), to implement streamer data and multichannel acquisition geometries. This allows performing joint travel-time tomographic inversion based on refracted and reflected phases from both WAS and MCS data sets. We show with a series of synthetic tests following a layer-stripping strategy that combining these two data sets into joint travel-time tomographic method the drawbacks of each data set are notably reduced. First, we have tested traditional travel-time inversion scheme using only WAS data (refracted and reflected phases) with typical acquisition geometry with one ocean bottom seismometer (OBS) each 10 km. Second, we have jointly inverted WAS refracted and reflected phases with only streamer (MCS) reflection travel-times. And at the end we have performed joint inversion of combined refracted and reflected phases from both data sets. MCS data set (synthetic) has been produced for a 8 km-long streamer and refracted phases used for the streamer have been downward continued (projected on the seafloor). Taking advantage of high redundancy of MCS data, the definition of geometry of reflectors and velocity of uppermost layers are much improved. Additionally, long- offset wide-angle refracted phases minimize velocity-depth trade-off of reflection travel-time inversion. As a result, the obtained models have increased accuracy in both velocity and reflector's geometry as compared to the independent inversion of each data set. This is further corroborated by performing a statistical parameter uncertainty analysis to explore the effects of unknown initial model and data noise in the linearized inversion scheme.

Refractive-index measurement and inverse correction using optical coherence tomography.

PubMed

Stritzel, Jenny; Rahlves, Maik; Roth, Bernhard

2015-12-01

We describe a novel technique for determination of the refractive index of hard biological tissue as well as nonopaque technical samples based on optical coherence tomography (OCT). Our method relies on an inverse refractive-index correction (I-RIC), which matches a measured feature geometry distorted due to refractive-index boundaries to its real geometry. For known feature geometry, the refractive index can be determined with high precision from the best match between the distorted and corrected images. We provide experimental data for refractive-index measurements on a polymethylmethacrylate (PMMA) and on an ex vivo porcine cranial-bone, which are compared to reference measurements and previously published data. Our method is potentially capable of in vivo measurements on rigid biological tissue such as bone as, for example, is required to improve guidance in robot-aided surgical interventions and also for retrieving complex refractive-index profiles of compound materials.

Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity. [numerical tests for water-haze aerosol model

NASA Technical Reports Server (NTRS)

Smith, C. B.

1982-01-01

The Fymat analytic inversion method for retrieving a particle-area distribution function from anomalous diffraction multispectral extinction data and total area is generalized to the case of a variable complex refractive index m(lambda) near unity depending on spectral wavelength lambda. Inversion tests are presented for a water-haze aerosol model. An upper-phase shift limit of 5 pi/2 retrieved an accurate peak area distribution profile. Analytical corrections using both the total number and area improved the inversion.

Terahertz multistatic reflection imaging.

PubMed

Dorney, Timothy D; Symes, William W; Baraniuk, Richard G; Mittleman, Daniel M

2002-07-01

We describe a new imaging method using single-cycle pulses of terahertz (THz) radiation. This technique emulates the data collection and image processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a migration procedure to solve the inverse problem; this permits us to reconstruct the location, the shape, and the refractive index of targets. We show examples for both metallic and dielectric model targets, and we perform velocity analysis on dielectric targets to estimate the refractive indices of imaged components. These results broaden the capabilities of THz imaging systems and also demonstrate the viability of the THz system as a test bed for the exploration of new seismic processing methods.

S-Genius, a universal software platform with versatile inverse problem resolution for scatterometry

NASA Astrophysics Data System (ADS)

Fuard, David; Troscompt, Nicolas; El Kalyoubi, Ismael; Soulan, Sébastien; Besacier, Maxime

2013-05-01

S-Genius is a new universal scatterometry platform, which gathers all the LTM-CNRS know-how regarding the rigorous electromagnetic computation and several inverse problem solver solutions. This software platform is built to be a userfriendly, light, swift, accurate, user-oriented scatterometry tool, compatible with any ellipsometric measurements to fit and any types of pattern. It aims to combine a set of inverse problem solver capabilities — via adapted Levenberg- Marquard optimization, Kriging, Neural Network solutions — that greatly improve the reliability and the velocity of the solution determination. Furthermore, as the model solution is mainly vulnerable to materials optical properties, S-Genius may be coupled with an innovative material refractive indices determination. This paper will a little bit more focuses on the modified Levenberg-Marquardt optimization, one of the indirect method solver built up in parallel with the total SGenius software coding by yours truly. This modified Levenberg-Marquardt optimization corresponds to a Newton algorithm with an adapted damping parameter regarding the definition domains of the optimized parameters. Currently, S-Genius is technically ready for scientific collaboration, python-powered, multi-platform (windows/linux/macOS), multi-core, ready for 2D- (infinite features along the direction perpendicular to the incident plane), conical, and 3D-features computation, compatible with all kinds of input data from any possible ellipsometers (angle or wavelength resolved) or reflectometers, and widely used in our laboratory for resist trimming studies, etching features characterization (such as complex stack) or nano-imprint lithography measurements for instance. The work about kriging solver, neural network solver and material refractive indices determination is done (or about to) by other LTM members and about to be integrated on S-Genius platform.

Refraction traveltime tomography based on damped wave equation for irregular topographic model

NASA Astrophysics Data System (ADS)

Park, Yunhui; Pyun, Sukjoon

2018-03-01

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.

Blind test of methods for obtaining 2-D near-surface seismic velocity models from first-arrival traveltimes

USGS Publications Warehouse

Zelt, Colin A.; Haines, Seth; Powers, Michael H.; Sheehan, Jacob; Rohdewald, Siegfried; Link, Curtis; Hayashi, Koichi; Zhao, Don; Zhou, Hua-wei; Burton, Bethany L.; Petersen, Uni K.; Bonal, Nedra D.; Doll, William E.

2013-01-01

Seismic refraction methods are used in environmental and engineering studies to image the shallow subsurface. We present a blind test of inversion and tomographic refraction analysis methods using a synthetic first-arrival-time dataset that was made available to the community in 2010. The data are realistic in terms of the near-surface velocity model, shot-receiver geometry and the data's frequency and added noise. Fourteen estimated models were determined by ten participants using eight different inversion algorithms, with the true model unknown to the participants until it was revealed at a session at the 2011 SAGEEP meeting. The estimated models are generally consistent in terms of their large-scale features, demonstrating the robustness of refraction data inversion in general, and the eight inversion algorithms in particular. When compared to the true model, all of the estimated models contain a smooth expression of its two main features: a large offset in the bedrock and the top of a steeply dipping low-velocity fault zone. The estimated models do not contain a subtle low-velocity zone and other fine-scale features, in accord with conventional wisdom. Together, the results support confidence in the reliability and robustness of modern refraction inversion and tomographic methods.

Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Greenberg, P. S.

1994-01-01

Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

Application of 2-D travel-time inversion of seismic refraction data to the mid-continent rift beneath Lake Superior

USGS Publications Warehouse

Lutter, William J.; Tréhu, Anne M.; Nowack, Robert L.

1993-01-01

The inversion technique of Nowack and Lutter (1988a) and Lutter et al. (1990) has been applied to first arrival seismic refraction data collected along Line A of the 1986 Lake Superior GLIMPCE experiment, permitting comparison of the inversion image with an independently derived forward model (Trehu et al., 1991; Shay and Trehu, in press). For this study, the inversion method was expanded to allow variable grid spacing for the bicubic spline parameterization of velocity. The variable grid spacing improved model delineation and data fit by permitting model parameters to be clustered at features of interest. Over 800 first-arrival travel-times were fit with a final RMS error of 0.045 s. The inversion model images a low velocity central graben and smaller flanking half-grabens of the Midcontinent Rift, and higher velocity regions (+0.5 to +0.75 km/s) associated with the Isle Royale and Keweenaw faults, which bound the central graben. Although the forward modeling interpretation gives finer details associated with the near surface expression of the two faults because of the inclusion of secondary reflections and refractions that were not included in the inversion, the inversion model reproduces the primary features of the forward model.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Accounting for the Complex Surface Structure in Ellipsometric Studies of the Effects of Magnetron Sputtering Modes on the Growth and Optical Properties of In2O3 Films

NASA Astrophysics Data System (ADS)

Tikhii, A. A.; Nikolaenko, Yu. M.; Gritskih, V. A.; Svyrydova, K. A.; Murga, V. V.; Zhikhareva, Yu. I.; Zhikharev, I. V.

2018-03-01

The efficiency of invoking additional information on optical transmission in solving the inverse problem of ellipsometry by a minimization method is demonstrated in practice for In2O3 fi doped and nondoped with Sn on Al2O3 (012) substrates. This approach allows the thickness and refractive index of thin films with rough surfaces to be uniquely determined. Solutions of the inverse problem in the framework of one-, two-, and multilayer models are compared. The last provides the best description of the experimental data and the correct parameters of the samples. The dependences of the investigated properties of films produced with different magnetron sputtering modes are found using the above methods and models and do not contradict general concepts about the film formation by this material.

Interface with weakly singular points always scatter

NASA Astrophysics Data System (ADS)

Li, Long; Hu, Guanghui; Yang, Jiansheng

2018-07-01

Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly singular point, we prove that the scattered field cannot vanish identically. This implies the absence of non-scattering energies for piecewise analytic interfaces with one singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.

Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

PubMed

Franssens, G; De Maziére, M; Fonteyn, D

2000-08-20

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

A Methodology to Seperate and Analyze a Seismic Wide Angle Profile

NASA Astrophysics Data System (ADS)

Weinzierl, Wolfgang; Kopp, Heidrun

2010-05-01

General solutions of inverse problems can often be obtained through the introduction of probability distributions to sample the model space. We present a simple approach of defining an a priori space in a tomographic study and retrieve the velocity-depth posterior distribution by a Monte Carlo method. Utilizing a fitting routine designed for very low statistics to setup and analyze the obtained tomography results, it is possible to statistically separate the velocity-depth model space derived from the inversion of seismic refraction data. An example of a profile acquired in the Lesser Antilles subduction zone reveals the effectiveness of this approach. The resolution analysis of the structural heterogeneity includes a divergence analysis which proves to be capable of dissecting long wide-angle profiles for deep crust and upper mantle studies. The complete information of any parameterised physical system is contained in the a posteriori distribution. Methods for analyzing and displaying key properties of the a posteriori distributions of highly nonlinear inverse problems are therefore essential in the scope of any interpretation. From this study we infer several conclusions concerning the interpretation of the tomographic approach. By calculating a global as well as singular misfits of velocities we are able to map different geological units along a profile. Comparing velocity distributions with the result of a tomographic inversion along the profile we can mimic the subsurface structures in their extent and composition. The possibility of gaining a priori information for seismic refraction analysis by a simple solution to an inverse problem and subsequent resolution of structural heterogeneities through a divergence analysis is a new and simple way of defining a priori space and estimating the a posteriori mean and covariance in singular and general form. The major advantage of a Monte Carlo based approach in our case study is the obtained knowledge of velocity depth distributions. Certainly the decision of where to extract velocity information on the profile for setting up a Monte Carlo ensemble is limiting the a priori space. However, the general conclusion of analyzing the velocity field according to distinct reference distributions gives us the possibility to define the covariance according to any geological unit if we have a priori information on the velocity depth distributions. Using the wide angle data recorded across the Lesser Antilles arc, we are able to resolve a shallow feature like the backstop by a robust and simple divergence analysis. We demonstrate the effectiveness of the new methodology to extract some key features and properties from the inversion results by including information concerning the confidence level of results.

Inverse Abbe-method for observing small refractive index changes in liquids.

PubMed

Räty, Jukka; Peiponen, Kai-Erik

2015-05-01

This study concerns an optical method for the detection of minuscule refractive index changes in the liquid phase. The proposed method reverses the operation of the traditional Abbe refractometer and thus utilizes the light dispersion properties of materials, i.e. it involves the dependence of the refractive index on light wavelength. In practice, the method includes the detection of light reflection spectra in the visible spectral range. This inverse Abbe method is suitable for liquid quality studies e.g. for monitoring water purity. Tests have shown that the method reveals less than per mil NaCl or ethanol concentrations in water. Copyright © 2015 Elsevier B.V. All rights reserved.

Radiation characteristics and effective optical properties of dumbbell-shaped cyanobacterium Synechocystis sp.

NASA Astrophysics Data System (ADS)

Heng, Ri-Liang; Pilon, Laurent

2016-05-01

This study presents experimental measurements of the radiation characteristics of unicellular freshwater cyanobacterium Synechocystis sp. during their exponential growth in F medium. Their scattering phase function at 633 nm average spectral absorption and scattering cross-sections between 400 and 750 nm were measured. In addition, an inverse method was used for retrieving the spectral effective complex index of refraction of overlapping or touching bispheres and quadspheres from their absorption and scattering cross-sections. The inverse method combines a genetic algorithm and a forward model based on Lorenz-Mie theory, treating bispheres and quadspheres as projected area and volume-equivalent coated spheres. The inverse method was successfully validated with numerically predicted average absorption and scattering cross-sections of suspensions consisting of bispheres and quadspheres, with realistic size distributions, using the T-matrix method. It was able to retrieve the monomers' complex index of refraction with size parameter up to 11, relative refraction index less than 1.3, and absorption index less than 0.1. Then, the inverse method was applied to retrieve the effective spectral complex index of refraction of Synechocystis sp. approximated as randomly oriented aggregates consisting of two overlapping homogeneous spheres. Both the measured absorption cross-section and the retrieved absorption index featured peaks at 435 and 676 nm corresponding to chlorophyll a, a peak at 625 nm corresponding to phycocyanin, and a shoulder around 485 nm corresponding to carotenoids. These results can be used to optimize and control light transfer in photobioreactors. The inverse method and the equivalent coated sphere model could be applied to other optically soft particles of similar morphologies.

Inverse Doppler Effects in Broadband Acoustic Metamaterials

PubMed Central

Zhai, S. L.; Zhao, X. P.; Liu, S.; Shen, F. L.; Li, L. L.; Luo, C. R.

2016-01-01

The Doppler effect refers to the change in frequency of a wave source as a consequence of the relative motion between the source and an observer. Veselago theoretically predicted that materials with negative refractions can induce inverse Doppler effects. With the development of metamaterials, inverse Doppler effects have been extensively investigated. However, the ideal material parameters prescribed by these metamaterial design approaches are complex and also challenging to obtain experimentally. Here, we demonstrated a method of designing and experimentally characterising arbitrary broadband acoustic metamaterials. These omni-directional, double-negative, acoustic metamaterials are constructed with ‘flute-like’ acoustic meta-cluster sets with seven double meta-molecules; these metamaterials also overcome the limitations of broadband negative bulk modulus and mass density to provide a region of negative refraction and inverse Doppler effects. It was also shown that inverse Doppler effects can be detected in a flute, which has been popular for thousands of years in Asia and Europe. PMID:27578317

Inverse Doppler Effects in Broadband Acoustic Metamaterials

NASA Astrophysics Data System (ADS)

Zhai, S. L.; Zhao, X. P.; Liu, S.; Shen, F. L.; Li, L. L.; Luo, C. R.

2016-08-01

The Doppler effect refers to the change in frequency of a wave source as a consequence of the relative motion between the source and an observer. Veselago theoretically predicted that materials with negative refractions can induce inverse Doppler effects. With the development of metamaterials, inverse Doppler effects have been extensively investigated. However, the ideal material parameters prescribed by these metamaterial design approaches are complex and also challenging to obtain experimentally. Here, we demonstrated a method of designing and experimentally characterising arbitrary broadband acoustic metamaterials. These omni-directional, double-negative, acoustic metamaterials are constructed with ‘flute-like’ acoustic meta-cluster sets with seven double meta-molecules; these metamaterials also overcome the limitations of broadband negative bulk modulus and mass density to provide a region of negative refraction and inverse Doppler effects. It was also shown that inverse Doppler effects can be detected in a flute, which has been popular for thousands of years in Asia and Europe.

A novel inverse method for determining the refractive indices of medium and dispersed particles simultaneously by turbidity measurement.

PubMed

Xu, Shenghua; Liu, Jie; Sun, Zhiwei; Zhang, Pu

2008-10-01

The refractive indices of particles and dispersion medium are important parameters in many colloidal experiments using optical techniques, such as turbidity and light scattering measurements. These data are in general wavelength-dependent and may not be available at some wavelengths fitting to the experimental requirement. In this study we present a novel approach to inversely determine the refractive indices of particles and dispersion medium by examining the consistency of measured extinction cross sections of particles with their theoretical values using a series of trial values of the refractive indices. The colloidal suspension of polystyrene particles dispersed in water was used as an example to demonstrate how this approach works and the data obtained via such a method are compared with those reported in literature, showing a good agreement between both. Furthermore, the factors that affect the accuracy of measurements are discussed. We also present some data of the refractive indices of polystyrene over a range of wavelengths smaller than 400 nm that have been not reported in the available literature.

Retrieval of Aerosol Microphysical Properties from AERONET Photo-Polarimetric Measurements. 2: A New Research Algorithm and Case Demonstration

NASA Technical Reports Server (NTRS)

Xu, Xiaoguang; Wang, Jun; Zeng, Jing; Spurr, Robert; Liu, Xiong; Dubovik, Oleg; Li, Li; Li, Zhengqiang; Mishchenko, Michael I.; Siniuk, Aliaksandr;

Delineation of sediments below flood basalts by joint inversion of seismic and magnetotelluric data

NASA Astrophysics Data System (ADS)

Manglik, A.; Verma, Saurabh K.

A one-dimensional joint-inversion (JI) scheme considering seismic reflection and refraction, and MT data is developed. Its efficacy to resolve low velocity conducting sediments below high velocity resistive flood basalts is tested for a representative geological model considering noisy, incomplete data. The JI is found to provide improved results in comparison to those obtained by individual seismic and MT inversions.

Frequency Domain Full-Waveform Inversion in Imaging Thrust Related Features

NASA Astrophysics Data System (ADS)

Jaiswal, P.; Zelt, C. A.

2010-12-01

Seismic acquisition in rough terrain such as mountain belts suffers from problems related to near-surface conditions such as statics, inconsistent energy penetration, rapid decay of signal, and imperfect receiver coupling. Moreover in the presence of weakly compacted soil, strong ground roll may obscure the reflection arrivals at near offsets further diminishing the scope of estimating a reliable near surface image though conventional processing. Traveltime and waveform inversion not only overcome the simplistic assumptions inherent in conventional processing such as hyperbolic moveout and convolution model, but also use parts of the seismic coda, such as the direct arrival and refractions, that are discarded in the latter. Traveltime and waveform inversion are model-based methods that honour the physics of wave propagation. Given the right set of preconditioned data and starting model, waveform inversion in particular has been realized as a powerful tool for velocity model building. This paper examines two case studies on waveform inversion using real data from the Naga Thrust Belt in the Northeast India. Waveform inversion in this paper is performed in the frequency domain and is multiscale in nature i.e., the inversion progressively ascends from the lower to the higher end of the frequency spectra increasing the wavenumber content of the recovered model. Since the real data are band limited, the success of waveform inversion depends on how well the starting model can account for the missing low wavenumbers. In this paper it is observed that the required starting model can be prepared using the regularized inversion of direct and reflected arrival times.

A tunable fiber-optic LED illumination system for non-invasive measurements of the characteristics of a transparent fiber

NASA Astrophysics Data System (ADS)

Świrniak, Grzegorz; Głomb, Grzegorz

2017-06-01

This study reports an application of a fiber-optic LED-based illumination system to solve an inverse problem in optical measurements of characteristics of a single-mode fiber. The illumination system has the advantages of low temporal coherence, high intensity, collimation, and thermal stability of the emission spectrum. The inverse analysis is investigated to predict the values of the diameter and refractive index of a single-mode fiber and applies to the far field scattering pattern in the vicinity of a polychromatic rainbow. As the inversion possibility depends considerably on the properties of the incident radiation, a detailed discussion is provided on both the specification of the illumination system as well as preliminary characteristics of the produced radiation. The illumination system uses a direct coupling between a thermally-stabilized LED junction and a plastic optical fiber, which transmits light to an optical collimator. A numerical study of fiber-to-LED coupling efficiency helps to understand the influence of lateral and longitudinal misalignments on the output power.

Apparatus and method to compensate for refraction of radiation

DOEpatents

Allen, Gary R.; Moskowitz, Philip E.

1990-01-01

An apparatus to compensate for refraction of radiation passing through a curved wall of an article is provided. The apparatus of a preferred embodiment is particularly advantageous for use in arc tube discharge diagnostics. The apparatus of the preferred embodiment includes means for pre-refracting radiation on a predetermined path by an amount equal and inverse to refraction which occurs when radiation passes through a first wall of the arc tube such that, when the radiation passes through the first wall of the arc tube and into the cavity thereof, the radiation passes through the cavity approximately on the predetermined path; means for releasably holding the article such that the radiation passes through the cavity thereof; and means for post-refracting radiation emerging from a point of the arc tube opposite its point of entry by an amount equal and inverse to refraction which occurs when radiation emerges from the arc tube. In one embodiment the means for pre-refracting radiation includes a first half tube comprising a longitudinally bisected tube obtained from a tube which is approximately identical to the arc tube's cylindrical portion and a first cylindrical lens, the first half tube being mounted with its concave side facing the radiation source and the first cylindrical lens being mounted between the first half tube and the arc tube and the means for post-refracting radiation includes a second half tube comprising a longitudinally bisected tube obtained from a tube which is approximately identical to the arc tube's cylindrical portion and a second cylindrical lens, the second half tube being mounted with its convex side facing the radiation source and the second cylindrical lens being mounted between the arc tube and the second half tube. Methods to compensate for refraction of radiation passing into and out of an arc tube is also provided.

Apparatus and method to compensate for refraction of radiation

DOEpatents

Allen, G.R.; Moskowitz, P.E.

1990-03-27

An apparatus to compensate for refraction of radiation passing through a curved wall of an article is provided. The apparatus of a preferred embodiment is particularly advantageous for use in arc tube discharge diagnostics. The apparatus of the preferred embodiment includes means for pre-refracting radiation on a predetermined path by an amount equal and inverse to refraction which occurs when radiation passes through a first wall of the arc tube such that, when the radiation passes through the first wall of the arc tube and into the cavity thereof, the radiation passes through the cavity approximately on the predetermined path; means for releasably holding the article such that the radiation passes through the cavity thereof; and means for post-refracting radiation emerging from a point of the arc tube opposite its point of entry by an amount equal and inverse to refraction which occurs when radiation emerges from the arc tube. In one embodiment the means for pre-refracting radiation includes a first half tube comprising a longitudinally bisected tube obtained from a tube which is approximately identical to the arc tube's cylindrical portion and a first cylindrical lens, the first half tube being mounted with its concave side facing the radiation source and the first cylindrical lens being mounted between the first half tube and the arc tube and the means for post-refracting radiation includes a second half tube comprising a longitudinally bisected tube obtained from a tube which is approximately identical to the arc tube's cylindrical portion and a second cylindrical lens, the second half tube being mounted with its convex side facing the radiation source and the second cylindrical lens being mounted between the arc tube and the second half tube. Methods to compensate for refraction of radiation passing into and out of an arc tube is also provided. 4 figs.

Crustal Structure Beneath Taiwan Using Frequency-band Inversion of Receiver Function Waveforms

NASA Astrophysics Data System (ADS)

Tomfohrde, D. A.; Nowack, R. L.

Receiver function analysis is used to determine local crustal structure beneath Taiwan. We have performed preliminary data processing and polarization analysis for the selection of stations and events and to increase overall data quality. Receiver function analysis is then applied to data from the Taiwan Seismic Network to obtain radial and transverse receiver functions. Due to the limited azimuthal coverage, only the radial receiver functions are analyzed in terms of horizontally layered crustal structure for each station. In order to improve convergence of the receiver function inversion, frequency-band inversion (FBI) is implemented, in which an iterative inversion procedure with sequentially higher low-pass corner frequencies is used to stabilize the waveform inversion. Frequency-band inversion is applied to receiver functions at six stations of the Taiwan Seismic Network. Initial 20-layer crustal models are inverted for using prior tomographic results for the initial models. The resulting 20-1ayer models are then simplified to 4 to 5 layer models and input into an alternating depth and velocity frequency-band inversion. For the six stations investigated, the resulting simplified models provide an average estimate of 38 km for the Moho thickness surrounding the Central Range of Taiwan. Also, the individual station estimates compare well with the recent tomographic model of and the refraction results of Rau and Wu (1995) and the refraction results of Ma and Song (1997).

Wide angle reflection effects on the uncertainty in layered models travel times tomography

NASA Astrophysics Data System (ADS)

Majdanski, Mariusz; Bialas, Sebastian; Trzeciak, Maciej; Gaczyński, Edward; Maksym, Andrzej

2015-04-01

Multi-phase layered model traveltimes tomography inversions can be realised in several ways depending on the inversion path. Inverting the shape of the boundaries based on reflection data and the velocity field based on refractions could be done jointly or sequentially. We analyse an optimal inversion path based on the uncertainty analysis of the final models. Additionally, we propose to use post critical wide-angle reflections in tomographic inversions for more reliable results especially in the deeper parts of each layer. We focus on the effects of using hard to pick post critical reflections on the final model uncertainty. Our study is performed using data collected during standard vibroseis and explosive sources seismic reflection experiment focused on shale gas reservoir characterisation realised by Polish Oil and Gas Company. Our data were gathered by a standalone single component stations deployed along the whole length of the 20 km long profile, resulting in significantly longer offsets. Our piggy back recordings resulted in good quality wide angle refraction and reflection recordings clearly observable up to the offsets of 12 km.

The prediction of zenith range refraction from surface measurements of meteorological parameters. [mathematical models of atmospheric refraction used to improve spacecraft tracking space navigation

NASA Technical Reports Server (NTRS)

Berman, A. L.

1976-01-01

In the last two decades, increasingly sophisticated deep space missions have placed correspondingly stringent requirements on navigational accuracy. As part of the effort to increase navigational accuracy, and hence the quality of radiometric data, much effort has been expended in an attempt to understand and compute the tropospheric effect on range (and hence range rate) data. The general approach adopted has been that of computing a zenith range refraction, and then mapping this refraction to any arbitrary elevation angle via an empirically derived function of elevation. The prediction of zenith range refraction derived from surface measurements of meteorological parameters is presented. Refractivity is separated into wet (water vapor pressure) and dry (atmospheric pressure) components. The integration of dry refractivity is shown to be exact. Attempts to integrate wet refractivity directly prove ineffective; however, several empirical models developed by the author and other researchers at JPL are discussed. The best current wet refraction model is here considered to be a separate day/night model, which is proportional to surface water vapor pressure and inversely proportional to surface temperature. Methods are suggested that might improve the accuracy of the wet range refraction model.

Uniform refraction in negative refractive index materials.

PubMed

Gutiérrez, Cristian E; Stachura, Eric

2015-11-01

We study the problem of constructing an optical surface separating two homogeneous, isotropic media, one of which has a negative refractive index. In doing so, we develop a vector form of Snell's law, which is used to study surfaces possessing a certain uniform refraction property, in both the near- and far-field cases. In the near-field problem, unlike the case when both materials have positive refractive indices, we show that the resulting surfaces can be neither convex nor concave.

Various Approaches to Forward and Inverse Wide-Angle Seismic Modelling Tested on Data from DOBRE-4 Experiment

NASA Astrophysics Data System (ADS)

Janik, Tomasz; Środa, Piotr; Czuba, Wojciech; Lysynchuk, Dmytro

2016-12-01

The interpretation of seismic refraction and wide angle reflection data usually involves the creation of a velocity model based on an inverse or forward modelling of the travel times of crustal and mantle phases using the ray theory approach. The modelling codes differ in terms of model parameterization, data used for modelling, regularization of the result, etc. It is helpful to know the capabilities, advantages and limitations of the code used compared to others. This work compares some popular 2D seismic modelling codes using the dataset collected along the seismic wide-angle profile DOBRE-4, where quite peculiar/uncommon reflected phases were observed in the wavefield. The 505 km long profile was realized in southern Ukraine in 2009, using 13 shot points and 230 recording stations. Double PMP phases with a different reduced time (7.5-11 s) and a different apparent velocity, intersecting each other, are observed in the seismic wavefield. This is the most striking feature of the data. They are interpreted as reflections from strongly dipping Moho segments with an opposite dip. Two steps were used for the modelling. In the previous work by Starostenko et al. (2013), the trial-and-error forward model based on refracted and reflected phases (SEIS83 code) was published. The interesting feature is the high-amplitude (8-17 km) variability of the Moho depth in the form of downward and upward bends. This model is compared with results from other seismic inversion methods: the first arrivals tomography package FAST based on first arrivals; the JIVE3D code, which can also use later refracted arrivals and reflections; and the forward and inversion code RAYINVR using both refracted and reflected phases. Modelling with all the codes tested showed substantial variability of the Moho depth along the DOBRE-4 profile. However, SEIS83 and RAYINVR packages seem to give the most coincident results.

A comparison of techniques for inversion of radio-ray phase data in presence of ray bending

NASA Technical Reports Server (NTRS)

Wallio, H. A.; Grossi, M. D.

1972-01-01

Derivations are presented of the straight-line Abel transform and the seismological Herglotz-Wiechert transform (which takes ray bending into account) that are used in the reconstruction of refractivity profiles from radio-wave phase data. Profile inversion utilizing these approaches, performed in computer-simulated experiments, are compared for cases of positive, zero, and negative ray bending. For thin atmospheres and ionospheres, such as the Martian atmosphere and ionosphere, radio wave signals are shown to be inverted accurately with both methods. For dense media, such as the solar corona or the lower Venus atmosphere, the refractive recovered by the seismological Herglotz-Wiechert transform provide a significant improvement compared with the straight-line Abel transform.

Refraction tomography mapping of near-surface dipping layers using landstreamer data at East Canyon Dam, Utah

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Markiewicz, R.D.; Xia, J.

2008-01-01

We apply the P-wave refraction-tomography method to seismic data collected with a landstreamer. Refraction-tomography inversion solutions were determined using regularization parameters that provided the most realistic near-surface solutions that best matched the dipping layer structure of nearby outcrops. A reasonably well matched solution was obtained using an unusual set of optimal regularization parameters. In comparison, the use of conventional regularization parameters did not provide as realistic results. Thus, we consider that even if there is only qualitative a-priori information about a site (i.e., visual) - in the case of the East Canyon Dam, Utah - it might be possible to minimize the refraction nonuniqueness by estimating the most appropriate regularization parameters.

Method for Remotely Measuring Fluctuations in the Optical Index of Refraction of a Medium

DTIC Science & Technology

2011-11-09

space where the spatial spectrum is multiplied by a Kolmogorv spectrum before an inverse transform is used to return to position space. An index of...electric field at the end of the first slab. A two-dimensional inverse transform at 50 is used to generate the electric field intensity E_\\r,L.j

Pluto's atmosphere - Models based on refraction, inversion, and vapor-pressure equilibrium

NASA Technical Reports Server (NTRS)

Eshleman, Von R.

1989-01-01

Viking spacecraft radio-occultation measurements indicate that, irrespective of substantial differences, the polar ice cap regions on Mars have inversions similar to those of Pluto, and may also share vapor pressure equilibrium characteristics at the surface. This temperature-inversion phenomenon occurs in a near-surface boundary layer; surface pressure-temperature may correspond to the vapor-pressure equilibrium with CH4 ice, or the temperature may be slightly higher to match the value derived from IRAS data.

[Correction of refractive errors in patients with strabismus. Part I. Clinical problems associated with refraction, accommodation and convergence].

PubMed

Tokarz-Sawińska, Ewa

2012-01-01

In Part I the problems associated with refraction, accommodation and convergence and their role in proper eye position/visual alignment of the eyes as well as convergent, divergent and vertical alignment of the eyes have been described.

Transmission eigenvalues

NASA Astrophysics Data System (ADS)

Cakoni, Fioralba; Haddar, Houssem

2013-10-01

In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission eigenvalue problem. The need to answer these questions became important after a series of papers by Cakoni et al [5], and Cakoni et al [6] suggesting that these transmission eigenvalues could be used to obtain qualitative information about the material properties of the scattering object from far-field data. The first answer to the existence of transmission eigenvalues in the general case was given in 2008 when Päivärinta and Sylvester showed the existence of transmission eigenvalues for the index of refraction sufficiently large [7] followed in 2010 by the paper of Cakoni et al who removed the size restriction on the index of refraction [8]. More importantly, in the latter it was shown that transmission eigenvalues yielded qualitative information on the material properties of the scattering object and Cakoni et al established in [9] that transmission eigenvalues could be determined from the Tikhonov regularized solution of the far-field equation. Since the appearance of these papers there has been an explosion of interest in the transmission eigenvalue problem (we refer the reader to our recent survey paper [10] for a detailed account of the developments in this field up to 2012) and the papers in this special issue are representative of the myriad directions that this research has taken. Indeed, we are happy to see that many open theoretical and numerical questions raised in [10] have been answered (totally or partially) in the contributions of this special issue: the existence of transmission eigenvalues with minimal assumptions on the contrast, the numerical evaluation of transmission eigenvalues, the inverse spectral problem, applications to non-destructive testing, etc. In addition to these topics, many other new investigations and research directions have been proposed as we shall see in the brief content summary below. A number of papers in this special issue are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano [11], Blasten and Päivärinta [12], and Lakshtanov and Vainberg [13] provide new complementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the (possibly complex valued) refractive index that mainly stipulates that the contrast does not change sign on the boundary. It is interesting here to see three different new methods to obtain these results. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel [14] addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary [15] for the case of frequency dependent materials in the context of Maxwell's equations, whereas the paper by Vesalainen [16] initiates the study of the transmission eigenvalue problem in unbounded domains by considering the transmission eigenvalues for Schrödinger equation with non-compactly supported potential. The paper by Monk and Selgas [17] addresses the case where the dielectric is mounted on a perfect conductor and provides some numerical examples of the localization of associated eigenvalues using the linear sampling method. A series of papers then addresses the question of localization of transmission eigenvalues and the associated inverse spectral problem for spherically stratified media. More specifically, the paper by Colton and Leung [18] provides new results on complex transmission eigenvalues and a new proof for uniqueness of a solution to the inverse spectral problem, whereas the paper by Sylvester [19] provides sharp results on how to locate all the transmission eigenvalues associated with angular independent eigenfunctions when the index of refraction is constant. The paper by Gintides and Pallikarakis [20] investigates an iterative least square method to identify the spherically stratified index of refraction from transmission eigenvalues. On the characterization of transmission eigenvalues in terms of far-field measurements, a promising new result is obtained by Kirsch and Lechleiter [21] showing how one can identify the transmission eigenvalues using the eigenvalues of the scattering operator which are available in terms of measured scattering data. In the paper by Kleefeld [22], an accurate method for computing transmission eigenvalues based on a surface integral formulation of the interior transmission problem and numerical methods for nonlinear eigenvalue problems is proposed and numerically validated for the scalar problem in three dimensions. On the other hand, the paper by Sun and Xu [23] investigates the computation of transmission eigenvalues for Maxwell's equations using a standard iterative method associated with a variational formulation of the interior transmission problem with an emphasis on the effect of anisotropy on transmission eigenvalues. From the perspective of using transmission eigenvalues in non-destructive testing, the paper by Cakoni and Moskow [24] investigates the asymptotic behavior of transmission eigenvalues with respect to small inhomogeneities. The paper by Nakamura and Wang [25] investigates the linear sampling method for the time dependent heat equation and analyses the interior transmission problem associated with this equation. Finally, in the paper by Finch and Hickmann [26], the spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. We hope that this collection of papers will stimulate further research in the rapidly growing area of transmission eigenvalues and inverse scattering theory.

Refraction effects of atmosphere on geodetic measurements to celestial bodies

NASA Technical Reports Server (NTRS)

Joshi, C. S.

1973-01-01

The problem is considered of obtaining accurate values of refraction corrections for geodetic measurements of celestial bodies. The basic principles of optics governing the phenomenon of refraction are defined, and differential equations are derived for the refraction corrections. The corrections fall into two main categories: (1) refraction effects due to change in the direction of propagation, and (2) refraction effects mainly due to change in the velocity of propagation. The various assumptions made by earlier investigators are reviewed along with the basic principles of improved models designed by investigators of the twentieth century. The accuracy problem for various quantities is discussed, and the conclusions and recommendations are summarized.

A pitfall in shallow shear-wave refraction surveying

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.; Wightman, E.; Nigbor, R.

2002-01-01

The shallow shear-wave refraction method works successfully in an area with a series of horizontal layers. However, complex near-surface geology may not fit into the assumption of a series of horizontal layers. That a plane SH-wave undergoes wave-type conversion along an interface in an area of nonhorizontal layers is theoretically inevitable. One real example shows that the shallow shear-wave refraction method provides velocities of a converted wave rather than an SH- wave. Moreover, it is impossible to identify the converted wave by refraction data itself. As most geophysical engineering firms have limited resources, an additional P-wave refraction survey is necessary to verify if velocities calculated from a shear-wave refraction survey are velocities of converted waves. The alternative at this time may be the surface wave method, which can provide reliable S-wave velocities, even in an area of velocity inversion (a higher velocity layer underlain by a lower velocity layer). ?? 2002 Elsevier Science B.V. All rights reserved.

Seismic Tomography

NASA Astrophysics Data System (ADS)

Nowack, Robert L.; Li, Cuiping

The inversion of seismic travel-time data for radially varying media was initially investigated by Herglotz, Wiechert, and Bateman (the HWB method) in the early part of the 20th century [1]. Tomographic inversions for laterally varying media began in seismology starting in the 1970’s. This included early work by Aki, Christoffersson, and Husebye who developed an inversion technique for estimating lithospheric structure beneath a seismic array from distant earthquakes (the ACH method) [2]. Also, Alekseev and others in Russia performed early inversions of refraction data for laterally varying upper mantle structure [3]. Aki and Lee [4] developed an inversion technique using travel-time data from local earthquakes.

Vectorial laws of refraction and reflection using the cross product and dot product.

PubMed

Tkaczyk, Eric R

2012-03-01

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal. © 2012 Optical Society of America

Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results.

PubMed

Martelli, F; Contini, D; Taddeucci, A; Zaccanti, G

1997-07-01

In our companion paper we presented a model to describe photon migration through a diffusing slab. The model, developed for a homogeneous slab, is based on the diffusion approximation and is able to take into account reflection at the boundaries resulting from the refractive index mismatch. In this paper the predictions of the model are compared with solutions of the radiative transfer equation obtained by Monte Carlo simulations in order to determine the applicability limits of the approximated theory in different physical conditions. A fitting procedure, carried out with the optical properties as fitting parameters, is used to check the application of the model to the inverse problem. The results show that significant errors can be made if the effect of the refractive index mismatch is not properly taken into account. Errors are more important when measurements of transmittance are used. The effects of using a receiver with a limited angular field of view and the angular distribution of the radiation that emerges from the slab have also been investigated.

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

NASA Astrophysics Data System (ADS)

Maslukha, M.; Lukito, A.; Ekawati, R.

2018-01-01

Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

Tomographic phase microscopy: principles and applications in bioimaging [Invited

PubMed Central

Jin, Di; Zhou, Renjie; Yaqoob, Zahid; So, Peter T. C.

2017-01-01

Tomographic phase microscopy (TPM) is an emerging optical microscopic technique for bioimaging. TPM uses digital holographic measurements of complex scattered fields to reconstruct three-dimensional refractive index (RI) maps of cells with diffraction-limited resolution by solving inverse scattering problems. In this paper, we review the developments of TPM from the fundamental physics to its applications in bioimaging. We first provide a comprehensive description of the tomographic reconstruction physical models used in TPM. The RI map reconstruction algorithms and various regularization methods are discussed. Selected TPM applications for cellular imaging, particularly in hematology, are reviewed. Finally, we examine the limitations of current TPM systems, propose future solutions, and envision promising directions in biomedical research. PMID:29386746

Improvements of Travel-time Tomography Models from Joint Inversion of Multi-channel and Wide-angle Seismic Data

NASA Astrophysics Data System (ADS)

Begović, Slaven; Ranero, César; Sallarès, Valentí; Meléndez, Adrià; Grevemeyer, Ingo

2016-04-01

Commonly multichannel seismic reflection (MCS) and wide-angle seismic (WAS) data are modeled and interpreted with different approaches. Conventional travel-time tomography models using solely WAS data lack the resolution to define the model properties and, particularly, the geometry of geologic boundaries (reflectors) with the required accuracy, specially in the shallow complex upper geological layers. We plan to mitigate this issue by combining these two different data sets, specifically taking advantage of the high redundancy of multichannel seismic (MCS) data, integrated with wide-angle seismic (WAS) data into a common inversion scheme to obtain higher-resolution velocity models (Vp), decrease Vp uncertainty and improve the geometry of reflectors. To do so, we have adapted the tomo2d and tomo3d joint refraction and reflection travel time tomography codes (Korenaga et al, 2000; Meléndez et al, 2015) to deal with streamer data and MCS acquisition geometries. The scheme results in a joint travel-time tomographic inversion based on integrated travel-time information from refracted and reflected phases from WAS data and reflected identified in the MCS common depth point (CDP) or shot gathers. To illustrate the advantages of a common inversion approach we have compared the modeling results for synthetic data sets using two different travel-time inversion strategies: We have produced seismic velocity models and reflector geometries following typical refraction and reflection travel-time tomographic strategy modeling just WAS data with a typical acquisition geometry (one OBS each 10 km). Second, we performed joint inversion of two types of seismic data sets, integrating two coincident data sets consisting of MCS data collected with a 8 km-long streamer and the WAS data into a common inversion scheme. Our synthetic results of the joint inversion indicate a 5-10 times smaller ray travel-time misfit in the deeper parts of the model, compared to models obtained using just wide-angle seismic data. As expected, there is an important improvement in the definition of the reflector geometry, which in turn, allows to improve the accuracy of the velocity retrieval just above and below the reflector. To test the joint inversion approach with real data, we combined wide-angle (WAS) seismic and coincident multichannel seismic reflection (MCS) data acquired in the northern Chile subduction zone into a common inversion scheme to obtain a higher-resolution information of upper plate and inter-plate boundary.

Integration of Electrical Resistivity and Seismic Refraction using Combine Inversion for Detecting Material Deposits of Impact Crater at Bukit Bunuh, Lenggong, Perak

NASA Astrophysics Data System (ADS)

Yusoh, R.; Saad, R.; Saidin, M.; Muhammad, S. B.; Anda, S. T.

2018-04-01

Both electrical resistivity and seismic refraction profiling has become a common method in pre-investigations for visualizing subsurface structure. The encouragement to use these methods is that combined of both methods can decrease the obscure inherent to the distinctive use of these methods. Both method have their individual software packages for data inversion, but potential to combine certain geophysical methods are restricted; however, the research algorithms that have this functionality was exists and are evaluated personally. The interpretation of subsurface were improve by combining inversion data from both method by influence each other models using closure coupling; thus, by implementing both methods to support each other which could improve the subsurface interpretation. These methods were applied on a field dataset from a pre-investigation for archeology in finding the material deposits of impact crater. There were no major changes in the inverted model by combining data inversion for this archetype which probably due to complex geology. The combine data analysis shows the deposit material start from ground surface to 20 meter depth which the class separation clearly separate the deposit material.

Errors incurred in profile reconstruction and methods for increasing inversion accuracies for occultation type measurements

NASA Technical Reports Server (NTRS)

Gross, S. H.; Pirraglia, J. A.

1972-01-01

A method for augmenting the occultation experiment is described for slightly refractive media. This method which permits separation of the components of the gradient of refractivity, appears applicable to most of the planets for a major portion of their atmospheres and ionospheres. The analytic theory is given, and the results of numerical tests with a radially and angularly varying model of an ionosphere are discussed.

PREVALENCE OF REFRACTIVE ERRORS IN MADRASSA STUDENTS OF HARIPUR DISTRICT.

PubMed

Atta, Zoia; Arif, Abdus Salam; Ahmed, Iftikhar; Farooq, Umer

2015-01-01

Visual impairment due to refractive errors is one of the most common problems among school-age children and is the second leading cause of treatable blindness. The Right to Sight, a global initiative launched by a coalition of non-government organizations and the World Health Organization (WHO), aims to eliminate avoidable visual impairment and blindness at a global level. In order to achieve this goal it is important to know the prevalence of different refractive errors in a community. Children and teenagers are the most susceptible groups to be affected by refractive errors. So, this population needs to be screened for different types of refractive errors. The study was done with the objective to find the frequency of different types of refractive errors in students of madrassas between the ages of 5-20 years in Haripur. This cross sectional study was done with 300 students between ages of 5-20 years in Madrassas of Haripur. The students were screened for refractive errors and the types of the errors were noted. After screening for refractive errors-the glasses were prescribed to the students. Myopia being 52.6% was the most frequent refractive error in students, followed by hyperopia 28.4% and astigmatism 19%. This study showed that myopia is an important problem in madrassa population. Females and males are almost equally affected. Spectacle correction of refractive errors is the cheapest and easy solution of this problem.

Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution

NASA Astrophysics Data System (ADS)

Veselovskii, Igor; Kolgotin, Alexei; Griaznov, Vadim; Müller, Detlef; Franke, Kathleen; Whiteman, David N.

2004-02-01

We report on the feasibility of deriving microphysical parameters of bimodal particle size distributions from Mie-Raman lidar based on a triple Nd:YAG laser. Such an instrument provides backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm. The inversion method employed is Tikhonov's inversion with regularization. Special attention has been paid to extend the particle size range for which this inversion scheme works to ~10 μm, which makes this algorithm applicable to large particles, e.g., investigations concerning the hygroscopic growth of aerosols. Simulations showed that surface area, volume concentration, and effective radius are derived to an accuracy of ~50% for a variety of bimodal particle size distributions. For particle size distributions with an effective radius of <1 μm the real part of the complex refractive index was retrieved to an accuracy of +/-0.05, the imaginary part was retrieved to 50% uncertainty. Simulations dealing with a mode-dependent complex refractive index showed that an average complex refractive index is derived that lies between the values for the two individual modes. Thus it becomes possible to investigate external mixtures of particle size distributions, which, for example, might be present along continental rims along which anthropogenic pollution mixes with marine aerosols. Measurement cases obtained from the Institute for Tropospheric Research six-wavelength aerosol lidar observations during the Indian Ocean Experiment were used to test the capabilities of the algorithm for experimental data sets. A benchmark test was attempted for the case representing anthropogenic aerosols between a broken cloud deck. A strong contribution of particle volume in the coarse mode of the particle size distribution was found.

Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution.

PubMed

Veselovskii, Igor; Kolgotin, Alexei; Griaznov, Vadim; Müller, Detlef; Franke, Kathleen; Whiteman, David N

2004-02-10

We report on the feasibility of deriving microphysical parameters of bimodal particle size distributions from Mie-Raman lidar based on a triple Nd:YAG laser. Such an instrument provides backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm. The inversion method employed is Tikhonov's inversion with regularization. Special attention has been paid to extend the particle size range for which this inversion scheme works to approximately 10 microm, which makes this algorithm applicable to large particles, e.g., investigations concerning the hygroscopic growth of aerosols. Simulations showed that surface area, volume concentration, and effective radius are derived to an accuracy of approximately 50% for a variety of bimodal particle size distributions. For particle size distributions with an effective radius of < 1 microm the real part of the complex refractive index was retrieved to an accuracy of +/- 0.05, the imaginary part was retrieved to 50% uncertainty. Simulations dealing with a mode-dependent complex refractive index showed that an average complex refractive index is derived that lies between the values for the two individual modes. Thus it becomes possible to investigate external mixtures of particle size distributions, which, for example, might be present along continental rims along which anthropogenic pollution mixes with marine aerosols. Measurement cases obtained from the Institute for Tropospheric Research six-wavelength aerosol lidar observations during the Indian Ocean Experiment were used to test the capabilities of the algorithm for experimental data sets. A benchmark test was attempted for the case representing anthropogenic aerosols between a broken cloud deck. A strong contribution of particle volume in the coarse mode of the particle size distribution was found.

Detailed p- and s-wave velocity models along the LARSE II transect, Southern California

USGS Publications Warehouse

Murphy, J.M.; Fuis, G.S.; Ryberg, T.; Lutter, W.J.; Catchings, R.D.; Goldman, M.R.

2010-01-01

Structural details of the crust determined from P-wave velocity models can be improved with S-wave velocity models, and S-wave velocities are needed for model-based predictions of strong ground motion in southern California. We picked P- and S-wave travel times for refracted phases from explosive-source shots of the Los Angeles Region Seismic Experiment, Phase II (LARSE II); we developed refraction velocity models from these picks using two different inversion algorithms. For each inversion technique, we calculated ratios of P- to S-wave velocities (VP/VS) where there is coincident P- and S-wave ray coverage.We compare the two VP inverse velocity models to each other and to results from forward modeling, and we compare the VS inverse models. The VS and VP/VS models differ in structural details from the VP models. In particular, dipping, tabular zones of low VS, or high VP/VS, appear to define two fault zones in the central Transverse Ranges that could be parts of a positive flower structure to the San Andreas fault. These two zones are marginally resolved, but their presence in two independent models lends them some credibility. A plot of VS versus VP differs from recently published plots that are based on direct laboratory or down-hole sonic measurements. The difference in plots is most prominent in the range of VP = 3 to 5 km=s (or VS ~ 1:25 to 2:9 km/s), where our refraction VS is lower by a few tenths of a kilometer per second from VS based on direct measurements. Our new VS - VP curve may be useful for modeling the lower limit of VS from a VP model in calculating strong motions from scenario earthquakes.

Microwave experiments with left-handed materials

NASA Astrophysics Data System (ADS)

Shelby, Richard Allen

It has previously been predicted that materials that have a simultaneous negative permittivity and negative permeability, called left-handed materials (LHM), will possess very unusual properties, such as negative refraction, inverse Doppler effect, and reversed Cherenkov radiation. In this dissertation I present results from microwave experiments designed to confirm that LHMs will exhibit negative refraction. I also present a discussion about the LHM design, and numerical, electromagnetic simulations. The experiments presented here include transmission experiments, refraction experiments, and surface plasmon experiments. The refraction experiments in Chapter 4 directly observe negative refraction for the first time. The results from the other experiments are consistent with theoretical models and support the claim that negative refraction has been observed. The materials used in the experiments presented here are fabricated, structured materials that contain fiberglass and copper with unit cell parameters on the order of millimeters. Metamaterials have been defined as being composite materials whose bulk properties are different than those of the constituent materials. By this definition, the LHMs used here are metamaterials, so long as the wavelength of the electromagnetic waves being used to probe the LHM are longer than the unit cell parameter.

Aerosol physical properties from satellite horizon inversion

NASA Technical Reports Server (NTRS)

Gray, C. R.; Malchow, H. L.; Merritt, D. C.; Var, R. E.; Whitney, C. K.

1973-01-01

The feasibility is investigated of determining the physical properties of aerosols globally in the altitude region of 10 to 100 km from a satellite horizon scanning experiment. The investigation utilizes a horizon inversion technique previously developed and extended. Aerosol physical properties such as number density, size distribution, and the real and imaginary components of the index of refraction are demonstrated to be invertible in the aerosol size ranges (0.01-0.1 microns), (0.1-1.0 microns), (1.0-10 microns). Extensions of previously developed radiative transfer models and recursive inversion algorithms are displayed.

Thermophysical properties of N, N-dimethylacetamide mixtures with n-butanol

NASA Astrophysics Data System (ADS)

Maharolkar, Aruna P.; Murugkar, A. G.; Khirade, P. W.; Mehrotra, S. C.

2017-09-01

The refraction, dielectric, viscosity, density, data of the binary mixtures of N, N-dimethylacetamide (DMA) with n-butanol at 308.15 and 313.15 K. The measured parameters used to obtain derived properties like Bruggeman factor, molar refraction and excess static dielectric constant, excess inverse relaxation time, excess molar volume and excess viscosity, excess molar refraction. The variation in magnitude with composition and temperature of these quantities has been used to discuss the type, strength and nature of binary interactions. Results confirm that there are strong hydrogen-bond interactions between unlike molecules of DMA+ n-butanol mixtures and that 1: 1 complexes are formed and strength of intermolecular interaction increases with temperature.

Non-uniform refractive index field measurement based on light field imaging technique

NASA Astrophysics Data System (ADS)

Du, Xiaokun; Zhang, Yumin; Zhou, Mengjie; Xu, Dong

2018-02-01

In this paper, a method for measuring the non-uniform refractive index field based on the light field imaging technique is proposed. First, the light field camera is used to collect the four-dimensional light field data, and then the light field data is decoded according to the light field imaging principle to obtain image sequences with different acquisition angles of the refractive index field. Subsequently PIV (Particle Image Velocimetry) technique is used to extract ray offset of each image. Finally, the distribution of non-uniform refractive index field can be calculated by inversing the deflection of light rays. Compared with traditional optical methods which require multiple optical detectors from multiple angles to synchronously collect data, the method proposed in this paper only needs a light field camera and shoot once. The effectiveness of the method has been verified by the experiment which quantitatively measures the distribution of the refractive index field above the flame of the alcohol lamp.

Ionosphere Profile Estimation Using Ionosonde & GPS Data in an Inverse Refraction Calculation

NASA Astrophysics Data System (ADS)

Psiaki, M. L.

2014-12-01

A method has been developed to assimilate ionosonde virtual heights and GPS slant TEC data to estimate the parameters of a local ionosphere model, including estimates of the topside and of latitude and longitude variations. This effort seeks to better assimilate a variety of remote sensing data in order to characterize local (and eventually regional and global) ionosphere electron density profiles. The core calculations involve a forward refractive ray-tracing solution and a nonlinear optimal estimation algorithm that inverts the forward model. The ray-tracing calculations solve a nonlinear two-point boundary value problem for the curved ionosonde or GPS ray path through a parameterized electron density profile. It implements a full 3D solution that can handle the case of a tilted ionosphere. These calculations use Hamiltonian equivalents of the Appleton-Hartree magneto-plasma refraction index model. The current ionosphere parameterization is a modified Booker profile. It has been augmented to include latitude and longitude dependencies. The forward ray-tracing solution yields a given signal's group delay and beat carrier phase observables. An auxiliary set of boundary value problem solutions determine the sensitivities of the ray paths and observables with respect to the parameters of the augmented Booker profile. The nonlinear estimation algorithm compares the measured ionosonde virtual-altitude observables and GPS slant-TEC observables to the corresponding values from the forward refraction model. It uses the parameter sensitivities of the model to iteratively improve its parameter estimates in a way the reduces the residual errors between the measurements and their modeled values. This method has been applied to data from HAARP in Gakona, AK and has produced good TEC and virtual height fits. It has been extended to characterize electron density perturbations caused by HAARP heating experiments through the use of GPS slant TEC data for an LOS through the heated zone. The next planned extension of the method is to estimate the parameters of a regional ionosphere profile. The input observables will be slant TEC from an array of GPS receivers and group delay and carrier phase observables from an array of high-frequency beacons. The beacon array will function as a sort of multi-static ionosonde.

Refractive Errors

MedlinePlus

... and lens of your eye helps you focus. Refractive errors are vision problems that happen when the shape ... cornea, or aging of the lens. Four common refractive errors are Myopia, or nearsightedness - clear vision close up ...

Observation of acoustic Dirac-like cone and double zero refractive index

PubMed Central

Dubois, Marc; Shi, Chengzhi; Zhu, Xuefeng; Wang, Yuan; Zhang, Xiang

2017-01-01

Zero index materials where sound propagates without phase variation, holds a great potential for wavefront and dispersion engineering. Recently explored electromagnetic double zero index metamaterials consist of periodic scatterers whose refractive index is significantly larger than that of the surrounding medium. This requirement is fundamentally challenging for airborne acoustics because the sound speed (inversely proportional to the refractive index) in air is among the slowest. Here, we report the first experimental realization of an impedance matched acoustic double zero refractive index metamaterial induced by a Dirac-like cone at the Brillouin zone centre. This is achieved in a two-dimensional waveguide with periodically varying air channel that modulates the effective phase velocity of a high-order waveguide mode. Using such a zero-index medium, we demonstrated acoustic wave collimation emitted from a point source. For the first time, we experimentally confirm the existence of the Dirac-like cone at the Brillouin zone centre. PMID:28317927

A new approach for implementation of associative memory using volume holographic materials

NASA Astrophysics Data System (ADS)

Habibi, Mohammad; Pashaie, Ramin

2012-02-01

Associative memory, also known as fault tolerant or content-addressable memory, has gained considerable attention in last few decades. This memory possesses important advantages over the more common random access memories since it provides the capability to correct faults and/or partially missing information in a given input pattern. There is general consensus that optical implementation of connectionist models and parallel processors including associative memory has a better record of success compared to their electronic counterparts. In this article, we describe a novel optical implementation of associative memory which not only has the advantage of all optical learning and recalling capabilities, it can also be realized easily. We present a new approach, inspired by tomographic imaging techniques, for holographic implementation of associative memories. In this approach, a volume holographic material is sandwiched within a matrix of inputs (optical point sources) and outputs (photodetectors). The memory capacity is realized by the spatial modulation of refractive index of the holographic material. Constructing the spatial distribution of the refractive index from an array of known inputs and outputs is formulated as an inverse problem consisting a set of linear integral equations.

Macular pigment optical density and its relationship with refractive status and foveal thickness in Chinese school-aged children.

PubMed

Zheng, Wenjing; Zhang, Zhengwei; Jiang, Kelimu; Zhu, Jianfeng; He, Guixian; Ke, Bilian

2013-01-01

To investigate macular pigment optical density (MPOD) and its relationship with refractive status and foveal thickness in Chinese school-aged children. Ninety-four healthy Chinese children, 6 to 12 years old, were recruited to the study. MPOD was measured with a heterochromatic flicker photometer (HFP), and foveal thickness, including both minimum and central foveal thicknesses (MFT and CFT, respectively), were measured by optical coherence tomography (OCT) with fast macular map scan. A noncontact tonometer was used to measure intraocular pressure (IOP) followed by determination of the refraction using an autorefractor after cycloplegia. Information on body mass index (BMI) was obtained. The correlation between MPOD values and foveal thickness, spherical equivalent (SE) refraction, IOP, BMI, sex, and age was statistically analyzed using SAS 8.2 statistical software. The MPOD in examined school-aged children was 0.56 ± 0.25, without any significant difference between boys and girls (p = 0.12). MPOD showed no significant association with age, BMI, IOP, SE, MFT, or CFT. In the myopia group, however, there was an inverse relationship between MPOD and MFT (R =-0.66, p = 0.028) and a positive relationship between MPOD and CFT (R = 0.67, p = 0.025). MPOD was inversely related to MFT and positively related to CFT in Chinese school-age children with low-to-moderate myopia. MPOD showed no significant association with age, BMI, IOP, SE or foveal thickness.

Pioneer 10 and 11 radio occultations by Jupiter. [atmospheric temperature structure

NASA Technical Reports Server (NTRS)

Kliore, A. J.; Woiceshyn, P. M.; Hubbard, W. B.

1977-01-01

Results on the temperature structure of the Jovian atmosphere are reviewed which were obtained by applying an integral inversion technique combined with a model for the planet's shape based on gravity data to Pioneer 10 and 11 radio-occultation data. The technique applied to obtain temperature profiles from the Pioneer data consisted of defining a center of refraction based on a computation of the radius of curvature in the plane of refraction and the normal direction to the equipotential surface at the closest approach point of a ray. Observations performed during the Pioneer 10 entry and exit and the Pioneer 11 exit are analyzed, sources of uncertainty are identified, and representative pressure-temperature profiles are presented which clearly show a temperature inversion between 10 and 100 mb. Effects of zonal winds on the reliability of radio-occultation temperature profiles are briefly discussed.

Nonscanning Moiré deflectometry for measurement of nonlinear refractive index and absorption coefficient of liquids.

PubMed

Farahani, Shahrzad Shahrabi; Madanipour, Khosro; Koohian, Ata

2017-05-01

In this work, a nonscanning measurement technique is presented for determining the nonlinear refractive index and absorption coefficient of liquid media based on Moiré deflectometry. In the proposed method two lasers are used: a low power, wide beam as probe and a high power with specific wavelength as a pump. Interaction of the pump laser beam with the nonlinear sample changes the refractive index, which leads to change in convergence/divergence of the collimated incident probe laser beam. The induced deflection is monitored by Moiré deflectometry. If the pump laser has a Gaussian intensity profile, the refractive index profile of the sample is Gaussian, too. Measuring the deflection angle of the probe beam by Moiré fringes deflection, and by using the inverse Abel transform integral, the refractive index profile and nonlinear refractive index can be determined. This method is fast, easy, and insensitive to environmental noise and allows real-time measurement. Also, the refractive index profile of the interacted medium with pump laser can be achieved by this technique. As a liquid sample, a DCJ dye in water solution was studied. The value of nonlinear refractive index, n₂, and absorption coefficient, α, were obtained -2.54×10^-4  cm² w^-1 and 1.368  cm^-1, respectively.

Seismic Characterization of Basalt Topography at Two Candidate Sites for the INL Remote-Handled Low-Level Waste Disposal Project

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeff Sondrup; Gail Heath; Trent Armstrong

2011-04-01

This report presents the seismic refraction results from the depth to bed rock surveys for two areas being considered for the Remote-Handled Low-Level Waste (RH-LLW) disposal facility at the Idaho National Laboratory. The first area (Site 5) surveyed is located southwest of the Advanced Test Reactor Complex and the second (Site 34) is located west of Lincoln Boulevard near the southwest corner of the Idaho Nuclear Technology and Engineering Center (INTEC). At Site 5, large area and smaller-scale detailed surveys were performed. At Site 34, a large area survey was performed. The purpose of the surveys was to define themore » topography of the interface between the surficial alluvium and underlying basalt. Seismic data were first collected and processed using seismic refraction tomographic inversion. Three-dimensional images for both sites were rendered from the data to image the depth and velocities of the subsurface layers. Based on the interpreted top of basalt data at Site 5, a more detailed survey was conducted to refine depth to basalt. This report briefly covers relevant issues in the collection, processing and inversion of the seismic refraction data and in the imaging process. Included are the parameters for inversion and result rendering and visualization such as the inclusion of physical features. Results from the processing effort presented in this report include fence diagrams of the earth model, for the large area surveys and iso-velocity surfaces and cross sections from the detailed survey.« less

Computational optical tomography using 3-D deep convolutional neural networks

NASA Astrophysics Data System (ADS)

Nguyen, Thanh; Bui, Vy; Nehmetallah, George

2018-04-01

Deep convolutional neural networks (DCNNs) offer a promising performance for many image processing areas, such as super-resolution, deconvolution, image classification, denoising, and segmentation, with outstanding results. Here, we develop for the first time, to our knowledge, a method to perform 3-D computational optical tomography using 3-D DCNN. A simulated 3-D phantom dataset was first constructed and converted to a dataset of phase objects imaged on a spatial light modulator. For each phase image in the dataset, the corresponding diffracted intensity image was experimentally recorded on a CCD. We then experimentally demonstrate the ability of the developed 3-D DCNN algorithm to solve the inverse problem by reconstructing the 3-D index of refraction distributions of test phantoms from the dataset from their corresponding diffraction patterns.

A Theory and Experiments for Detecting Shock Locations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Johnson, D. K.; Adamovsky, G.

1994-01-01

In this paper we present a simplified one-dimensional theory for predicting locations of normal shocks in a converging diverging nozzle. The theory assumes that the flow is quasi one-dimensional and the flow is accelerated in the throat area. Optical aspects of the model consider propagation of electromagnetic fields transverse to the shock front. The theory consists of an inverse problem in which from the measured intensity it reconstructs an index of refraction profile for the shock. From this profile and the Dale-Gladstone relation, the density in the flow field is determined, thus determining the shock location. Experiments show agreement with the theory. In particular the location is determined within 10 percent of accuracy. Both the theoretical as well as the experimental results are presented to validate the procedures in this work.

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

NASA Astrophysics Data System (ADS)

Rolla, L. Barrera; Rice, H. J.

2006-09-01

In this paper a "forward-advancing" field discretization method suitable for solving the Helmholtz equation in large-scale problems is proposed. The forward wave expansion method (FWEM) is derived from a highly efficient discretization procedure based on interpolation of wave functions known as the wave expansion method (WEM). The FWEM computes the propagated sound field by means of an exclusively forward advancing solution, neglecting the backscattered field. It is thus analogous to methods such as the (one way) parabolic equation method (PEM) (usually discretized using standard finite difference or finite element methods). These techniques do not require the inversion of large system matrices and thus enable the solution of large-scale acoustic problems where backscatter is not of interest. Calculations using FWEM are presented for two propagation problems and comparisons to data computed with analytical and theoretical solutions and show this forward approximation to be highly accurate. Examples of sound propagation over a screen in upwind and downwind refracting atmospheric conditions at low nodal spacings (0.2 per wavelength in the propagation direction) are also included to demonstrate the flexibility and efficiency of the method.

Seismic attenuation structure of the Seattle Basin, Washington State from explosive-source refraction data

USGS Publications Warehouse

Li, Q.; Wilcock, W.S.D.; Pratt, T.L.; Snelson, C.M.; Brocher, T.M.

2006-01-01

We used waveform data from the 1999 SHIPS (Seismic Hazard Investigation of Puget Sound) seismic refraction experiment to constrain the attenuation structure of the Seattle basin, Washington State. We inverted the spectral amplitudes of compressional- and shear-wave arrivals for source spectra, site responses, and one- and two-dimensional Q-1 models at frequencies between 1 and 40 Hz for P waves and 1 and 10 Hz for S waves. We also obtained Q-1 models from t* values calculated from the spectral slopes of P waves between 10 and 40 Hz. One-dimensional inversions show that Qp at the surface is 22 at 1 Hz, 130 at 5 Hz, and 390 at 20 Hz. The corresponding values at 18 km depth are 100, 440, and 1900. Qs at the surface is 16 and 160 at 1 Hz and 8 Hz, respectively, increasing to 80 and 500 at 18 km depth. The t* inversion yields a Qp model that is consistent with the amplitude inversions at 20 and 30 Hz. The basin geometry is clearly resolved in the t* inversion, but the amplitude inversions only imaged the basin structure after removing anomalously high-amplitude shots near Seattle. When these shots are removed, we infer that Q-1 values may be ???30% higher in the center of the basin than the one-dimensional models predict. We infer that seismic attenuation in the Seattle basin will significantly reduce ground motions at frequencies at and above 1 Hz, partially countering amplification effects within the basin.

Seismic refraction analysis: the path forward

USGS Publications Warehouse

Haines, Seth S.; Zelt, Colin; Doll, William

2012-01-01

Seismic Refraction Methods: Unleashing the Potential and Understanding the Limitations; Tucson, Arizona, 29 March 2012 A workshop focused on seismic refraction methods took place on 29 May 2012, associated with the 2012 Symposium on the Application of Geophysics to Engineering and Environmental Problems. This workshop was convened to assess the current state of the science and discuss paths forward, with a primary focus on near-surface problems but with an eye on all applications. The agenda included talks on these topics from a number of experts interspersed with discussion and a dedicated discussion period to finish the day. Discussion proved lively at times, and workshop participants delved into many topics central to seismic refraction work.

[Trends of refractive correction in the Japanese Ground Self-Defense Forces: examination after the Great East Japan earthquake].

PubMed

Harimoto, Kouzo; Kato, Naoko; Shoji, Takuhei; Goto, Hiroya; Tokuno, Shinichi; Fujii, Manabu; Takeuchi, Masaru

2014-02-01

To investigate the trends in refractive correction in Japanese Ground Self-Defense Forces' (JGSDF) soldiers. A questionnaire was distributed to 519 soldiers of the Camp Funaoka in the northeastern region. Five hundred and sixteen subjects (99.4%) responded. In total, 246 soldiers (47.7%) wore spectacles or contact lenses. Among the contact lens wearers, 52 had experienced problems previously and 35 reported problems that occurred during military exercises. With regard to military exercises, 66.9% and 63.5% of the spectacle or disposable soft contact lens-users reported inconvenience. Among contact lens users, 33.1% reported that they changed to new sterilized contact lenses only occasionally and 61.9% did not change their contact lenses at all during exercises. During disaster-relief work, subjects worried 'very' (21.5%) or 'somewhat' (46.9%) about problems associated with their spectacles or contact lenses. Twenty-four had undergone refractive surgery (4.9%). About one-half of the JGSDF soldiers surveyed required refractive correction. Attention to convenient and safe refractive correction in the military is warranted.

Aerosol properties from spectral extinction and backscatter estimated by an inverse Monte Carlo method.

PubMed

Ligon, D A; Gillespie, J B; Pellegrino, P

2000-08-20

The feasibility of using a generalized stochastic inversion methodology to estimate aerosol size distributions accurately by use of spectral extinction, backscatter data, or both is examined. The stochastic method used, inverse Monte Carlo (IMC), is verified with both simulated and experimental data from aerosols composed of spherical dielectrics with a known refractive index. Various levels of noise are superimposed on the data such that the effect of noise on the stability and results of inversion can be determined. Computational results show that the application of the IMC technique to inversion of spectral extinction or backscatter data or both can produce good estimates of aerosol size distributions. Specifically, for inversions for which both spectral extinction and backscatter data are used, the IMC technique was extremely accurate in determining particle size distributions well outside the wavelength range. Also, the IMC inversion results proved to be stable and accurate even when the data had significant noise, with a signal-to-noise ratio of 3.

Femtosecond laser-induced inverted microstructures inside glasses by tuning refractive index of objective's immersion liquid.

PubMed

Luo, Fangfang; Song, Juan; Hu, Xiao; Sun, Haiyi; Lin, Geng; Pan, Huaihai; Cheng, Ya; Liu, Li; Qiu, Jianrong; Zhao, Quanzhong; Xu, Zhizhan

2011-06-01

We report the formation of inverted microstructures inside glasses after femtosecond laser irradiation by tuning the refractive index contrast between the immersion liquid and the glass sample. By using water as well as 1-bromonaphthalene as immersion liquids, microstructures with similar shape but opposite directions are induced after femtosecond laser irradiation. Interestingly, the elemental distribution in the induced structures is also inverted. The simulation of laser intensity distribution along the laser propagation direction indicates that the interfacial spherical aberration effect is responsible for the inversion of microstructures and elemental distribution. © 2011 Optical Society of America

Dielectric constant extraction of graphene nanostructured on SiC substrates from spectroscopy ellipsometry measurement using Gauss–Newton inversion method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maulina, Hervin; Santoso, Iman, E-mail: iman.santoso@ugm.ac.id; Subama, Emmistasega

2016-04-19

The extraction of the dielectric constant of nanostructured graphene on SiC substrates from spectroscopy ellipsometry measurement using the Gauss-Newton inversion (GNI) method has been done. This study aims to calculate the dielectric constant and refractive index of graphene by extracting the value of ψ and Δ from the spectroscopy ellipsometry measurement using GNI method and comparing them with previous result which was extracted using Drude-Lorentz (DL) model. The results show that GNI method can be used to calculate the dielectric constant and refractive index of nanostructured graphene on SiC substratesmore faster as compared to DL model. Moreover, the imaginary partmore » of the dielectric constant values and coefficient of extinction drastically increases at 4.5 eV similar to that of extracted using known DL fitting. The increase is known due to the process of interband transition and the interaction between the electrons and electron-hole at M-points in the Brillouin zone of graphene.« less

Negative Refraction in a Uniaxial Absorbent Dielectric Material

ERIC Educational Resources Information Center

Jen, Yi-Jun; Lakhtakia, Akhlesh; Yu, Ching-Wei; Lin, Chin-Te

2009-01-01

Refraction of light from an isotropic dielectric medium to an anisotropic dielectric material is a complicated phenomenon that can have several different characteristics not usually discussed in electromagnetics textbooks for undergraduate students. With a simple problem wherein the refracting material is uniaxial with its optic axis normal to the…

Sparse source configurations in radio tomography of asteroids

NASA Astrophysics Data System (ADS)

Pursiainen, S.; Kaasalainen, M.

2014-07-01

Our research targets at progress in non-invasive imaging of asteroids to support future planetary research and extra-terrestrial mining activities. This presentation concerns principally radio tomography in which the permittivity distribution inside an asteroid is to be recovered based on the radio frequency signal transmitted from the asteroid's surface and gathered by an orbiter. The focus will be on a sparse distribution (Pursiainen and Kaasalainen, 2013) of signal sources that can be necessary in the challenging in situ environment and within tight payload limits. The general goal in our recent research has been to approximate the minimal number of source positions needed for robust localization of anomalies caused, for example, by an internal void. Characteristic to the localization problem are the large relative changes in signal speed caused by the high permittivity of typical asteroid minerals (e.g. basalt), meaning that a signal path can include strong refractions and reflections. This presentation introduces results of a laboratory experiment in which real travel time data was inverted using a hierarchical Bayesian approach combined with the iterative alternating sequential (IAS) posterior exploration algorithm. Special interest was paid to robustness of the inverse results regarding changes of the prior model and source positioning. According to our results, strongly refractive anomalies can be detected with three or four sources independently of their positioning.

Inverse Opal Photonic Crystals as an Optofluidic Platform for Fast Analysis of Hydrocarbon Mixtures.

PubMed

Xu, Qiwei; Mahpeykar, Seyed Milad; Burgess, Ian B; Wang, Xihua

2018-06-13

Most of the reported optofluidic devices analyze liquid by measuring its refractive index. Recently, the wettability of liquid on various substrates has also been used as a key sensing parameter in optofluidic sensors. However, the above-mentioned techniques face challenges in the analysis of the relative concentration of components in an alkane hydrocarbon mixture, as both refractive indices and wettabilities of alkane hydrocarbons are very close. Here, we propose to apply volatility of liquid as the key sensing parameter, correlate it to the optical property of liquid inside inverse opal photonic crystals, and construct powerful optofluidic sensors for alkane hydrocarbon identification and analysis. We have demonstrated that via evaporation of hydrocarbons inside the periodic structure of inverse opal photonic crystals and observation of their reflection spectra, an inverse opal film could be used as a fast-response optofluidic sensor to accurately differentiate pure hydrocarbon liquids and relative concentrations of their binary and ternary mixtures in tens of seconds. In these 3D photonic crystals, pure chemicals with different volatilities would have different evaporation rates and can be easily identified via the total drying time. For multicomponent mixtures, the same strategy is applied to determine the relative concentration of each component simply by measuring drying time under different temperatures. Using this optofluidic sensing platform, we have determined the relative concentrations of ternary hydrocarbon mixtures with the difference of only one carbon between alkane hydrocarbons, which is a big step toward detailed hydrocarbon analysis for practical use.

The refractive index and electronic gap of water and ice increase with increasing pressure

PubMed Central

Pan, Ding; Wan, Quan; Galli, Giulia

2014-01-01

Determining the electronic and dielectric properties of water at high pressure and temperature is an essential prerequisite to understand the physical and chemical properties of aqueous environments under supercritical conditions, for example, in the Earth interior. However, optical measurements of compressed ice and water remain challenging, and it has been common practice to assume that their band gap is inversely correlated with the measured refractive index, consistent with observations reported for hundreds of materials. Here we report ab initio molecular dynamics and electronic structure calculations showing that both the refractive index and the electronic gap of water and ice increase with increasing pressure, at least up to 30 GPa. Subtle electronic effects, related to the nature of interband transitions and band edge localization under pressure, are responsible for this apparently anomalous behaviour. PMID:24861665

Problem of image superresolution with a negative-refractive-index slab.

PubMed

Nieto-Vesperinas, Manuel

2004-04-01

By means of the angular spectrum representation of wave fields, a discussion is given on the propagation and restoration of the wave-front structure in a slab of a left-handed medium (or negative-index medium) whose surface impedance matches that of vacuum, namely, one whose effective optical parameters are n = epsilon = mu = -1. This restoration was previously discussed [Phys. Rev. Lett. 85, 3866 (2000)] in regard to whether it may yield superresolved images. The divergence of the wave field in the slab, and its equivalence with that of the inverse diffraction propagator in free space, is addressed. Further, the existence of absorption, its regularization of this divergence, and the trade-off of a resulting limited superresolution are analyzed in detail in terms of its effect on the evanescent components of the wave field and hence on the transfer function width.

Simultaneous identification of optical constants and PSD of spherical particles by multi-wavelength scattering-transmittance measurement

NASA Astrophysics Data System (ADS)

Zhang, Jun-You; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2018-04-01

An accurate and stable identification technique is developed to retrieve the optical constants and particle size distributions (PSDs) of particle system simultaneously from the multi-wavelength scattering-transmittance signals by using the improved quantum particle swarm optimization algorithm. The Mie theory are selected to calculate the directional laser intensity scattered by particles and the spectral collimated transmittance. The sensitivity and objective function distribution analysis were conducted to evaluate the mathematical properties (i.e. ill-posedness and multimodality) of the inverse problems under three different optical signals combinations (i.e. the single-wavelength multi-angle light scattering signal, the single-wavelength multi-angle light scattering and spectral transmittance signal, and the multi-angle light scattering and spectral transmittance signal). It was found the best global convergence performance can be obtained by using the multi-wavelength scattering-transmittance signals. Meanwhile, the present technique have been tested under different Gaussian measurement noise to prove its feasibility in a large solution space. All the results show that the inverse technique by using multi-wavelength scattering-transmittance signals is effective and suitable for retrieving the optical complex refractive indices and PSD of particle system simultaneously.

Understanding the surface chemical and mechanical properties of hydrogel materials for contact lens applications

NASA Astrophysics Data System (ADS)

Huang, Fu-Chung

Vision problems such as near-sightedness, far-sightedness, as well as others, are due to optical aberrations in the human eye. These conditions are prevalent, and the population is growing rapidly. Correcting optical aberrations is traditionally done optically using eyeglasses, contact lenses, or refractive surgeries; these are sometime not convenient or not always available to everyone. Furthermore, higher order aberrations are not correctable with eyeglasses. In this work, we introduce a new computation based aberration-correcting light field display: by incorporating the persons own optical aberration into the computation, we alter the content shown on the display, such that he or she will be able to see it in sharp focus without wearing eyewear. We analyze the image formation models; through the retinal light field projection, we find it is possible to compensate for the optical blurring on the target image by prefiltering with the inverse blur. Using off-the-shelf components, we built a light field display prototype that supports our desired inverse light field prefiltering. The results show a significant contrast improvement and resolution enhancement over prior approaches. Finally, we also demonstrate the capability to correct for higher order aberrations.

Development of highly-ordered, ferroelectric inverse opal films using sol gel infiltration

NASA Astrophysics Data System (ADS)

Matsuura, N.; Yang, S.; Sun, P.; Ruda, H. E.

2005-07-01

Highly-ordered, ferroelectric, Pb-doped Ba0.7Sr0.3TiO3, inverse opal films were fabricated by spin-coating a sol gel precursor into a polystyrene artificial opal template followed by heat treatment. Thin films of the ferroelectric were independently studied and were shown to exhibit good dielectric properties and high refractive indices. The excellent quality of the final inverse opal film using this spin-coating infiltration method was confirmed by scanning electron microscopy images and the good correspondence between optical reflection data and theoretical simulations. Using this method, the structural and material parameters of the final ferroelectric inverse opal film were easily adjusted by template heating and through repeated infiltrations, without changes in the initial template or precursor. Also, crack-free inverse opal thin films were fabricated over areas comparable to that of the initial crack-free polystyrene template (˜100 by 100 μm2).

[Analysis of visible extinction spectrum of particle system and selection of optimal wavelength].

PubMed

Sun, Xiao-gang; Tang, Hong; Yuan, Gui-bin

2008-09-01

In the total light scattering particle sizing technique, the extinction spectrum of particle system contains some information about the particle size and refractive index. The visible extinction spectra of the common monomodal and biomodal R-R particle size distribution were computed, and the variation in the visible extinction spectrum with the particle size and refractive index was analyzed. The corresponding wavelengths were selected as the measurement wavelengths at which the second order differential extinction spectrum was discontinuous. Furthermore, the minimum and the maximum wavelengths in the visible region were also selected as the measurement wavelengths. The genetic algorithm was used as the inversion method under the dependent model The computer simulation and experiments illustrate that it is feasible to make an analysis of the extinction spectrum and use this selection method of the optimal wavelength in the total light scattering particle sizing. The rough contour of the particle size distribution can be determined after the analysis of visible extinction spectrum, so the search range of the particle size parameter is reduced in the optimal algorithm, and then a more accurate inversion result can be obtained using the selection method. The inversion results of monomodal and biomodal distribution are all still satisfactory when 1% stochastic noise is put in the transmission extinction measurement values.

Las Vegas Basin Seismic Response Project: Measured Shallow Soil Velocities

NASA Astrophysics Data System (ADS)

Luke, B. A.; Louie, J.; Beeston, H. E.; Skidmore, V.; Concha, A.

2002-12-01

The Las Vegas valley in Nevada is a deep (up to 5 km) alluvial basin filled with interlayered gravels, sands, and clays. The climate is arid. The water table ranges from a few meters to many tens of meters deep. Laterally extensive thin carbonate-cemented lenses are commonly found across parts of the valley. Lenses range beyond 2 m in thickness, and occur at depths exceeding 200 m. Shallow seismic datasets have been collected at approximately ten sites around the Las Vegas valley, to characterize shear and compression wave velocities in the near surface. Purposes for the surveys include modeling of ground response to dynamic loads, both natural and manmade, quantification of soil stiffness to aid structural foundation design, and non-intrusive materials identification. Borehole-based measurement techniques used include downhole and crosshole, to depths exceeding 100 m. Surface-based techniques used include refraction and three different methods involving inversion of surface-wave dispersion datasets. This latter group includes two active-source techniques, the Spectral Analysis of Surface Waves (SASW) method and the Multi-Channel Analysis of Surface Waves (MASW) method; and a new passive-source technique, the Refraction Mictrotremor (ReMi) method. Depths to halfspace for the active-source measurements ranged beyond 50 m. The passive-source method constrains shear wave velocities to 100 m depths. As expected, the stiff cemented layers profoundly affect local velocity gradients. Scale effects are evident in comparisons of (1) very local measurements typified by borehole methods, to (2) the broader coverage of the SASW and MASW measurements, to (3) the still broader and deeper resolution made possible by the ReMi measurements. The cemented layers appear as sharp spikes in the downhole datasets and are problematic in crosshole measurements due to refraction. The refraction method is useful only to locate the depth to the uppermost cemented layer. The surface-wave methods, on the other hand, can process velocity inversions. With the broader coverage of the active-source surface wave measurements, through careful inversion that takes advantage of prior information to the greatest extent possible, multiple, shallow, stiff layers can be resolved. Data from such broader-coverage methods also provide confidence regarding continuity of the cemented layers. For the ReMi measurements, which provide the broadest coverage of all methods used, the more generalized shallow profile is sometimes characterized by a strong stiffness inversion at a depth of approximately 10 m. We anticipate that this impedance contrast represents the vertical extent of the multiple layered deposits of cemented media.

[Polar and non polar notations of refraction].

PubMed

Touzeau, O; Gaujoux, T; Costantini, E; Borderie, V; Laroche, L

2010-01-01

Refraction can be expressed by four polar notations which correspond to four different combinations of spherical or cylindrical lenses. Conventional expressions of refraction (plus and minus cylinder notation) are described by sphere, cylinder, and axis. In the plus cylinder notation, the axis visualizes the most powerful meridian. The axis usually corresponds to the bow tie axis in curvature maps. Plus cylinder notation is also valuable for all relaxing procedures (i.e., selective suture ablation, arcuate keratotomy, etc.). In the cross-cylinder notation, two orthogonal cylinders can describe (without the sphere component) the actual refraction of both the principal meridians. This notation must be made before performing the vertex calculation. Using an association of a Jackson cross-cylinder and a spherical equivalent, refraction can be broken down into two pure components: astigmatism and sphere. All polar notations of refraction may perfectly characterize a single refraction but are not suitable for statistical analysis, which requires nonpolar expression. After doubling the axis, a rectangular projection breaks down the Jackson cross-cylinder, which has a polar axis, into two Jackson cross-cylinders on the 0 degrees /90 degrees and 45 degrees /135 degrees axis. This procedure results in the loss of the directional nature of the data. Refraction can be written in a nonpolar notation by three rectangular coordinates (x,y,z), which can also represent the spherocylinder by one point in a dioptric space. These three independent (orthogonal) variables have a concrete optical significance: a spherical component, a direct/inverse (WTR/ATR) component, and an oblique component of the astigmatism. Finally, nonpolar notations are useful for statistical analysis and graphical representation of refraction. Copyright (c) 2009 Elsevier Masson SAS. All rights reserved.

Peripheral refraction and retinal contour in stable and progressive myopia.

PubMed

Faria-Ribeiro, Miguel; Queirós, António; Lopes-Ferreira, Daniela; Jorge, Jorge; González-Méijome, José Manuel

2013-01-01

To compare the patterns of relative peripheral astigmatic refraction (tangential and sagittal power errors) and eccentric eye length between progressing and stable young-adult myopes. Sixty-two right eyes of 62 white patients participated in the study, of which 30 were nonprogressing myopes (NP group) for the last 2 years and 32 were progressing myopes (P group). Groups were matched for mean spherical refraction, axial length, and age. Peripheral refraction and eye length were measured along the horizontal meridian up to 35 and 30 degrees of eccentricity, respectively. There were statistically significant differences between groups (p < 0.001) in the nasal retina for the astigmatic components of peripheral refraction. The P group presented a hyperopic relative sagittal focus at 35 degrees in the nasal retina of +1.00 ± 0.83 diopters, as per comparison with a myopic relative sagittal focus of -0.10 ± 0.98 diopters observed in the NP group (p < 0.001). Retinal contour in the P group had a steeper shape in the nasal region than that in the NP group (t test, p = 0.001). An inverse correlation was found (r = -0.775; p < 0.001) between retinal contour and peripheral refraction. Thus, steeper retinas presented a more hyperopic trend in the periphery. Stable and progressing myopes of matched age, axial length, and central refraction showed significantly different characteristics in their peripheral retinal shape and astigmatic components of tangential and sagittal power errors. The present findings may help explain the mechanisms that regulate ocular growth in humans.

Semiannual Technical Summary, 1 October 1985-31 March 1986

DTIC Science & Technology

1986-05-01

see Braille , 1973; Ruud, 1986) to estimate velocities and crustal thick- ness. The outcome of such an experiment, on the basis of ŗ-component...Phys. Earth Planet. Inter., 15, 13-27. Braille , L.W. (1973): Inversion of crustal seismic refraction and reflection data, J. Geophy. Res., 78, 7738-7744

Inverse medium scattering from periodic structures with fixed-direction incoming waves

NASA Astrophysics Data System (ADS)

Gibson, Peter; Hu, Guanghui; Zhao, Yue

2018-07-01

This paper is concerned with inverse time-harmonic acoustic and electromagnetic scattering from an infinite biperiodic medium (diffraction grating) in three dimensions. In the acoustic case, we prove that the near-field data of fixed-direction plane waves incited at multiple frequencies uniquely determine a refractive index function which depends on two variables. An analogous uniqueness result holds for time-harmonic Maxwell’s system if the inhomogeneity is periodic in one direction and remains invariant along the other two directions. Uniqueness for recovering (non-periodic) compactly supported contrast functions are also presented.

The role of axial length-corneal radius of curvature ratio in refractive state categorization in a nigerian population.

PubMed

Iyamu, Eghosasere; Iyamu, Joy; Obiakor, Christian Izuchukwu

2011-01-01

The aim of this study was to investigate the association of axial length (AL)/corneal radius of curvature (CRC) ratio (AL/CRC) with spherical equivalent refractive state (SER) in young adults. A total of seventy (n = 70) subjects consisting of 31 males and 39 females participated in this study. Subjects were categorized into emmetropia, hyperopia and myopia using the spherical equivalent refraction. The axial length was measured with I-2100 A-Scan ultrasonography/Biometer (CIMA Technology, USA), the corneal radius of curvature with Bausch & Lomb H-135A (Bausch & Lomb Corp., USA), and the refractive state by static retinoscopy and subjective refraction. The mean AL, CRC and AL/CRC ratio of all subjects were 23.74 ± 0.70 mm, 7.84 ± 0.19 mm, and 3.03 ± 0.14, respectively. Myopes had significantly longer AL, steeper CRC and higher AL/CRC ratio than the emmetropes and hyperopes. There was statistically significant inverse correlation between AL and CRC (r = -0.53, P < 0.0001), SER (r = -0.64, P < 0.0001), and between SER and AL/CRC (r = -0.78, P < 0.0001). A significant positive correlation was found between CRC and SER (r = -0.69, P < 0.0001). The categorization of the refractive state of an individual is better done by using the AL/CRC ratio index.

Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic-monostatic lidar and solar radiometer measurements

NASA Technical Reports Server (NTRS)

Reagan, J. A.; Byrne, D. M.; Herman, B. M.; King, M. D.; Spinhirne, J. D.

1980-01-01

A method is presented for inferring both the size distribution and the complex refractive index of atmospheric particulates from combined bistatic-monostatic lidar and solar radiometer observations. The basic input measurements are spectral optical depths at several visible and near-infrared wavelengths as obtained with a solar radiometer and backscatter and angular scatter coefficients as obtained from a biostatic-monostatic lidar. The spectral optical depth measurements obtained from the radiometer are mathematically inverted to infer a columnar particulate size distribution. Advantage is taken of the fact that the shape of the size distribution obtained by inverting the particulate optical depth is relatively insensitive to the particle refractive index assumed in the inversion. Bistatic-monostatic angular scatter and backscatter lidar data are then processed to extract an optimum value for the particle refractive index subject to the constraint that the shape of the particulate size distribution be the same as that inferred from the solar radiometer data. Specifically, the scattering parameters obtained from the bistatic-monostatic lidar data are compared with corresponding theoretical computations made for various assumed refractive index values. That value which yields best agreement, in a weighted least squares sense, is selected as the optimal refractive index estimate. The results of this procedure applied to a set of simulated measurements as well as to measurements collected on two separate days are presented and discussed.

Three-dimensional optical tomographic imaging of supersonic jets through inversion of phase data obtained through the transport-of-intensity equation.

PubMed

Hemanth, Thayyullathil; Rajesh, Langoju; Padmaram, Renganathan; Vasu, R Mohan; Rajan, Kanjirodan; Patnaik, Lalit M

2004-07-20

We report experimental results of quantitative imaging in supersonic circular jets by using a monochromatic light probe. An expanding cone of light interrogates a three-dimensional volume of a supersonic steady-state flow from a circular jet. The distortion caused to the spherical wave by the presence of the jet is determined through our measuring normal intensity transport. A cone-beam tomographic algorithm is used to invert wave-front distortion to changes in refractive index introduced by the flow. The refractive index is converted into density whose cross sections reveal shock and other characteristics of the flow.

Thick lens chromatic effective focal length variation versus bending

NASA Astrophysics Data System (ADS)

Sparrold, Scott

2017-11-01

Longitudinal chromatic aberration (LCA) can limit the optical performance in refractive optical systems. Understanding a singlet's chromatic change of effective focal leads to insights and methods to control LCA. Long established, first order theory, shows the chromatic change in focal length for a zero thickness lens is proportional to it's focal length divided by the lens V number or inverse dispersion. This work presents the derivation of an equation for a thick singlet's chromatic change in effective focal length as a function of center thickness, t, dispersion, V, index of refraction, n, and the Coddington shape factor, K. A plot of bending versus chromatic focal length variation is presented. Lens thickness does not influence chromatic variation of effective focal length for a convex plano or plano convex lens. A lens's center thickness'influence on chromatic focal length variation is more pronounced for lower indices of refraction.

Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.

Vectorial approach of determining the wave propagation at metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Daniel, E-mail: D.Smith1966@outlook.com; Campbell, Michael, E-mail: mhl.campbell@gmail.com; Bergmann, Andreas, E-mail: a.bergmann@hotmail.com

2015-10-15

Vector approach often benefits optical engineers and physicists, and a vector formulation of the laws of reflection and refraction has been studied (Tkaczyk, 2012). However, the conventional reflection and refraction laws may be violated in the presence of a metasurface, and reflection and refraction at the metasurface obey generalized laws of reflection and refraction (Yu et al., 2011). In this letter, the vectorial laws of reflection and refraction at the metasurface were derived, and the matrix formulation of these vectorial laws are also obtained. These results enable highly efficient and unambiguous computations in ray-tracing problems that involve a metasurface.

Accurate measurement of volume and shape of resting and activated blood platelets from light scattering.

PubMed

Moskalensky, Alexander E; Yurkin, Maxim A; Konokhova, Anastasiya I; Strokotov, Dmitry I; Nekrasov, Vyacheslav M; Chernyshev, Andrei V; Tsvetovskaya, Galina A; Chikova, Elena D; Maltsev, Valeri P

2013-01-01

We introduce a novel approach for determination of volume and shape of individual blood platelets modeled as an oblate spheroid from angle-resolved light scattering with flow-cytometric technique. The light-scattering profiles (LSPs) of individual platelets were measured with the scanning flow cytometer and the platelet characteristics were determined from the solution of the inverse light-scattering problem using the precomputed database of theoretical LSPs. We revealed a phenomenon of parameter compensation, which is partly explained in the framework of anomalous diffraction approximation. To overcome this problem, additional a priori information on the platelet refractive index was used. It allowed us to determine the size of each platelet with subdiffraction precision and independent of the particular value of the platelet aspect ratio. The shape (spheroidal aspect ratio) distributions of platelets showed substantial differences between native and activated by 10 μM adenosine diphosphate samples. We expect that the new approach may find use in hematological analyzers for accurate measurement of platelet volume distribution and for determination of the platelet activation efficiency.

Account of an optical beam spreading caused by turbulence for the problem of partially coherent wavefield propagation through inhomogeneous absorbing media

NASA Astrophysics Data System (ADS)

Dudorov, Vadim V.; Kolosov, Valerii V.

2003-04-01

The propagation problem for partially coherent wave fields in inhomogeneous media is considered in this work. The influence of refraction, inhomogeneity of gain medium properties and refraction parameter fluctuations on target characteristics of radiation are taken into consideration. Such problems arise in the study of laser propagation on atmosphere paths, under investigation of directional radiation pattern forming for lasers which gain media is characterized by strong fluctuation of dielectric constant and for lasers which resonator have an atmosphere area. The ray-tracing technique allows us to make effective algorithms for modeling of a partially coherent wave field propagation through inhomogeneous random media is presented for case when the influecne of an optical wave refraction, the influence of the inhomogeiety of radiaitn amplification or absorption, and also the influence of fluctuations of a refraction parameter on target radiation parameters are basic. Novelty of the technique consists in the account of the additional refraction caused by inhomogeneity of gain, and also in the method of an account of turbulent distortions of a beam with any initial coherence allowing to execute construction of effective numerical algorithms. The technique based on the solution of the equation for coherence function of the second order.

Investigating the transverse optical structure of spider silk micro-fibers using quantitative optical microscopy

NASA Astrophysics Data System (ADS)

Little, Douglas J.; Kane, Deb M.

2017-01-01

The transverse optical structure of two orb-weaver (family Araneidae) spider dragline silks was investigated using a variant of the inverse-scattering technique. Immersing the silks in a closely refractive index-matched liquid, the minimum achievable image contrast was greater than expected for an optically homogeneous silk, given what is currently known about the optical absorption of these silks. This "excess contrast" indicated the presence of transverse optical structure within the spider silk. Applying electromagnetic scattering theory to a transparent double cylinder, the minimum achievable irradiance contrast for the Plebs eburnus and Argiope keyserlingi dragline silks was determined to be consistent with step index refractive index contrasts of 1-4×10-4 and 6-7×10-4, respectively, supposing outer-layer thicknesses consistent with previous TEM studies (50 nm and 100 nm, respectively). The possibility of graded index refractive index contrasts within the spider silks is also discussed. This is the strongest evidence, to date, that there is a refractive index contrast associated with the layered morphology of spider silks and/or variation of proportion of nanocrystalline components within the spider silk structure. The method is more generally applicable to optical micro-fibers, including those with refractive index variations on a sub-wavelength scale.

Advances and Limitations of Atmospheric Boundary Layer Observations with GPS Occultation over Southeast Pacific Ocean

NASA Technical Reports Server (NTRS)

Xie, F.; Wu, D. L.; Ao, C. O.; Mannucci, A. J.; Kursinski, E. R.

2012-01-01

The typical atmospheric boundary layer (ABL) over the southeast (SE) Pacific Ocean is featured with a strong temperature inversion and a sharp moisture gradient across the ABL top. The strong moisture and temperature gradients result in a sharp refractivity gradient that can be precisely detected by the Global Positioning System (GPS) radio occultation (RO) measurements. In this paper, the Constellation Observing System for Meteorology, Ionosphere & Climate (COSMIC) GPS RO soundings, radiosondes and the high-resolution ECMWF analysis over the SE Pacific are analyzed. COSMIC RO is able to detect a wide range of ABL height variations (1-2 kilometer) as observed from the radiosondes. However, the ECMWF analysis systematically underestimates the ABL heights. The sharp refractivity gradient at the ABL top frequently exceeds the critical refraction (e.g., -157 N-unit per kilometer) and becomes the so-called ducting condition, which results in a systematic RO refractivity bias (or called N-bias) inside the ABL. Simulation study based on radiosonde profiles reveals the magnitudes of the N-biases are vertical resolution dependent. The N-bias is also the primary cause of the systematically smaller refractivity gradient (rarely exceeding -110 N-unit per kilometer) at the ABL top from RO measurement. However, the N-bias seems not affect the ABL height detection. Instead, the very large RO bending angle and the sharp refractivity gradient due to ducting allow reliable detection of the ABL height from GPS RO. The seasonal mean climatology of ABL heights derived from a nine-month composite of COSMIC RO soundings over the SE Pacific reveals significant differences from the ECMWF analysis. Both show an increase of ABL height from the shallow stratocumulus near the coast to a much higher trade wind inversion further off the coast. However, COSMIC RO shows an overall deeper ABL and reveals different locations of the minimum and maximum ABL heights as compared to the ECMWF analysis. At low latitudes, despite the decreasing number of COSMIC RO soundings and the lower percentage of soundings that penetrate into the lowest 500-m above the mean-sea-level, there are small sampling errors in the mean ABL height climatology. The difference of ABL height climatology between COSMIC RO and ECMWF analysis over SE Pacific is significant and requires further studies.

IOL calculation using paraxial matrix optics.

PubMed

Haigis, Wolfgang

2009-07-01

Matrix methods have a long tradition in paraxial physiological optics. They are especially suited to describe and handle optical systems in a simple and intuitive manner. While these methods are more and more applied to calculate the refractive power(s) of toric intraocular lenses (IOL), they are hardly used in routine IOL power calculations for cataract and refractive surgery, where analytical formulae are commonly utilized. Since these algorithms are also based on paraxial optics, matrix optics can offer rewarding approaches to standard IOL calculation tasks, as will be shown here. Some basic concepts of matrix optics are introduced and the system matrix for the eye is defined, and its application in typical IOL calculation problems is illustrated. Explicit expressions are derived to determine: predicted refraction for a given IOL power; necessary IOL power for a given target refraction; refractive power for a phakic IOL (PIOL); predicted refraction for a thick lens system. Numerical examples with typical clinical values are given for each of these expressions. It is shown that matrix optics can be applied in a straightforward and intuitive way to most problems of modern routine IOL calculation, in thick or thin lens approximation, for aphakic or phakic eyes.

SIPT: a seismic refraction inverse modeling program for timeshare terminal computer systems

USGS Publications Warehouse

Scott, James Henry

1977-01-01

SIPB is an interactive Fortran computer program that was developed for use with a timeshare computer system with program control information submitted from a remote terminal, and output data displayed on the terminal or printed on a line printer. The program is an upgraded version of FSIPI (Scott, Tibbetts, and Burdick, 1972) with several major improvements in addition to .its adaptation to timeshare operation. The most significant improvement was made in the procedure for handling data from in-line offset shotpoints beyond the end shotpoints of the geophone spread. The changes and improvements are described, user's instructions are outlined, examples of input and output data for a test problem are presented, and the Fortran program is listed in this report. An upgraded batch-mode program, SIPB, is available for users who do not have a timeshare computer system available (Scott, 1977).

SIPB: a seismic refraction inverse modeling program for batch computer systems

USGS Publications Warehouse

Scott, James Henry

1977-01-01

SIPB is an interactive Fortran computer program that was developed for use with a timeshare computer system with program control information submitted from a remote terminal, and output data displayed on the terminal or printed on a line printer. The program is an upgraded version of FSIPI (Scott, Tibbetts, and Burdick, 1972) with several major improvements in addition to .its adaptation to timeshare operation. The most significant improvement was made in the procedure for handling data from in-line offset shotpoints beyond the end shotpoints of the geophone spread. The changes and improvements are described, user's instructions are outlined, examples of input and output data for a test problem are presented, and the Fortran program is listed in this report. An upgraded batch-mode program, SIPB, is available for users who do not have a timeshare computer system available (Scott, 1977).

Designing perturbative metamaterials from discrete models.

PubMed

Matlack, Kathryn H; Serra-Garcia, Marc; Palermo, Antonio; Huber, Sebastian D; Daraio, Chiara

2018-04-01

Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce 'perturbative metamaterials', a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells.

Developments in spectrophotometry III: Multiple-field-of-view spectrometer to determine particle-size distribution and refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1975-01-01

Instrument is based on inverse solution ot equations for light scattered by a transparent medium. Measurements are taken over several angles of incidence rather than over several frequencies. Measurements can be used to simultaneously determine chemical and physical properties of particles in mixed gas or liquid.

High-quality photonic crystals with a nearly complete band gap obtained by direct inversion of woodpile templates with titanium dioxide.

PubMed

Marichy, Catherine; Muller, Nicolas; Froufe-Pérez, Luis S; Scheffold, Frank

2016-02-25

Photonic crystal materials are based on a periodic modulation of the dielectric constant on length scales comparable to the wavelength of light. These materials can exhibit photonic band gaps; frequency regions for which the propagation of electromagnetic radiation is forbidden due to the depletion of the density of states. In order to exhibit a full band gap, 3D PCs must present a threshold refractive index contrast that depends on the crystal structure. In the case of the so-called woodpile photonic crystals this threshold is comparably low, approximately 1.9 for the direct structure. Therefore direct or inverted woodpiles made of high refractive index materials like silicon, germanium or titanium dioxide are sought after. Here we show that, by combining multiphoton lithography and atomic layer deposition, we can achieve a direct inversion of polymer templates into TiO2 based photonic crystals. The obtained structures show remarkable optical properties in the near-infrared region with almost perfect specular reflectance, a transmission dip close to the detection limit and a Bragg length comparable to the lattice constant.

On the interpolation of light-scattering responses from irregularly shaped particles

NASA Astrophysics Data System (ADS)

Videen, Gorden; Zubko, Evgenij; Arnold, Jessica A.; MacCall, Benjamin; Weinberger, Alycia J.; Shkuratov, Yuriy; Muñoz, Olga

2018-05-01

Common particle characteristics needed for many applications may include size, eccentricity, porosity and refractive index. Determining such characteristics from scattered light is a primary goal of remote sensing. For other applications, like differentiating a hazardous particle from the natural background, information about higher fidelity particle characteristics may be required, including specific shape or chemical composition. While a complete characterization of a particle system from its scattered light through the inversion process remains unachievable, great strides have been made in providing information in the form of constraints on particle characteristics. Recent advances have been made in quantifying the characteristics of polydispersions of irregularly shaped particles by making comparisons of the light-scattering signals from model simulant particles. We show that when the refractive index is changed, the light-scattering characteristics from polydispersions of such particles behave monotonically over relatively large parameter ranges compared with those of monodisperse distributions of particles having regular shapes, like spheres, spheroids, etc. This allows for their properties to be interpolated, which results in a significant reduction of the computational load when performing inversions.

Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method

NASA Astrophysics Data System (ADS)

Bao, Yuan; Wang, Yan; Gao, Kun; Wang, Zhi-Li; Zhu, Pei-Ping; Wu, Zi-Yu

2015-10-01

The relationship between noise variance and spatial resolution in grating-based x-ray phase computed tomography (PCT) imaging is investigated with reverse projection extraction method, and the noise variances of the reconstructed absorption coefficient and refractive index decrement are compared. For the differential phase contrast method, the noise variance in the differential projection images follows the same inverse-square law with spatial resolution as in conventional absorption-based x-ray imaging projections. However, both theoretical analysis and simulations demonstrate that in PCT the noise variance of the reconstructed refractive index decrement scales with spatial resolution follows an inverse linear relationship at fixed slice thickness, while the noise variance of the reconstructed absorption coefficient conforms with the inverse cubic law. The results indicate that, for the same noise variance level, PCT imaging may enable higher spatial resolution than conventional absorption computed tomography (ACT), while ACT benefits more from degraded spatial resolution. This could be a useful guidance in imaging the inner structure of the sample in higher spatial resolution. Project supported by the National Basic Research Program of China (Grant No. 2012CB825800), the Science Fund for Creative Research Groups, the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant Nos. KJCX2-YW-N42 and Y4545320Y2), the National Natural Science Foundation of China (Grant Nos. 11475170, 11205157, 11305173, 11205189, 11375225, 11321503, 11179004, and U1332109).

Observation of a Saharan dust outbreaks in the frame of the Convective and Orographically-induced Precipitation Study

NASA Astrophysics Data System (ADS)

Di Girolamo, Paolo; Summa, Donato; Bhawar, Rohini; Di Iorio, Tatiana; Caccaini, Marco; Veselovskii, Igor; Kolgotin, Alexey

2009-03-01

The Raman lidar system BASIL was operational in Achern (Supersite R, Lat: 48.64° N, Long: 8.06° E, Elev.: 140 m) in the frame of the Convective and Orographically-induced Precipitation Study. BASIL operated continuously over a period of approx. 36 hours from 06:22 UTC on 1 August to 18:28 UTC on 2 August 2007, to cover IOPs 13 a-b. In this timeframe the signature of a severe Saharan dust outbreak episode was captured. An inversion algorithm was used to retrieve particle size distribution parameters, i.e., mean and effective radius, number, surface area, and volume concentration, and complex refractive index, as well as the parameters of a bimodal particle size distribution, from the multi-wavelength lidar data of particle backscattering and extinction. The inversion method employs Tikhonov's inversion with regularization. Size distribution parameters are estimated as a function of altitude at different times during the dust outbreak event. Retrieval results reveal the dominance in the upper dust layer of a coarse mode with radii 3-4 μm. Number density and volume concentration are in the range 100-800 cm-3 and 5-40 μm3/cm3, respectively, while real and imaginary part of the complex refractive index are in the range 1.41-1.53 and 0.003-0.014, respectively.

Formal integration of controlled-source and passive seismic data: Utilization of the CD-ROM experiment

NASA Astrophysics Data System (ADS)

Rumpfhuber, E.; Keller, G. R.; Velasco, A. A.

2005-12-01

Many large-scale experiments conduct both controlled-source and passive deployments to investigate the lithospheric structure of a targeted region. Many of these studies utilize each data set independently, resulting in different images of the Earth depending on the data set investigated. In general, formal integration of these data sets, such as joint inversions, with other data has not been performed. The CD-ROM experiment, which included both 2-D controlled-source and passive recording along a profile extending from southern Wyoming to northern New Mexico serves as an excellent data set to develop a formal integration strategy between both controlled source and passive experiments. These data are ideal to develop this strategy because: 1) the analysis of refraction/wide-angle reflection data yields Vp structure, and sometimes Vs structure, of the crust and uppermost mantle; 2) analysis of the PmP phase (Moho reflection) yields estimates of the average Vp of the crust for the crust; and 3) receiver functions contain full-crustal reverberations and yield the Vp/Vs ratio, but do not constrain the absolute P and S velocity. Thus, a simple form of integration involves using the Vp/Vs ratio from receiver functions and the average Vp from refraction measurements, to solve for the average Vs of the crust. When refraction/ wide-angle reflection data and several receiver functions nearby are available, an integrated 2-D model can be derived. In receiver functions, the PS conversion gives the S-wave travel-time (ts) through the crust along the raypath traveled from the Moho to the surface. Since the receiver function crustal reverberation gives the Vp/Vs ratio, it is also possible to use the arrival time of the converted phase, PS, to solve for the travel time of the direct teleseismic P-wave through the crust along the ray path. Raytracing can yield the point where the teleseismic wave intersects the Moho. In this approach, the conversion point is essentially a pseudo-shotpoint, thus the converted arrival at the surface can be jointly modeled with refraction data using a 3-D inversion code. Employing the combined CD-ROM data sets, we will be investigating the joint inversion results of controlled source data and receiver functions.

Correcting negatively biased refractivity below ducts in GNSS radio occultation: an optimal estimation approach towards improving planetary boundary layer (PBL) characterization

NASA Astrophysics Data System (ADS)

Wang, Kuo-Nung; de la Torre Juárez, Manuel; Ao, Chi O.; Xie, Feiqin

2017-12-01

Global Navigation Satellite System (GNSS) radio occultation (RO) measurements are promising in sensing the vertical structure of the Earth's planetary boundary layer (PBL). However, large refractivity changes near the top of PBL can cause ducting and lead to a negative bias in the retrieved refractivity within the PBL (below ˜ 2 km). To remove the bias, a reconstruction method with assumption of linear structure inside the ducting layer models has been proposed by Xie et al. (2006). While the negative bias can be reduced drastically as demonstrated in the simulation, the lack of high-quality surface refractivity constraint makes its application to real RO data difficult. In this paper, we use the widely available precipitable water (PW) satellite observation as the external constraint for the bias correction. A new framework is proposed to incorporate optimization into the RO reconstruction retrievals in the presence of ducting conditions. The new method uses optimal estimation to select the best refractivity solution whose PW and PBL height best match the externally retrieved PW and the known a priori states, respectively. The near-coincident PW retrievals from AMSR-E microwave radiometer instruments are used as an external observational constraint. This new reconstruction method is tested on both the simulated GNSS-RO profiles and the actual GNSS-RO data. Our results show that the proposed method can greatly reduce the negative refractivity bias when compared to the traditional Abel inversion.

Ultrahigh refractive index chalcogenide based copolymers for infrared optics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Anderson, Laura E.; Namnabat, Soha; Char, Kookheon; Glass, Richard; Norwood, Robert A.; Pyun, Jeffrey

2016-09-01

Current trends in technology development demand increased miniaturization and higher level integration of electronic and photonic components. Such needs arise in emerging imaging systems, optoelectronic devices, optical interconnects and photonic integrated circuits. Compact, integrated photonics requires high refractive index materials, which primarily comprise crystalline and amorphous semiconductors, as well as chalcogenide glasses, which can possess refractive indices higher than 4 and good infrared transparency. There is currently no high refractive index (n 2 or above) that has the low cost production and ease of processing available in optical polymers. Such polymers would potentially cover applications that are not convenient or possible with crystalline and vitreous semiconductors. Examples of such applications include micro lens arrays for image sensors, optical adhesives for bonding and antireflection coatings, and high contrast optical waveguides. While much of the focus has been in the telecommunications transparency regions, significant new opportunities exist for a polymer which is capable of transmitting efficiently in the MWIR region. While there are polymers that have been synthesized with refractive indices as high as 1.75, these polymers are generally conjugated and incorporate heteroatoms such as sulfur or metals, and generally have complex and expensive syntheses. Here we report on new chalcogenide based copolymers with very high refractive index (n 2) that also have good optical transmission properties in the near-, short- and mid-wave infrared up to 5µm. These polymers are rich in sulfur, have low hydrogen content and were made using inverse vulcanization.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

REVIEWS OF TOPICAL PROBLEMS: Recent advances in X-ray refractive optics

NASA Astrophysics Data System (ADS)

Aristov, V. V.; Shabel'nikov, L. G.

2008-01-01

X-ray refractive optics has made rapid strides to a large degree due to the work of Russian scientists, and has now become one of the most rapidly advancing areas in modern physical optics. This review outlines the results of investigation of refractive devices and analysis of their properties. The conception of planar lenses made of silicon and other materials is set forth. We discuss the applications of refractive lenses to the transformation of X-ray images, photonic crystal research, and the development of focusing devices in high-energy X-ray telescopes.

Asronomical refraction: Computational methods for all zenith angles

NASA Technical Reports Server (NTRS)

Auer, L. H.; Standish, E. M.

2000-01-01

It is shown that the problem of computing astronomical refraction for any value of the zenith angle may be reduced to a simple, nonsingular, numerical quadrature when the proper choice is made for the independent variable of integration.

Inversion of scattered radiance horizon profiles for gaseous concentrations and aerosol parameters

NASA Technical Reports Server (NTRS)

Malchow, H. L.; Whitney, C. K.

1977-01-01

Techniques have been developed and used to invert limb scan measurements for vertical profiles of atmospheric state parameters. The parameters which can be found are concentrations of Rayleigh scatters, ozone, NO2, and aerosols, and aerosol physical properties including a Junge-size distribution parameter and real and imaginary parts of the index of refraction.

Identification of a Candidate Gene for Astigmatism

PubMed Central

Lopes, Margarida C.; Hysi, Pirro G.; Verhoeven, Virginie J. M.; Macgregor, Stuart; Hewitt, Alex W.; Montgomery, Grant W.; Cumberland, Phillippa; Vingerling, Johannes R.; Young, Terri L.; van Duijn, Cornelia M.; Oostra, Ben; Uitterlinden, Andre G.; Rahi, Jugnoo S.; Mackey, David A.; Klaver, Caroline C. W.; Andrew, Toby; Hammond, Christopher J.

2013-01-01

Purpose. Astigmatism is a common refractive error that reduces vision, where the curvature and refractive power of the cornea in one meridian are less than those of the perpendicular axis. It is a complex trait likely to be influenced by both genetic and environmental factors. Twin studies of astigmatism have found approximately 60% of phenotypic variance is explained by genetic factors. This study aimed to identify susceptibility loci for astigmatism. Methods. We performed a meta-analysis of seven genome-wide association studies that included 22,100 individuals of European descent, where astigmatism was defined as the number of diopters of cylinder prescription, using fixed effect inverse variance-weighted methods. Results. A susceptibility locus was identified with lead single nucleotide polymorphism rs3771395 on chromosome 2p13.3 (meta-analysis, P = 1.97 × 10−7) in the VAX2 gene. VAX2 plays an important role in the development of the dorsoventral axis of the eye. Animal studies have shown a gradient in astigmatism along the vertical plane, with corresponding changes in refraction, particularly in the ventral field. Conclusions. This finding advances the understanding of refractive error, and provides new potential pathways to be evaluated with regard to the development of astigmatism. PMID:23322567

Resolvent-Techniques for Multiple Exercise Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christensen, Sören, E-mail: christensen@math.uni-kiel.de; Lempa, Jukka, E-mail: jukka.lempa@hioa.no

2015-02-15

We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristicsmore » of the problems can be identified more explicitly. We illustrate the main results with explicit examples.« less

Virtual and super - virtual refraction method: Application to synthetic data and 2012 of Karangsambung survey data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nugraha, Andri Dian; Adisatrio, Philipus Ronnie

2013-09-09

Seismic refraction survey is one of geophysical method useful for imaging earth interior, definitely for imaging near surface. One of the common problems in seismic refraction survey is weak amplitude due to attenuations at far offset. This phenomenon will make it difficult to pick first refraction arrival, hence make it challenging to produce the near surface image. Seismic interferometry is a new technique to manipulate seismic trace for obtaining Green's function from a pair of receiver. One of its uses is for improving first refraction arrival quality at far offset. This research shows that we could estimate physical properties suchmore » as seismic velocity and thickness from virtual refraction processing. Also, virtual refraction could enhance the far offset signal amplitude since there is stacking procedure involved in it. Our results show super - virtual refraction processing produces seismic image which has higher signal-to-noise ratio than its raw seismic image. In the end, the numbers of reliable first arrival picks are also increased.« less

An algorithm for hyperspectral remote sensing of aerosols: 1. Development of theoretical framework

NASA Astrophysics Data System (ADS)

Hou, Weizhen; Wang, Jun; Xu, Xiaoguang; Reid, Jeffrey S.; Han, Dong

2016-07-01

This paper describes the first part of a series of investigations to develop algorithms for simultaneous retrieval of aerosol parameters and surface reflectance from a newly developed hyperspectral instrument, the GEOstationary Trace gas and Aerosol Sensor Optimization (GEO-TASO), by taking full advantage of available hyperspectral measurement information in the visible bands. We describe the theoretical framework of an inversion algorithm for the hyperspectral remote sensing of the aerosol optical properties, in which major principal components (PCs) for surface reflectance is assumed known, and the spectrally dependent aerosol refractive indices are assumed to follow a power-law approximation with four unknown parameters (two for real and two for imaginary part of refractive index). New capabilities for computing the Jacobians of four Stokes parameters of reflected solar radiation at the top of the atmosphere with respect to these unknown aerosol parameters and the weighting coefficients for each PC of surface reflectance are added into the UNified Linearized Vector Radiative Transfer Model (UNL-VRTM), which in turn facilitates the optimization in the inversion process. Theoretical derivations of the formulas for these new capabilities are provided, and the analytical solutions of Jacobians are validated against the finite-difference calculations with relative error less than 0.2%. Finally, self-consistency check of the inversion algorithm is conducted for the idealized green-vegetation and rangeland surfaces that were spectrally characterized by the U.S. Geological Survey digital spectral library. It shows that the first six PCs can yield the reconstruction of spectral surface reflectance with errors less than 1%. Assuming that aerosol properties can be accurately characterized, the inversion yields a retrieval of hyperspectral surface reflectance with an uncertainty of 2% (and root-mean-square error of less than 0.003), which suggests self-consistency in the inversion framework. The next step of using this framework to study the aerosol information content in GEO-TASO measurements is also discussed.

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

NASA Technical Reports Server (NTRS)

Liu, A. S.

1978-01-01

When the radio link between two satellites (GEOS-3/ATS-6) is intercepted by the earth's ionosphere and neutral atmosphere, a change in the Doppler frequency results. Travel through the atmosphere causes the Doppler phase to be advanced in the ionosphere's portion and retarded in the neutral portion of the atmosphere. Analysis of the shortening and lengthening of the phase of the Satellite-to-Satellite Tracking (SST) data that passed within 40-700 km above the earth's surface during its ATS-6 to GEOS-3 to ATS-6 path, caused by the atmosphere, results in refractivity versus height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbation from the Moon, Sun and a 15th order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occultation period and a model ionosphere was estimated by a least-square adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the 2 methods were caused by orbital errors, which propagated into the solution. The SST data yielded refractive index profiles in a novel economical manner because no additional or special on-board equipment were required.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

Role of nonlinear refraction in the generation of terahertz field pulses by light fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zabolotskii, A. A., E-mail: zabolotskii@iae.nsk.su

2013-07-15

The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equationsmore » is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.« less

Measurements of electron density and temperature profiles in plasma produced by Nike KrF laser for laser plasma instability research

NASA Astrophysics Data System (ADS)

Oh, Jaechul; Weaver, J. L.; Karasik, M.; Chan, L. Y.

2015-08-01

A grid image refractometer (GIR) has been implemented at the Nike krypton fluoride laser facility of the Naval Research Laboratory. This instrument simultaneously measures propagation angles and transmissions of UV probe rays (λ = 263 nm, Δt = 10 ps) refracted through plasma. We report results of the first Nike-GIR measurement on a CH plasma produced by the Nike laser pulse (˜1 ns FWHM) with the intensity of 1.1 × 1015 W/cm2. The measured angles and transmissions were processed to construct spatial profiles of electron density (ne) and temperature (Te) in the underdense coronal region of the plasma. Using an inversion algorithm developed for the strongly refracted rays, the deployed GIR system probed electron densities up to 4 × 1021 cm-3 with the density scale length of 120 μm along the plasma symmetry axis. The resulting ne and Te profiles are verified to be self-consistent with the measured quantities of the refracted probe light.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

PubMed

Robinson, Katherine M; Ninowski, Jerilyn E

2003-12-01

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Inverse relationship between sleep duration and myopia.

PubMed

Jee, Donghyun; Morgan, Ian G; Kim, Eun Chul

2016-05-01

To investigate the association between sleep duration and myopia. This population-based, cross-sectional study using a nationwide, systemic, stratified, multistage, clustered sampling method included a total of 3625 subjects aged 12-19 years who participated in the Korean National Health and Nutrition Examination Survey 2008-2012. All participants underwent ophthalmic examination and a standardized interview including average sleep duration (hr/day), education, physical activity and economic status (annual household income). Refractive error was measured by autorefraction without cycloplegia. Myopia and high myopia were defined as ≤-0.50 dioptres (D) and ≤-6.0 D, respectively. Sleep durations were classified into 5 categories: <5, 6, 7, 8 and >9 hr. The overall prevalence of myopia and high myopia were 77.8% and 9.4%, respectively, and the overall sleep duration was 7.1 hr/day. The refractive error increased by 0.10 D per 1 hr increase in sleep after adjusting for potential confounders including sex, age, height, education level, economic status and physical activity. The adjusted odds ratio (OR) for refractive error was 0.90 (95% confidence interval [CI], 0.83-0.97) per 1 hr increase in sleep. The adjusted OR for myopia was decreased in those with >9 hr of sleep (OR, 0.59; 95% CI, 0.38-0.93; p for trend = 0.006) than in those with <5 hr of sleep. However, high myopia was not associated with sleep duration. This study provides the population-based, epidemiologic evidence for an inverse relationship between sleep duration and myopia in a representative population of Korean adolescents. © 2015 Acta Ophthalmologica Scandinavica Foundation. Published by John Wiley & Sons Ltd.

Refractive Changes Induced by Spherical Aberration in Laser Correction Procedures: An Adaptive Optics Study.

PubMed

Amigó, Alfredo; Martinez-Sorribes, Paula; Recuerda, Margarita

2017-07-01

To study the effect on vision of induced negative and positive spherical aberration within the range of laser vision correction procedures. In 10 eyes (mean age: 35.8 years) under cyclopegic conditions, spherical aberration values from -0.75 to +0.75 µm in 0.25-µm steps were induced by an adaptive optics system. Astigmatism and spherical refraction were corrected, whereas the other natural aberrations remained untouched. Visual acuity, depth of focus defined as the interval of vision for which the target was still perceived acceptable, contrast sensitivity, and change in spherical refraction associated with the variation in pupil diameter from 6 to 2.5 mm were measured. A refractive change of 1.60 D/µm of induced spherical aberration was obtained. Emmetropic eyes became myopic when positive spherical aberration was induced and hyperopic when negative spherical aberration was induced (R 2 = 81%). There were weak correlations between spherical aberration and visual acuity or depth of focus (R 2 = 2% and 3%, respectively). Contrast sensitivity worsened with the increment of spherical aberration (R 2 = 59%). When pupil size decreased, emmetropic eyes became hyperopic when preexisting spherical aberration was positive and myopic when spherical aberration was negative, with an average refractive change of 0.60 D/µm of spherical aberration (R 2 = 54%). An inverse linear correlation exists between the refractive state of the eye and spherical aberration induced within the range of laser vision correction. Small values of spherical aberration do not worsen visual acuity or depth of focus, but positive spherical aberration may induce night myopia. In addition, the changes in spherical refraction when the pupil constricts may worsen near vision when positive spherical aberration is induced or improve it when spherical aberration is negative. [J Refract Surg. 2017;33(7):470-474.]. Copyright 2017, SLACK Incorporated.

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

AERONET derived (BC) aerosol absorption

NASA Astrophysics Data System (ADS)

Kinne, S.

2015-12-01

AERONET is a ground-based sun-/sky-photometer network with good annual statistics at more than 400 sites worldwide. Inversion methods applied to these data define all relevant column aerosol optical properties and reveal even microphysical detail. The extracted data include estimates for aerosol size-distributions and for aerosol refractive indices at four different solar wavelengths. Hereby, the imaginary parts of the refractive indices define the aerosol column absorption. For regional and global averages and radiative impact assessment with off-line radiative transfer, these local data have been extended with distribution patterns offered by AeroCom modeling experiments. Annual and seasonal absorption distributions for total aerosol and estimates for component contributions (such as BC) are presented and associated direct forcing impacts are quantified.

Probing multi-scale self-similarity of tissue structures using light scattering spectroscopy: prospects in pre-cancer detection

NASA Astrophysics Data System (ADS)

Chatterjee, Subhasri; Das, Nandan K.; Kumar, Satish; Mohapatra, Sonali; Pradhan, Asima; Panigrahi, Prasanta K.; Ghosh, Nirmalya

2013-02-01

Multi-resolution analysis on the spatial refractive index inhomogeneities in the connective tissue regions of human cervix reveals clear signature of multifractality. We have thus developed an inverse analysis strategy for extraction and quantification of the multifractality of spatial refractive index fluctuations from the recorded light scattering signal. The method is based on Fourier domain pre-processing of light scattering data using Born approximation, and its subsequent analysis through Multifractal Detrended Fluctuation Analysis model. The method has been validated on several mono- and multi-fractal scattering objects whose self-similar properties are user controlled and known a-priori. Following successful validation, this approach has initially been explored for differentiating between different grades of precancerous human cervical tissues.

Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba

NASA Astrophysics Data System (ADS)

Charrière, Florian; Pavillon, Nicolas; Colomb, Tristan; Depeursinge, Christian; Heger, Thierry J.; Mitchell, Edward A. D.; Marquet, Pierre; Rappaz, Benjamin

2006-08-01

This paper presents an optical diffraction tomography technique based on digital holographic microscopy. Quantitative 2-dimensional phase images are acquired for regularly-spaced angular positions of the specimen covering a total angle of π, allowing to built 3-dimensional quantitative refractive index distributions by an inverse Radon transform. A 20x magnification allows a resolution better than 3 μm in all three dimensions, with accuracy better than 0.01 for the refractive index measurements. This technique is for the first time to our knowledge applied to living specimen (testate amoeba, Protista). Morphometric measurements are extracted from the tomographic reconstructions, showing that the commonly used method for testate amoeba biovolume evaluation leads to systematic under evaluations by about 50%.

Children's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Evaluation of a flow cytometry method to determine size and real refractive index distributions in natural marine particle populations.

PubMed

Agagliate, Jacopo; Röttgers, Rüdiger; Twardowski, Michael S; McKee, David

2018-03-01

A flow cytometric (FC) method was developed to retrieve particle size distributions (PSDs) and real refractive index (n r ) information in natural waters. Geometry and signal response of the sensors within the flow cytometer (CytoSense, CytoBuoy b.v., Netherlands) were characterized to form a scattering inversion model based on Mie theory. The procedure produced a mesh of diameter and n r isolines where each particle is assigned the diameter and n r values of the closest node, producing PSDs and particle real refractive index distributions. The method was validated using polystyrene bead standards of known diameter and polydisperse suspensions of oil with known n r , and subsequently applied to natural samples collected across a broad range of UK shelf seas. FC PSDs were compared with independent PSDs produced from data of two LISST-100X instruments (type B and type C). PSD slopes and features were found to be consistent between the FC and the two LISST-100X instruments, but LISST concentrations were found in disagreement with FC concentrations and with each other. FC n r values were found to agree with expected refractive index values of typical marine particle components across all samples considered. The determination of particle size and refractive index distributions enabled by the FC method has potential to facilitate identification of the contribution of individual subpopulations to the bulk inherent optical properties and biogeochemical properties of the particle population.

Optical-mechanical properties of diseased cells measured by interferometry

NASA Astrophysics Data System (ADS)

Shaked, Natan T.; Bishitz, Y.; Gabai, H.; Girshovitz, P.

2013-04-01

Interferometric phase microscopy (IPM) enables to obtain quantitative optical thickness profiles of transparent samples, including live cells in-vitro, and track them in time with sub-nanometer accuracy without any external labeling, contact or force application on the sample. The optical thickness measured by IPM is a multiplication between the cell integral refractive index differences and its physical thickness. Based on the time-dependent optical thickness profile, one can generate the optical thickness fluctuation map. For biological cells that are adhered to the surface, the variance of the physical thickness fluctuations in time is inversely proportional to the spring factor indicating on cell stiffness, where softer cells are expected fluctuating more than more rigid cells. For homogenous refractive index cells, such as red blood cells, we can calculate a map indicating on the cell stiffness per each spatial point on the cell. Therefore, it is possible to obtain novel diagnosis and monitoring tools for diseases changing the morphology and the mechanical properties of these cells such as malaria, certain types of anaemia and thalassemia. For cells with a complex refractive-index structure, such as cancer cells, decoupling refractive index and physical thickness is not possible in single-exposure mode. In these cases, we measure a closely related parameter, under the assumption that the refractive index does not change much within less than a second of measurement. Using these techniques, we lately found that cancer cells fluctuate significantly more than healthy cells, and that metastatic cancer cells fluctuate significantly more than primary cancer cells.

Amblyopia and refractive errors among school-aged children with low socioeconomic status in southeastern Turkey.

PubMed

Caca, Ihsan; Cingu, Abdullah Kursat; Sahin, Alparslan; Ari, Seyhmus; Dursun, Mehmet Emin; Dag, Umut; Balsak, Selahattin; Alakus, Fuat; Yavuz, Abdullah; Palanci, Yilmaz

2013-01-01

To investigate the prevalence of refractive errors and other eye diseases, incidence and types of amblyopia in school-aged children, and their relation to gender, age, parental education, and socioeconomic factors. A total of 21,062 children 6 to 14 years old were screened. The examination included visual acuity measurements and ocular motility evaluation. Autorefraction under cycloplegia and examination of the external eye, anterior segment, media, and fundus were performed. There were 11,118 females and 9,944 males. The average age was 10.56 ± 3.59 years. When all of the children were evaluated, 3.2% had myopia and 5.9% had hyperopia. Astigmatism 0.50 D or greater was present in 14.3% of children. Myopia was associated with older age, female gender, and higher parental education. Hyperopia was inversely proportional with older age. Spectacles were needed in 4,476 (22.7%) children with refractive errors, and 10.6% of children were unaware of their spectacle needs. Amblyopia was detected in 2.6% of all children. The most common causes of amblyopia were anisometropia (1.2%) and strabismus (0.9%). Visual impairment is a common disorder in school-aged children. Eye health screening programs are beneficial in early detection and proper treatment of refractive errors. Copyright 2013, SLACK Incorporated.

Determination of point of incidence for the case of reflection or refraction at spherical surface knowing two points lying on the ray.

PubMed

Mikš, Antonín; Novák, Pavel

2017-09-01

The paper is focused on the problem of determination of the point of incidence of a light ray for the case of reflection or refraction at the spherical optical surface, assuming that two fixed points in space that the sought light ray should go through are given. The requirement is that one of these points lies on the incident ray and the other point on the reflected/refracted ray. Although at first glance it seems to be a simple problem, it will be shown that it has no simple analytical solution. The basic idea of the solution is given, and it is shown that the problem leads to a nonlinear equation in one variable. The roots of the resulting nonlinear equation can be found by numerical methods of mathematical optimization. The proposed methods were implemented in MATLAB, and the proper function of these algorithms was verified on several examples.

Early screening of an infant's visual system

NASA Astrophysics Data System (ADS)

Costa, Manuel F. M.; Jorge, Jorge M.

1999-06-01

It is of utmost importance to the development of the child's visual system that she perceives clear focused retinal images. Furthermore if the refractive problems are not corrected in due time amblyopia may occur--myopia and hyperopia can only cause important problems in the future when they are significantly large, however for the astigmatism (rather frequent in infants) and anisometropia the problems tend to be more stringent. The early evaluation of the visual status of human infants is thus of critical importance. Photorefraction is a convenient technique for this kind of subjects. Essentially a light beam is delivered into the eyes. It is refracted by the ocular media, strikes the retina, focusing or not, reflects off and is collected by a camera. The photorefraction setup we established using new technological breakthroughs on the fields of imaging devices, digital image processing and fiber optics, allows a fast noninvasive evaluation of children visual status (refractive errors, accommodation, strabismus, ...). Results of the visual screening of a group of risk' child descents of blinds or amblyopes will be presented.

[The status quo and expectation of optometry research in China].

PubMed

Qu, Jia

2015-01-01

The eye care problems related to optometry involve a wide range, including visual problems during eye disease recovery, visual quality in surgical or non-surgical refractive corrections, and the etiological investigation of functional eye diseases like myopia. This article covers the current challenges to visual health care and the academic developments and contributions of optometry in China, including fundamental researches of myopia, refractive surgery and visual quality, and functional eye disease investigations. Some of the researches have certain impacts both domestically and overseas. Furthermore, scientific evidences to solve clinical problems and the current academic focuses that we should pay attention to are provided.

Remote Measurement of the Atmospheric Isoplanatic Angle and Determination of Refractive Turbulence Profiles by Direct Inversion of the Scintillation Amplitude Covariance Function with Tikhonov Regularization.

DTIC Science & Technology

1985-12-01

shows Good’s 2 data between 500 m and 40 km. Good obtained thisCn profile by differential temperature measurement between two balloon-borne microthermal ...Cn profiles. However, they are difficult to obtain by remote measurements. In Chapters IV and V, I presented a profile measured by microthermal probes

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

NASA Astrophysics Data System (ADS)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight into the nature of inverse problems and the appropriate mode of thought, chapter 1 offers historical vignettes, most of which have played an essential role in the development of natural science. These vignettes cover the first successful application of `non-destructive testing' by Archimedes (page 4) via Newton's laws of motion up to literary tomography, and readers will be able to enjoy a wide overview of inverse problems. Therefore, as the author asks, the reader should not skip this chapter. This may not be hard to do, since the headings of the sections are quite intriguing (`Archimedes' Bath', `Another World', `Got the Time?', `Head Games', etc). The author embarks on the technical approach to inverse problems in chapter 2. He has elegantly designed each section with a guide specifying course level, objective, mathematical and scientifical background and appropriate technology (e.g. types of calculators required). The guides are designed such that teachers may be able to construct effective and attractive courses by themselves. The book is not intended to offer one rigidly determined course, but should be used flexibly and independently according to the situation. Moreover, every section closes with activities which can be chosen according to the students' interests and levels of ability. Some of these exercises do not have ready solutions, but require long-term study, so readers are not required to solve all of them. After chapter 5, which contains discrete inverse problems such as the algebraic reconstruction technique and the Backus - Gilbert method, there are answers and commentaries to the activities. Finally, scripts in MATLAB are attached, although they can also be downloaded from the author's web page (http://math.uc.edu/~groetsch/). This book is aimed at students but it will be very valuable to researchers wishing to retain a wide overview of inverse problems in the midst of busy research activities. A Japanese version was published in 2002.

Error Analysis of Indirect Broadband Monitoring of Multilayer Optical Coatings using Computer Simulations

NASA Astrophysics Data System (ADS)

Semenov, Z. V.; Labusov, V. A.

2017-11-01

Results of studying the errors of indirect monitoring by means of computer simulations are reported. The monitoring method is based on measuring spectra of reflection from additional monitoring substrates in a wide spectral range. Special software (Deposition Control Simulator) is developed, which allows one to estimate the influence of the monitoring system parameters (noise of the photodetector array, operating spectral range of the spectrometer and errors of its calibration in terms of wavelengths, drift of the radiation source intensity, and errors in the refractive index of deposited materials) on the random and systematic errors of deposited layer thickness measurements. The direct and inverse problems of multilayer coatings are solved using the OptiReOpt library. Curves of the random and systematic errors of measurements of the deposited layer thickness as functions of the layer thickness are presented for various values of the system parameters. Recommendations are given on using the indirect monitoring method for the purpose of reducing the layer thickness measurement error.

Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products.

PubMed

Pust, Nathan J; Dahlberg, Andrew R; Thomas, Michael J; Shaw, Joseph A

2011-09-12

Visible-band and near infrared polarization and radiance images measured with a ground-based full-sky polarimeter are compared against a successive orders of scattering (SOS) radiative transfer model for 2009 summer cloud-free days in Bozeman, Montana, USA. The polarimeter measures radiance and polarization in 10-nm bands centered at 450 nm, 490 nm, 530 nm, 630 nm, and 700 nm. AERONET products are used to represent aerosols in the SOS model, while MISR satellite BRF products are used for the surface reflectance. While model results generally agree well with observation, the simulated degree of polarization is typically higher than observed data. Potential sources of this difference may include cloud contamination and/or underestimation of the AERONET-retrieved aerosol real refractive index. Problems with the retrieved parameters are not unexpected given the low aerosol optical depth range (0.025 to 0.17 at 500 nm) during the study and the corresponding difficulties that these conditions pose to the AERONET inversion algorithm.

Prevalence and associations of anisometropia with spherical ametropia, cylindrical power, age, and sex in refractive surgery candidates.

PubMed

Linke, Stephan J; Richard, Gisbert; Katz, Toam

2011-09-29

To analyze the prevalence and associations of anisometropia with spherical ametropia, astigmatism, age, and sex in a refractive surgery population. Medical records of 27,070 eyes of 13,535 refractive surgery candidates were reviewed. Anisometropia, defined as the absolute difference in mean spherical equivalent powers between right and left eyes, was analyzed for subjective (A(subj)) and cycloplegic refraction (A(cycl)). Correlations between anisometropia (>1 diopter) and spherical ametropia, cylindrical power, age, and sex, were analyzed using χ² and nonparametric Kruskal-Wallis or Mann-Whitney tests and binomial logistic regression analyses. Power vector analysis was applied for further analysis of cylindrical power. Prevalence of A(subj) was 18.5% and of A(cycl) was 19.3%. In hyperopes, logistic regression analysis revealed that only spherical refractive error (odds ratio [OR], 0.72) and age (OR, 0.97) were independently associated with anisometropia. A(subj) decreased with increasing spherical ametropia and advancing age. Cylindrical power and sex did not significantly affect A(subj). In myopes all explanatory variables (spherical power OR, 0.93; cylindrical power OR, 0.75; age OR, 1.02; sex OR, 0.8) were independently associated with anisometropia. Cylindrical power was most strongly associated with anisometropia. Advancing age and increasing spherical/cylindrical power correlated positively with increasing anisometropia in myopic subjects. Female sex was more closely associated with anisometropia. This large-scale retrospective analysis confirmed an independent association between anisometropia and both spherical ametropia and age in refractive surgery candidates. Notably, an inverse relationship between these parameters in hyperopes was observed. Cylindrical power and female sex were independently associated with anisometropia in myopes.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

NASA Astrophysics Data System (ADS)

Bender, Michael; Dick, Galina; Ge, Maorong; Deng, Zhiguo; Wickert, Jens; Kahle, Hans-Gert; Raabe, Armin; Tetzlaff, Gerd

2011-05-01

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

DTIC Science & Technology

2017-03-07

please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics-based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics-based Inverse Problem to Deduce Marine...SUPPLEMENTARY NOTES 14. ABSTRACT This report describes research results related to the development and implementation of an inverse problem approach for

Autonomous satellite navigation using starlight refraction angle measurements

NASA Astrophysics Data System (ADS)

Ning, Xiaolin; Wang, Longhua; Bai, Xinbei; Fang, Jiancheng

2013-05-01

An on-board autonomous navigation capability is required to reduce the operation costs and enhance the navigation performance of future satellites. Autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth's horizon. In previous studies, the refraction apparent height has typically been used for such navigation. However, the apparent height cannot be measured directly by a star sensor and can only be calculated by the refraction angle and an atmospheric refraction model. Therefore, additional errors are introduced by the uncertainty and nonlinearity of atmospheric refraction models, which result in reduced navigation accuracy and reliability. A new navigation method based on the direct measurement of the refraction angle is proposed to solve this problem. Techniques for the determination of the refraction angle are introduced, and a measurement model for the refraction angle is established. The method is tested and validated by simulations. When the starlight refraction height ranges from 20 to 50 km, a positioning accuracy of better than 100 m can be achieved for a low-Earth-orbit (LEO) satellite using the refraction angle, while the positioning accuracy of the traditional method using the apparent height is worse than 500 m under the same conditions. Furthermore, an analysis of the factors that affect navigation accuracy, including the measurement accuracy of the refraction angle, the number of visible refracted stars per orbit and the installation azimuth of star sensor, is presented. This method is highly recommended for small satellites in particular, as no additional hardware besides two star sensors is required.

Headaches associated with refractive errors: myth or reality?

PubMed

Gil-Gouveia, R; Martins, I P

2002-04-01

Headache and refractive errors are very common conditions in the general population, and those with headache often attribute their pain to a visual problem. The International Headache Society (IHS) criteria for the classification of headache includes an entity of headache associated with refractive errors (HARE), but indicates that its importance is widely overestimated. To compare overall headache frequency and HARE frequency in healthy subjects with uncorrected or miscorrected refractive errors and a control group. We interviewed 105 individuals with uncorrected refractive errors and a control group of 71 subjects (with properly corrected or without refractive errors) regarding their headache history. We compared the occurrence of headache and its diagnosis in both groups and assessed its relation to their habits of visual effort and type of refractive errors. Headache frequency was similar in both subjects and controls. Headache associated with refractive errors was the only headache type significantly more common in subjects with refractive errors than in controls (6.7% versus 0%). It was associated with hyperopia and was unrelated to visual effort or to the severity of visual error. With adequate correction, 72.5% of the subjects with headache and refractive error reported improvement in their headaches, and 38% had complete remission of headache. Regardless of the type of headache present, headache frequency was significantly reduced in these subjects (t = 2.34, P =.02). Headache associated with refractive errors was rarely identified in individuals with refractive errors. In those with chronic headache, proper correction of refractive errors significantly improved headache complaints and did so primarily by decreasing the frequency of headache episodes.

Method for detecting a mass density image of an object

DOEpatents

Wernick, Miles N [Chicago, IL; Yang, Yongyi [Westmont, IL

2008-12-23

A method for detecting a mass density image of an object. An x-ray beam is transmitted through the object and a transmitted beam is emitted from the object. The transmitted beam is directed at an angle of incidence upon a crystal analyzer. A diffracted beam is emitted from the crystal analyzer onto a detector and digitized. A first image of the object is detected from the diffracted beam emitted from the crystal analyzer when positioned at a first angular position. A second image of the object is detected from the diffracted beam emitted from the crystal analyzer when positioned at a second angular position. A refraction image is obtained and a regularized mathematical inversion algorithm is applied to the refraction image to obtain a mass density image.

Real refractive indices and formation yields of secondary organic aerosol generated from photooxidation of limonene and α-pinene: the effect of the HC/NO(x) ratio.

PubMed

Kim, Hwajin; Barkey, Brian; Paulson, Suzanne E

2012-06-21

The refractive index is an important property affecting aerosol optical properties, which in turn help determine the aerosol direct effect and satellite retrieval results. Here, we investigate the real refractive indices (m(r)) of secondary organic aerosols (SOA) generated from the photooxidation of limonene and α-pinene with different HC/NO(x) ratios. Refractive indices were obtained from polar nephelometer data using parallel and perpendicular polarized 532 nm light combined with measured size distributions, and retrievals were performed using a genetic algorithm and Mie-Lorenz scattering theory. The absolute error associated with the m(r) retrieval is ±0.03, and reliable retrievals are possible for mass concentrations above 5-20 μg/m(3) depending on particle size. The limonene SOA data suggest the most important factor controlling the refractive index is the HC/NO(x) ratio; the refractive index is much less sensitive to the aerosol age or mass concentration. The refractive index ranges from about 1.34 to 1.56 for limonene and from 1.36 to 1.52 for α-pinene, and generally decreases as the HC/NO(x) ratio increases. Especially for limonene, the particle diameter is also inversely related to the HC/NO(x) ratio; the final size mode increases from 220 to 330 nm as the HC/NO(x) ratio decreases from 33 to 6. In an effort to explore the ability of models from the literature to explain the observed refractive indices, a recent limonene oxidation mechanism was combined with SOA partitioning and a structure-property relationship for estimating refractive indices of condensing species. The resulting refractive indices fell in a much narrower range (1.475 ± 0.02) of m(r) than observed experimentally. We hypothesize the experimentally observed high m(r) values are due to oligomerization and the low values to water uptake, small soluble molecules such as glyoxal and other factors, each of which is not included in the oxidation mechanism. Aerosol formation yields were measured over the mass concentration range from 6 to ∼150 μg/m(3), over which they increased steadily, and were higher for high HC/NO(x) ratio experiments.

The light wave flow effect in a plane-parallel layer with a quasi-zero refractive index under the action of bounded light beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gadomsky, O. N., E-mail: gadomsky@mail.ru; Shchukarev, I. A., E-mail: blacxpress@gmail.com

2016-08-15

It is shown that external optical radiation in the 450–1200 nm range can be efficiently transformed under the action of bounded light beams to a surface wave that propagates along the external and internal boundaries of a plane-parallel layer with a quasi-zero refractive index. Reflection regimes with complex and real angles of refraction in the layer are considered. The layer with a quasi-zero refractive index in this boundary problem is located on a highly reflective metal substrate; it is shown that the uniform low reflection of light is achieved in the wavelength range under study.

A method for the detection of the refractive index of irregular shape solid pigments in light absorbing liquid matrix.

PubMed

Niskanen, Ilpo; Räty, Jukka; Peiponen, Kai-Erik

2010-06-15

The immersion liquid method is powerful for the measurement of the refractive index of solid particles in a liquid matrix. However, this method applies best for cases when the liquid matrix is transparent. A problem is usually how to assess the refractive index of a pigment when it is in a colored host liquid. In this article we introduce a method, and show that by combining so-called multifunction spectrophotometer, immersion liquid method and detection of light transmission and reflection we can assess the refractive index of a pigment in a colored liquid, and also the extinction or absorption coefficient of the host liquid.

Acoustic computer tomographic pyrometry for two-dimensional measurement of gases taking into account the effect of refraction of sound wave paths

NASA Astrophysics Data System (ADS)

Lu, J.; Wakai, K.; Takahashi, S.; Shimizu, S.

2000-06-01

The algorithm which takes into account the effect of refraction of sound wave paths for acoustic computer tomography (CT) is developed. Incorporating the algorithm of refraction into ordinary CT algorithms which are based on Fourier transformation is very difficult. In this paper, the least-squares method, which is capable of considering the refraction effect, is employed to reconstruct the two-dimensional temperature distribution. The refraction effect is solved by writing a set of differential equations which is derived from Fermat's theorem and the calculus of variations. It is impossible to carry out refraction analysis and the reconstruction of temperature distribution simultaneously, so the problem is solved using the iteration method. The measurement field is assumed to take the shape of a circle and 16 speakers, also serving as the receivers, are set around it isometrically. The algorithm is checked through computer simulation with various kinds of temperature distributions. It is shown that the present method which takes into account the algorithm of the refraction effect can reconstruct temperature distributions with much greater accuracy than can methods which do not include the refraction effect.

Development of a subjective refraction simulator

NASA Astrophysics Data System (ADS)

Perches, S.; Ares, J.; Collados, M. V.

2013-11-01

We have developed simulation software by Matlab (MathworksInc.) with a graphical interface designed for non-expert users. This simulator allows you to complete the process of subjective refraction starting from the aberrometry of the patients and analyse the influence of different factors during the exam. In addition to explain the graphical interface and its working, we show two examples about a complete process of subjective refraction with the influence of high order aberrations and without them showing the retinal image obtained in each step of the refraction process. When the Jackson Cross-Cylinder technique is made with this software, it becomes clear the difficulty of chosen between two images when high order aberrations are present. Therefore, the variability of response during the refraction can be a problem when the examiner has to reach an adequate optical prescription.

Investigation on optical properties of Bi2.85La0.15TiNbO9 thin films by prism coupling technique

NASA Astrophysics Data System (ADS)

Zhang, Mingfu; Chen, Hengzhi; Yang, Bin; Cao, Wenwu

2009-12-01

Layered-perovskite ferroelectric Bi2.85La0.15TiNbO9 (LBTN) optical waveguiding thin films were grown on fused silica substrates by pulsed laser deposition (PLD). X-ray diffraction (XRD) revealed that the film is highly (00 l) textured. We observed sharp and distinct transverse electric (TE) and transverse magnetic (TM) multimodes and measured the refractive indices of LBTN thin films at 632.8 nm. The ordinary and extraordinary refractive indices were calculated to be n TE=2.358 and n TM=2.464, respectively. The film homogeneity and the film-substrate interface were analyzed using an improved version of the inverse Wentzel-Kramer-Brillouin (iWKB) method. The refractive index of the film remains constant at n 0 within the waveguiding layer. The average transmittance of the film is 70% in the wavelength range of 400-1400 nm and the optical waveguiding properties were evaluated by the optical prism coupling method. Our results showed that the LBTN films are very good electro-optical active material.

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

NASA Astrophysics Data System (ADS)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

We describe a method for the explicit determination of the segment density profile φ(z) of surface-attached polymer brushes with multiple angle of incidence null-ellipsometry. Because the refractive index contrast between the brush layer and the solvent is weak, multiple reflections are of minor influence and the ellipsometric spectrum is closely related to the Fourier transform of the refractive index profile, thereby allowing for explicit inversion of the ellipsometric data. We chose surface-attached monolayers of polymethacrylic acid (PMAA), a weak polyelectrolyte, as a model system and determined the segment density profile of this system as a function of the pH value of the surrounding medium by the Fourier method. Complementary to the Fourier analysis, fits with error functions are given as well. The brushes were prepared on the bases of high refractive index prisms with the "grafting-from" technique. In water, the brushes swell by more than a factor of 30. The swelling increases with increasing pH because of a growing fraction of dissociated acidic groups leading to a larger electrostatic repulsion.

Measurements of electron density and temperature profiles in plasma produced by Nike KrF laser for laser plasma instability research.

PubMed

Oh, Jaechul; Weaver, J L; Karasik, M; Chan, L Y

2015-08-01

A grid image refractometer (GIR) has been implemented at the Nike krypton fluoride laser facility of the Naval Research Laboratory. This instrument simultaneously measures propagation angles and transmissions of UV probe rays (λ = 263 nm, Δt = 10 ps) refracted through plasma. We report results of the first Nike-GIR measurement on a CH plasma produced by the Nike laser pulse (∼1 ns FWHM) with the intensity of 1.1 × 10(15) W/cm(2). The measured angles and transmissions were processed to construct spatial profiles of electron density (ne) and temperature (Te) in the underdense coronal region of the plasma. Using an inversion algorithm developed for the strongly refracted rays, the deployed GIR system probed electron densities up to 4 × 10(21) cm(-3) with the density scale length of 120 μm along the plasma symmetry axis. The resulting n(e) and T(e) profiles are verified to be self-consistent with the measured quantities of the refracted probe light.

Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis.

PubMed

Kwon, Young-Hoo; Casebolt, Jeffrey B

2006-01-01

One of the most serious obstacles to accurate quantification of the underwater motion of a swimmer's body is image deformation caused by refraction. Refraction occurs at the water-air interface plane (glass) owing to the density difference. Camera calibration-reconstruction algorithms commonly used in aquatic research do not have the capability to correct this refraction-induced nonlinear image deformation and produce large reconstruction errors. The aim of this paper is to provide a through review of: the nature of the refraction-induced image deformation and its behaviour in underwater object-space plane reconstruction; the intrinsic shortcomings of the Direct Linear Transformation (DLT) method in underwater motion analysis; experimental conditions that interact with refraction; and alternative algorithms and strategies that can be used to improve the calibration-reconstruction accuracy. Although it is impossible to remove the refraction error completely in conventional camera calibration-reconstruction methods, it is possible to improve the accuracy to some extent by manipulating experimental conditions or calibration frame characteristics. Alternative algorithms, such as the localized DLT and the double-plane method are also available for error reduction. The ultimate solution for the refraction problem is to develop underwater camera calibration and reconstruction algorithms that have the capability to correct refraction.

Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis.

PubMed

Kwon, Young-Hoo; Casebolt, Jeffrey B

2006-07-01

One of the most serious obstacles to accurate quantification of the underwater motion of a swimmer's body is image deformation caused by refraction. Refraction occurs at the water-air interface plane (glass) owing to the density difference. Camera calibration-reconstruction algorithms commonly used in aquatic research do not have the capability to correct this refraction-induced nonlinear image deformation and produce large reconstruction errors. The aim of this paper is to provide a thorough review of: the nature of the refraction-induced image deformation and its behaviour in underwater object-space plane reconstruction; the intrinsic shortcomings of the Direct Linear Transformation (DLT) method in underwater motion analysis; experimental conditions that interact with refraction; and alternative algorithms and strategies that can be used to improve the calibration-reconstruction accuracy. Although it is impossible to remove the refraction error completely in conventional camera calibration-reconstruction methods, it is possible to improve the accuracy to some extent by manipulating experimental conditions or calibration frame characteristics. Alternative algorithms, such as the localized DLT and the double-plane method are also available for error reduction. The ultimate solution for the refraction problem is to develop underwater camera calibration and reconstruction algorithms that have the capability to correct refraction.

Design of embedded system to determine liquid refractive index based on ultrasonic sensor using an ATMega328

NASA Astrophysics Data System (ADS)

Radiyonoa, Y.; Surantoro, S.; Pujayanto, P.; Budiharti, R.; Respati, Y. S.; Saputro, D. E.

2018-05-01

The occurrence of the broken pencil shadow into a glass of water becomes an interesting matter to be learned. The students of senior high school still find difficulty in determining liquid refractive index. To overcome this problem, it needs to develop an experimental tool to determine liquid refractive index by utilizing the newest technology. It is expected to be useful for students. This study is aimed to (1) make the design of physics learning experimental tool determinant of a liquid refractive index assisted by microcontroller based on ultrasonic sensors ATMega328 (2) explain the working principle and experimental result of liquid refractive indexing instrument assisted with ATMega328 microcontroller based ultrasonic sensor. This research used the experimental method. The result of the research shows design of physics learning experimental tool determinant of a liquid refractive index assisted by microcontroller based on ultrasonic sensors ATMega328 that has relative counting mistake of 0.36% on the measurement of aquades liquid refractive index, relative mistake of 0.18% on the 5% NaCl measurement, 0.24% on 5% glucose, and relative mistake of 0.50% on the measurement of 5 % fructose liquid refractive index. It has been created a proper device to be used in determining liquid refractive index.

An Interactive Program on Digitizing Historical Seismograms

NASA Astrophysics Data System (ADS)

Xu, Y.; Xu, T.

2013-12-01

Retrieving information from historical seismograms is of great importance since they are considered the unique sources that provide quantitative information of historical earthquakes. Modern techniques of seismology require digital forms of seismograms that are essentially a sequence of time-amplitude pairs. However, the historical seismograms, after scanned into computers, are two dimensional arrays. Each element of the arrays contains the grayscale value or RGB value of the corresponding pixel. The problem of digitizing historical seismograms, referred to as converting historical seismograms to digital seismograms, can be formulated as an inverse problem that generating sequences of time-amplitude pairs from a two dimension arrays. This problem has infinite solutions. The algorithm for automatic digitization of historical seismogram presented considers several features of seismograms, including continuity, smoothness of the seismic traces as the prior information, and assumes that the amplitude is a single-valued function of time. An interactive program based on the algorithm is also presented. The program is developed using Matlab GUI and has both automatic and manual modality digitization. Users can easily switch between them, and try different combinations to get the optimal results. Several examples are given to illustrate the results of digitizing seismograms using the program, including a photographic record and a wide-angle reflection/refraction seismogram. Digitized result of the program (redrawn using Golden Software Surfer for high resolution image). (a) shows the result of automatic digitization, and (b) is the result after manual correction.

Processing grounded-wire TEM signal in time-frequency-pseudo-seismic domain: A new paradigm

NASA Astrophysics Data System (ADS)

Khan, M. Y.; Xue, G. Q.; Chen, W.; Huasen, Z.

2017-12-01

Grounded-wire TEM has received great attention in mineral, hydrocarbon and hydrogeological investigations for the last several years. Conventionally, TEM soundings have been presented as apparent resistivity curves as function of time. With development of sophisticated computational algorithms, it became possible to extract more realistic geoelectric information by applying inversion programs to 1-D & 3-D problems. Here, we analyze grounded-wire TEM data by carrying out analysis in time, frequency and pseudo-seismic domain supported by borehole information. At first, H, K, A & Q type geoelectric models are processed using a proven inversion program (1-D Occam inversion). Second, time-to-frequency transformation is conducted from TEM ρa(t) curves to magneto telluric MT ρa(f) curves for the same models based on all-time apparent resistivity curves. Third, 1-D Bostick's algorithm was applied to the transformed resistivity. Finally, EM diffusion field is transformed into propagating wave field obeying the standard wave equation using wavelet transformation technique and constructed pseudo-seismic section. The transformed seismic-like wave indicates that some reflection and refraction phenomena appear when the EM wave field interacts with geoelectric interface at different depth intervals due to contrast in resistivity. The resolution of the transformed TEM data is significantly improved in comparison to apparent resistivity plots. A case study illustrates the successful hydrogeophysical application of proposed approach in recovering water-filled mined-out area in a coal field located in Ye county, Henan province, China. The results support the introduction of pseudo-seismic imaging technology in short-offset version of TEM which can also be an useful aid if integrated with seismic reflection technique to explore possibilities for high resolution EM imaging in future.

A Forward Glimpse into Inverse Problems through a Geology Example

ERIC Educational Resources Information Center

Winkel, Brian J.

2012-01-01

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

EDITORIAL: Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications

NASA Astrophysics Data System (ADS)

Dorn, O.; Lesselier, D.

2010-07-01

Inverse problems in electromagnetics have a long history and have stimulated exciting research over many decades. New applications and solution methods are still emerging, providing a rich source of challenging topics for further investigation. The purpose of this special issue is to combine descriptions of several such developments that are expected to have the potential to fundamentally fuel new research, and to provide an overview of novel methods and applications for electromagnetic inverse problems. There have been several special sections published in Inverse Problems over the last decade addressing fully, or partly, electromagnetic inverse problems. Examples are: Electromagnetic imaging and inversion of the Earth's subsurface (Guest Editors: D Lesselier and T Habashy) October 2000 Testing inversion algorithms against experimental data (Guest Editors: K Belkebir and M Saillard) December 2001 Electromagnetic and ultrasonic nondestructive evaluation (Guest Editors: D Lesselier and J Bowler) December 2002 Electromagnetic characterization of buried obstacles (Guest Editors: D Lesselier and W C Chew) December 2004 Testing inversion algorithms against experimental data: inhomogeneous targets (Guest Editors: K Belkebir and M Saillard) December 2005 Testing inversion algorithms against experimental data: 3D targets (Guest Editors: A Litman and L Crocco) February 2009 In a certain sense, the current issue can be understood as a continuation of this series of special sections on electromagnetic inverse problems. On the other hand, its focus is intended to be more general than previous ones. Instead of trying to cover a well-defined, somewhat specialized research topic as completely as possible, this issue aims to show the broad range of techniques and applications that are relevant to electromagnetic imaging nowadays, which may serve as a source of inspiration and encouragement for all those entering this active and rapidly developing research area. Also, the construction of this special issue is likely to have been different from preceding ones. In addition to the invitations sent to specific research groups involved in electromagnetic inverse problems, the Guest Editors also solicited recommendations, from a large number of experts, of potential authors who were thereupon encouraged to contribute. Moreover, an open call for contributions was published on the homepage of Inverse Problems in order to attract as wide a scope of contributions as possible. This special issue's attempt at generality might also define its limitations: by no means could this collection of papers be exhaustive or complete, and as Guest Editors we are well aware that many exciting topics and potential contributions will be missing. This, however, also determines its very special flavor: besides addressing electromagnetic inverse problems in a broad sense, there were only a few restrictions on the contributions considered for this section. One requirement was plausible evidence of either novelty or the emergent nature of the technique or application described, judged mainly by the referees, and in some cases by the Guest Editors. The technical quality of the contributions always remained a stringent condition of acceptance, final adjudication (possibly questionable either way, not always positive) being made in most cases once a thorough revision process had been carried out. Therefore, we hope that the final result presented here constitutes an interesting collection of novel ideas and applications, properly refereed and edited, which will find its own readership and which can stimulate significant new research in the topics represented. Overall, as Guest Editors, we feel quite fortunate to have obtained such a strong response to the call for this issue and to have a really wide-ranging collection of high-quality contributions which, indeed, can be read from the first to the last page with sustained enthusiasm. A large number of applications and techniques is represented, overall via 16 contributions with 45 authors in total. This shows, in our opinion, that electromagnetic imaging and inversion remain amongst the most challenging and active research areas in applied inverse problems today. Below, we give a brief overview of the contributions included in this issue, ordered alphabetically by the surname of the leading author. 1. The complexity of handling potential randomness of the source in an inverse scattering problem is not minor, and the literature is far from being replete in this configuration. The contribution by G Bao, S N Chow, P Li and H Zhou, `Numerical solution of an inverse medium scattering problem with a stochastic source', exemplifies how to hybridize Wiener chaos expansion with a recursive linearization method in order to solve the stochastic problem as a set of decoupled deterministic ones. 2. In cases where the forward problem is expensive to evaluate, database methods might become a reliable method of choice, while enabling one to deliver more information on the inversion itself. The contribution by S Bilicz, M Lambert and Sz Gyimóthy, `Kriging-based generation of optimal databases as forward and inverse surrogate models', describes such a technique which uses kriging for constructing an efficient database with the goal of achieving an equidistant distribution of points in the measurement space. 3. Anisotropy remains a considerable challenge in electromagnetic imaging, which is tackled in the contribution by F Cakoni, D Colton, P Monk and J Sun, `The inverse electromagnetic scattering problem for anisotropic media', via the fact that transmission eigenvalues can be retrieved from a far-field scattering pattern, yielding, in particular, lower and upper bounds of the index of refraction of the unknown (dielectric anisotropic) scatterer. 4. So-called subspace optimization methods (SOM) have attracted a lot of interest recently in many fields. The contribution by X Chen, `Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium', illustrates how to address a realistic situation in which the medium containing the unknown obstacles is not homogeneous, via blending a properly developed SOM with a finite-element approach to the required Green's functions. 5. H Egger, M Hanke, C Schneider, J Schöberl and S Zaglmayr, in their contribution `Adjoint-based sampling methods for electromagnetic scattering', show how to efficiently develop sampling methods without explicit knowledge of the dyadic Green's function once an adjoint problem has been solved at much lower computational cost. This is demonstrated by examples in demanding propagative and diffusive situations. 6. Passive sensor arrays can be employed to image reflectors from ambient noise via proper migration of cross-correlation matrices into their embedding medium. This is investigated, and resolution, in particular, is considered in detail, as a function of the characteristics of the sensor array and those of the noise, in the contribution by J Garnier and G Papanicolaou, `Resolution analysis for imaging with noise'. 7. A direct reconstruction technique based on the conformal mapping theorem is proposed and investigated in depth in the contribution by H Haddar and R Kress, `Conformal mapping and impedance tomography'. This paper expands on previous work, with inclusions in homogeneous media, convergence results, and numerical illustrations. 8. The contribution by T Hohage and S Langer, `Acceleration techniques for regularized Newton methods applied to electromagnetic inverse medium scattering problems', focuses on a spectral preconditioner intended to accelerate regularized Newton methods as employed for the retrieval of a local inhomogeneity in a three-dimensional vector electromagnetic case, while also illustrating the implementation of a Lepskiĭ-type stopping rule outsmarting a traditional discrepancy principle. 9. Geophysical applications are a rich source of practically relevant inverse problems. The contribution by M Li, A Abubakar and T Habashy, `Application of a two-and-a-half dimensional model-based algorithm to crosswell electromagnetic data inversion', deals with a model-based inversion technique for electromagnetic imaging which addresses novel challenges such as multi-physics inversion, and incorporation of prior knowledge, such as in hydrocarbon recovery. 10. Non-stationary inverse problems, considered as a special class of Bayesian inverse problems, are framed via an orthogonal decomposition representation in the contribution by A Lipponen, A Seppänen and J P Kaipio, `Reduced order estimation of nonstationary flows with electrical impedance tomography'. The goal is to simultaneously estimate, from electrical impedance tomography data, certain characteristics of the Navier--Stokes fluid flow model together with time-varying concentration distribution. 11. Non-iterative imaging methods of thin, penetrable cracks, based on asymptotic expansion of the scattering amplitude and analysis of the multi-static response matrix, are discussed in the contribution by W-K Park, `On the imaging of thin dielectric inclusions buried within a half-space', completing, for a shallow burial case at multiple frequencies, the direct imaging of small obstacles (here, along their transverse dimension), MUSIC and non-MUSIC type indicator functions being used for that purpose. 12. The contribution by R Potthast, `A study on orthogonality sampling' envisages quick localization and shaping of obstacles from (portions of) far-field scattering patterns collected at one or more time-harmonic frequencies, via the simple calculation (and summation) of scalar products between those patterns and a test function. This is numerically exemplified for Neumann/Dirichlet boundary conditions and homogeneous/heterogeneous embedding media. 13. The contribution by J D Shea, P Kosmas, B D Van Veen and S C Hagness, `Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms', aims at microwave medical imaging, namely the early detection of breast cancer. The use of contrast enhancing agents is discussed in detail and a number of reconstructions in three-dimensional geometry of realistic numerical breast phantoms are presented. 14. The contribution by D A Subbarayappa and V Isakov, `Increasing stability of the continuation for the Maxwell system', discusses enhanced log-type stability results for continuation of solutions of the time-harmonic Maxwell system, adding a fresh chapter to the interesting story of the study of the Cauchy problem for PDE. 15. In their contribution, `Recent developments of a monotonicity imaging method for magnetic induction tomography in the small skin-depth regime', A Tamburrino, S Ventre and G Rubinacci extend the recently developed monotonicity method toward the application of magnetic induction tomography in order to map surface-breaking defects affecting a damaged metal component. 16. The contribution by F Viani, P Rocca, M Benedetti, G Oliveri and A Massa, `Electromagnetic passive localization and tracking of moving targets in a WSN-infrastructured environment', contributes to what could still be seen as a niche problem, yet both useful in terms of applications, e.g., security, and challenging in terms of methodologies and experiments, in particular, in view of the complexity of environments in which this endeavor is to take place and the variability of the wireless sensor networks employed. To conclude, we would like to thank the able and tireless work of Kate Watt and Zoë Crossman, as past and present Publishers of the Journal, on what was definitely a long and exciting journey (sometimes a little discouraging when reports were not arriving, or authors were late, or Guest Editors overwhelmed) that started from a thorough discussion at the `Manchester workshop on electromagnetic inverse problems' held mid-June 2009, between Kate Watt and the Guest Editors. We gratefully acknowledge the fact that W W Symes gave us his full backing to carry out this special issue and that A K Louis completed it successfully. Last, but not least, the staff of Inverse Problems should be thanked, since they work together to make it a premier journal.

Retrieval of spheroid particle size distribution from spectral extinction data in the independent mode using PCA approach

NASA Astrophysics Data System (ADS)

Tang, Hong; Lin, Jian-Zhong

2013-01-01

An improved anomalous diffraction approximation (ADA) method is presented for calculating the extinction efficiency of spheroids firstly. In this approach, the extinction efficiency of spheroid particles can be calculated with good accuracy and high efficiency in a wider size range by combining the Latimer method and the ADA theory, and this method can present a more general expression for calculating the extinction efficiency of spheroid particles with various complex refractive indices and aspect ratios. Meanwhile, the visible spectral extinction with varied spheroid particle size distributions and complex refractive indices is surveyed. Furthermore, a selection principle about the spectral extinction data is developed based on PCA (principle component analysis) of first derivative spectral extinction. By calculating the contribution rate of first derivative spectral extinction, the spectral extinction with more significant features can be selected as the input data, and those with less features is removed from the inversion data. In addition, we propose an improved Tikhonov iteration method to retrieve the spheroid particle size distributions in the independent mode. Simulation experiments indicate that the spheroid particle size distributions obtained with the proposed method coincide fairly well with the given distributions, and this inversion method provides a simple, reliable and efficient method to retrieve the spheroid particle size distributions from the spectral extinction data.

Reconstruction of the temperature field for inverse ultrasound hyperthermia calculations at a muscle/bone interface.

PubMed

Liauh, Chihng-Tsung; Shih, Tzu-Ching; Huang, Huang-Wen; Lin, Win-Li

2004-02-01

An inverse algorithm with Tikhonov regularization of order zero has been used to estimate the intensity ratios of the reflected longitudinal wave to the incident longitudinal wave and that of the refracted shear wave to the total transmitted wave into bone in calculating the absorbed power field and then to reconstruct the temperature distribution in muscle and bone regions based on a limited number of temperature measurements during simulated ultrasound hyperthermia. The effects of the number of temperature sensors are investigated, as is the amount of noise superimposed on the temperature measurements, and the effects of the optimal sensor location on the performance of the inverse algorithm. Results show that noisy input data degrades the performance of this inverse algorithm, especially when the number of temperature sensors is small. Results are also presented demonstrating an improvement in the accuracy of the temperature estimates by employing an optimal value of the regularization parameter. Based on the analysis of singular-value decomposition, the optimal sensor position in a case utilizing only one temperature sensor can be determined to make the inverse algorithm converge to the true solution.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory.

PubMed

Kolgotin, Alexei; Müller, Detlef; Chemyakin, Eduard; Romanov, Anton

2016-12-01

Multiwavelength Raman/high spectral resolution lidars that measure backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm can be used for the retrieval of particle microphysical parameters, such as effective and mean radius, number, surface-area and volume concentrations, and complex refractive index, from inversion algorithms. In this study, we carry out a correlation analysis in order to investigate the degree of dependence that may exist between the optical data taken with lidar and the underlying microphysical parameters. We also investigate if the correlation properties identified in our study can be used as a priori or a posteriori constraints for our inversion scheme so that the inversion results can be improved. We made the simplifying assumption of error-free optical data in order to find out what correlations exist in the best case situation. Clearly, for practical applications, erroneous data need to be considered too. On the basis of simulations with synthetic optical data, we find the following results, which hold true for arbitrary particle size distributions, i.e., regardless of the modality or the shape of the size distribution function: surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99. We also find a correlation coefficient above 0.99 for the extinction coefficient versus (1) the ratio of the volume concentration to effective radius and (2) the product of the number concentration times the sum of the squares of the mean radius and standard deviation of the investigated particle size distributions. Besides that, we find that for particles of any mode fraction of the particle size distribution, the complex refractive index is uniquely defined by extinction- and backscatter-related Ångström exponents, lidar ratios at two wavelengths, and an effective radius.

Applications of hybrid genetic algorithms in seismic tomography

NASA Astrophysics Data System (ADS)

Soupios, Pantelis; Akca, Irfan; Mpogiatzis, Petros; Basokur, Ahmet T.; Papazachos, Constantinos

2011-11-01

Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopting an iterative procedure which typically employs partial derivatives in order to optimize the starting (initial) model by minimizing a misfit (penalty) function. Unfortunately, especially for highly non-linear cases, the final model strongly depends on the initial model, hence it is prone to solution-entrapment in local minima of the misfit function, while the derivative calculation is often computationally inefficient and creates instabilities when numerical approximations are used. An alternative is to employ global techniques which do not rely on partial derivatives, are independent of the misfit form and are computationally robust. Such methods employ pseudo-randomly generated models (sampling an appropriately selected section of the model space) which are assessed in terms of their data-fit. A typical example is the class of methods known as genetic algorithms (GA), which achieves the aforementioned approximation through model representation and manipulations, and has attracted the attention of the earth sciences community during the last decade, with several applications already presented for several geophysical problems. In this paper, we examine the efficiency of the combination of the typical regularized least-squares and genetic methods for a typical seismic tomography problem. The proposed approach combines a local (LOM) and a global (GOM) optimization method, in an attempt to overcome the limitations of each individual approach, such as local minima and slow convergence, respectively. The potential of both optimization methods is tested and compared, both independently and jointly, using the several test models and synthetic refraction travel-time date sets that employ the same experimental geometry, wavelength and geometrical characteristics of the model anomalies. Moreover, real data from a crosswell tomographic project for the subsurface mapping of an ancient wall foundation are used for testing the efficiency of the proposed algorithm. The results show that the combined use of both methods can exploit the benefits of each approach, leading to improved final models and producing realistic velocity models, without significantly increasing the required computation time.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Improved planetary boundary layer retrievals using a combination of direct and reflected bending angles from radio occultations

NASA Astrophysics Data System (ADS)

Wang, K. N.; Ao, C. O.; de la Torre Juarez, M.

2017-12-01

As a remote sensing technique, Global Positioning System (GPS) radio occultation (RO) is a suitable method to observe lower troposphere due to its high vertical resolution and cloud-penetrating capability. However, super-refraction (SR), or ducting, caused by large refractivity gradients usually associated with the top of the planetary boundary layer, can violate the uniqueness condition necessary for the traditional inverse Abel transform. Consequently, the retrieved refractivity, which is the minimum profile among an infinite number of potential solutions corresponding to the same bending angle profile, will be negatively biased under ducting layers. Previous research has shown that optimal estimation techniques that combine low altitude RO retrievals and the collocated precipitable water (PW) estimates can effectively reduce the negative RO bias and enhance the data quality under the ducting layer (Wang et al, 2017). Here we propose an improvement that uses the reflected RO bending angle observation information as a source for refractivity constraints. The RO signal reflected from the Earth surface profile can be reconstructed by solely using GPS-RO data without requiring external information such as PW. The radio holographic (RH) method is adapted here to calculate the reflected RO bending angle, and the forward model simulation is implemented to validate this preliminary concept. Our results suggest that this new approach can distinguish between different refractivity profiles when ducting occurs and theoretically this should reduce the negative bias. In addition, It also improves the RO observation in lower troposphere by capturing the sharpness and height of the critical layer separating the free troposphere from the boundary layer.

A novel navigation method used in a ballistic missile

NASA Astrophysics Data System (ADS)

Qian, Hua-ming; Sun, Long; Cai, Jia-nan; Peng, Yu

2013-10-01

The traditional strapdown inertial/celestial integrated navigation method used in a ballistic missile cannot accurately estimate the accelerometer bias. It might cause a divergence of navigation errors. To solve this problem, a new navigation method named strapdown inertial/starlight refractive celestial integrated navigation is proposed. To verify the feasibility of the proposed method, a simulated program of a ballistic missile is presented. The simulation results indicated that, when multiple refraction stars are used, the proposed method can accurately estimate the accelerometer bias, and suppress the divergence of navigation errors completely. Specifically, in order to apply this method to a ballistic missile, a novel measurement equation based on stellar refraction was developed. Furthermore a method to calculate the number of refraction stars observed by the stellar sensor was given. Finally, the relationship between the number of refraction stars used and the navigation accuracy is analysed.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

From unseen to seen: tackling the global burden of uncorrected refractive errors.

PubMed

Durr, Nicholas J; Dave, Shivang R; Lage, Eduardo; Marcos, Susana; Thorn, Frank; Lim, Daryl

2014-07-11

Worldwide, more than one billion people suffer from poor vision because they do not have the eyeglasses they need. Their uncorrected refractive errors are a major cause of global disability and drastically reduce productivity, educational opportunities, and overall quality of life. The problem persists most prevalently in low-resource settings, even though prescription eyeglasses serve as a simple, effective, and largely affordable solution. In this review, we discuss barriers to obtaining, and approaches for providing, refractive eye care. We also highlight emerging technologies that are being developed to increase the accessibility of eye care. Finally, we describe opportunities that exist for engineers to develop new solutions to positively impact the diagnosis and treatment of correctable refractive errors in low-resource settings.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

Multiband infrared inversion for low-concentration methane monitoring in a confined dust-polluted atmosphere.

PubMed

Wang, Wenzheng; Wang, Yanming; Song, Wujun; Li, Xueqin

2017-03-20

A multiband infrared diagnostic (MBID) method for methane emission monitoring in limited underground environments was presented considering the strong optical background of gas/solid attenuation. Based on spatial distribution of aerosols and complex refractive index of dust particles, forward calculations were carried out with/without methane to obtain the spectral transmittance through the participating atmosphere in a mine roadway. Considering the concurrent attenuation and absorption behavior of dust and gases, four infrared wavebands were selected to retrieve the methane concentration combined with a stochastic particle swarm optimization (SPSO) algorithm. Inversion results prove that the presented MBID method is robust and effective in identifying methane at concentrations of 0.1% or even lower with inversed relative error within 10%. Further analyses illustrate that the four selected wavebands are indispensable, and the MBID method is still valid with transmission signal disturbance in a conventional dust-polluted atmosphere under mechanized mining condition. However, the effective detection distance should be limited within 50 m to ensure inversed relative error less than 5% at 1% methane concentration.

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

NASA Astrophysics Data System (ADS)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in atmospheric sciences and oceanography. Last but not least is our gratitude. As editors we would like to express our sincere thanks to all the plenary and invited speakers, the members of the International Scientific Committee and the Advisory Board for the success of the conference, which has given rise to this present volume of selected papers. We would also like to thank Mr Wang Yanbo, Miss Wan Xiqiong and the graduate students at Fudan University for their effective work to make this conference a success. The conference was financially supported by the NFS of China, the Mathematical Center of Ministry of Education of China, E-Institutes of Shanghai Municipal Education Commission (No E03004) and Fudan University, Grant 15340027 from the Japan Society for the Promotion of Science, and Grant 15654015 from the Ministry of Education, Cultures, Sports and Technology.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

The Visual Effects of Intraocular Colored Filters

PubMed Central

Hammond, Billy R.

2012-01-01

Modern life is associated with a myriad of visual problems, most notably refractive conditions such as myopia. Human ingenuity has addressed such problems using strategies such as spectacle lenses or surgical correction. There are other visual problems, however, that have been present throughout our evolutionary history and are not as easily solved by simply correcting refractive error. These problems include issues like glare disability and discomfort arising from intraocular scatter, photostress with the associated transient loss in vision that arises from short intense light exposures, or the ability to see objects in the distance through a veil of atmospheric haze. One likely biological solution to these more long-standing problems has been the use of colored intraocular filters. Many species, especially diurnal, incorporate chromophores from numerous sources (e.g., often plant pigments called carotenoids) into ocular tissues to improve visual performance outdoors. This review summarizes information on the utility of such filters focusing on chromatic filtering by humans. PMID:24278692

Plate refractive camera model and its applications

NASA Astrophysics Data System (ADS)

Huang, Longxiang; Zhao, Xu; Cai, Shen; Liu, Yuncai

2017-03-01

In real applications, a pinhole camera capturing objects through a planar parallel transparent plate is frequently employed. Due to the refractive effects of the plate, such an imaging system does not comply with the conventional pinhole camera model. Although the system is ubiquitous, it has not been thoroughly studied. This paper aims at presenting a simple virtual camera model, called a plate refractive camera model, which has a form similar to a pinhole camera model and can efficiently model refractions through a plate. The key idea is to employ a pixel-wise viewpoint concept to encode the refraction effects into a pixel-wise pinhole camera model. The proposed camera model realizes an efficient forward projection computation method and has some advantages in applications. First, the model can help to compute the caustic surface to represent the changes of the camera viewpoints. Second, the model has strengths in analyzing and rectifying the image caustic distortion caused by the plate refraction effects. Third, the model can be used to calibrate the camera's intrinsic parameters without removing the plate. Last but not least, the model contributes to putting forward the plate refractive triangulation methods in order to solve the plate refractive triangulation problem easily in multiviews. We verify our theory in both synthetic and real experiments.

Titania inverse opals for infrared optical applications

NASA Astrophysics Data System (ADS)

Lanata, M.; Cherchi, M.; Zappettini, A.; Pietralunga, S. M.; Martinelli, M.

2001-06-01

Photonic crystals have gathered great importance in recent years. In particular macroporous materials (inverse opals) show interesting properties as photonic crystals. Ordered macroporous titanium dioxide (TiO 2) is made using polystyrene spheres as a template. Titania is chosen for its high refractive index (>2.5). Following an already known technique [E.G. Judith, J. Wijnhoven, W.L. Vos, Science 281 (1998) 802; B.T. Holland, C.F. Blanford, A. Stein, Science 281 (1998) 538; B.T. Holland, C.F. Blanford, T. Do, A. Stein, Chem. Mater. 11 (1999) 795] large-scale order in macroporous TiO 2 is obtained both using the 778 and the 3190 nm beads as documented by optical microscope and SEM images. These structures would lead to applications in the mid-infrared range.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

ADRPM-VII applied to the long-range acoustic detection problem

NASA Technical Reports Server (NTRS)

Shalis, Edward; Koenig, Gerald

1990-01-01

An acoustic detection range prediction model (ADRPM-VII) has been written for IBM PC/AT machines running on the MS-DOS operating system. The software allows the user to predict detection distances of ground combat vehicles and their associated targets when they are involved in quasi-military settings. The program can also calculate individual attenuation losses due to spherical spreading, atmospheric absorption, ground reflection and atmospheric refraction due to temperature and wind gradients while varying parameters effecting the source-receiver problem. The purpose here is to examine the strengths and limitations of ADRPM-VII by modeling the losses due to atmospheric refraction and ground absorption, commonly known as excess attenuation, when applied to the long range detection problem for distances greater than 3 kilometers.

Optical and Gravimetric Partitioning of Coastal Ocean Suspended Particulate Inorganic Matter (PIM)

NASA Astrophysics Data System (ADS)

Stavn, R. H.; Zhang, X.; Falster, A. U.; Gray, D. J.; Rick, J. J.; Gould, R. W., Jr.

2016-02-01

Recent work on the composition of suspended particulates of estuarine and coastal waters increases our capabilities to investigate the biogeochemal processes occurring in these waters. The biogeochemical properties associated with the particulates involve primarily sorption/desorption of dissolved matter onto the particle surfaces, which vary with the types of particulates. Therefore, the breakdown into chemical components of suspended matter will greatly expand the biogeochemistry of the coastal ocean region. The gravimetric techniques for these studies are here expanded and refined. In addition, new optical inversions greatly expand our capabilities to study spatial extent of the components of suspended particulate matter. The partitioning of a gravimetric PIM determination into clay minerals and amorphous silica is aided by electron microprobe analysis. The amorphous silica is further partitioned into contributions by detrital material and by the tests of living diatoms based on an empirical formula relating the chlorophyll content of cultured living diatoms in log phase growth to their frustules determined after gravimetric analysis of the ashed diatom residue. The optical inversion of composition of suspended particulates is based on the entire volume scattering function (VSF) measured in the field with a Multispectral Volume Scattering Meter and a LISST 100 meter. The VSF is partitioned into an optimal combination of contributions by particle subpopulations, each of which is uniquely represented by a refractive index and a log-normal size distribution. These subpopulations are aggregated to represent the two components of PIM using the corresponding refractive indices and sizes which also yield a particle size distribution for the two components. The gravimetric results of partitioning PIM into clay minerals and amorphous silica confirm the optical inversions from the VSF.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

[Problems and challenges in the development of corneal refractive surgery].

PubMed

Wang, Y; Li, J

2018-01-11

Corneal refractive surgery, as one of the common visual correction methods, has been increasingly accepted in China. There are a large number of people in China who undergo the corneal refractive surgery due to the high incidence of myopia in the country. It is essential that the safest and most effective surgery should be used to correct refractive errors in the cases involved with relatively normal eyes and corneas. In recent years, corneal refractive surgery has been rapidly developing with new technologies and techniques emerging all the time, such as SMILE (small incision lenticule extraction) surgery, which has been extensively applied in China since five years ago when it was approved by FDA. However, little known are these new technologies and techniques, and the clinical and basic researches need further investigations by various approaches including histopathology and molecular biology, combined with mathematics, computer science, physics, chemistry and corneal biomechanics. To achieve minimal tissue damage and optimal clinical outcomes on visual quality by corneal refractive surgery requires the multidisciplinary partnerships of medical practitioners and researchers. (Chin J Ophthalmol, 2018, 54: 3-6) .

Children's Understanding of the Inverse Relation between Multiplication and Division

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

NASA Astrophysics Data System (ADS)

Zaikin, Oleg; Petrov, Pavel; Posypkin, Mikhail; Bulavintsev, Vadim; Kurochkin, Ilya

2017-12-01

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Jianjun; Shen, Dongyi; Feng, Yaming

Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here, we demonstrate theoretically and experimentally a scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin Beta barium borate slice serves as a negative refraction layer bendingmore » the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.« less

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

Indications for and outcomes of tertiary referrals in refractive surgery.

PubMed

Patryn, Eliza K; Vrijman, Violette; Nieuwendaal, Carla P; van der Meulen, Ivanka J E; Mourits, Maarten P; Lapid-Gortzak, Ruth

2014-01-01

To review the spectrum of disease, symptomatology, and management offered to patients referred for a second opinion after refractive surgery. A prospective cohort study was done on all patients referred from October 1, 2006, to September 30, 2011, to a tertiary eye clinic after refractive surgery of any kind (ie, corneal laser surgery, conductive keratoplasty, radial keratotomy, phakic implants, refractive lens exchanges, or any combination thereof). Data analysis was performed on all demographic and clinical aspects of this cohort, including the initial complaint, type of referral, number of complaints, procedure previously performed, diagnosis at our center, type of advice given, and rate and type of surgical intervention. One hundred thirty-one eyes (69 patients) were included. Corneal refractive surgery was performed in 82% (108 eyes), and 11% (14 eyes) were seen after phakic intraocular lens (PIOL) implantation and 7% (9 eyes) after refractive lens exchange. The most common diagnoses were tear film dysfunction (30 eyes, 23%), residual refractive error (25 eyes, 19%), and cataract (20 eyes, 15%). Most patients (42 patients, 61%) were treated conservatively. In 27 patients (39%), 36 eyes (28%) were managed surgically. Severe visual loss was seen in 1 eye. No major problems were found in most second opinions after refractive surgery referral. Dry eyes, small residual refractive error, or higher-order aberrations were the most common complaints. Surgical intervention was needed in 36 eyes (28%), almost half of which were cataract extractions. Severe visual loss was seen in 1 eye with a PIOL. There was no incidence of severe visual loss in keratorefractive and refractive lens exchange procedures. Copyright 2014, SLACK Incorporated.

Interpretation of a seismic refraction profile across the Roosevelt Hot Springs, Utah and vicinity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gertson, R.C.; Smith, R.B.

1979-03-01

In April 1977, a seismic refraction profile was recorded across the Milford Valley, the Roosevelt Hot Springs KGRA, and the northern Mineral Mountains in southwestern Utah. Seven shot points were used to provide multiple subsurface seismic refraction coverage along the 30 km east-west profile line. Since an inspection of power spectrums revealed large components of 60 Hz noise on some traces, computer routines were used to low-pass filter all seismograms. Amplitude information was utilized by normalizing all traces that recorded the same blast. Subsurface structural modeling was conducted by means of first arrival P-wave delay-time analysis and ray tracing. Herglotz-Wiechertmore » travel-time inversion was used for the velocity-depth distribution in the Mineral Mountains. The interpretation of the P-wave travel-times suggests that the Milford Valley fill consists of two units with a total thickness of at least 1.8 km. In the vicinity of the Roosevelt KGRA, a thin low velocity alluvial layer covers a basement igneous complex with a velocity of 5.2 km/s. Granite velocities between 3.3 km/s and 4.0 km/s were calculated from the travel-times in the Mineral Mountains.« less

Refractive index measurement based on confocal method

NASA Astrophysics Data System (ADS)

An, Zhe; Xu, XiPing; Yang, JinHua; Qiao, Yang; Liu, Yang

2017-10-01

The development of transparent materials is closed to optoelectronic technology. It plays an increasingly important role in various fields. It is not only widely used in optical lens, optical element, optical fiber grating, optoelectronics, but also widely used in the building material, pharmaceutical industry with vessel, aircraft windshield and daily wear glasses.Regard of solving the problem of refractive index measurement in optical transparent materials. We proposed that using the polychromatic confocal method to measuring the refractive index of transparent materials. In this article, we describes the principle of polychromatic confocal method for measuring the refractive index of glass,and sketched the optical system and its optimization. Then we establish the measurement model of the refractive index, and set up the experimental system. In this way, the refractive index of the glass has been calibrated for refractive index experiment. Due to the error in the experimental process, we manipulated the experiment data to compensate the refractive index measurement formula. The experiment taking the quartz glass for instance. The measurement accuracy of the refractive index of the glass is +/-1.8×10-5. This method is more practical and accurate, especially suitable for non-contact measurement occasions, which environmental requirements is not high. Environmental requirements are not high, the ordinary glass production line up to the ambient temperature can be fully adapted. There is no need for the color of the measured object that you can measure the white and a variety of colored glass.

Waveform Tomography Applied to Long Streamer MCS Data from the Scotian Slope

NASA Astrophysics Data System (ADS)

Delescluse, Matthias; Louden, Keith; Nedimovic, Mladen

2010-05-01

Detailed velocity models of the earth subsurface can be obtained through waveform tomography, a method that relies on using information from the full wavefield. Such models can be of significantly higher resolution than the corresponding models formed by more generic traveltime tomography methods, which are constrained only by the wave arrival times. However, to derive the detailed subsurface velocity, the waveform method is sensitive to modelling low-frequency refracted waves that have long paths through target structures. Thus field examples primarily have focused on the analysis of long-offset wide-angle datasets collected using autonomous receivers, in which refractions arrive at earlier times than reflections and there is a significant separation between the two wave arrivals. MCS datasets with shorter offsets typically lack these important features, which result in methodological problems (e.g. Hicks and Pratt, 2001), even though they benefit from a high density of raypaths and uniformity of receiver and shot properties. Modern marine seismic acquisition using long streamers now offers both the ability to record refracted waves at far offsets arriving ahead of the seafloor reflection, and the ability to do this at great density using uniform sources. In this study, we use 2D MCS data acquired with a 9-km-long streamer by ION GX-Technology over the Nova Scotia Slope in water depths of ~1600 m. We show that the refracted arrivals, although restricted to receivers between offsets of 7.5 and 9 km, provide sufficient information to successfully invert for a high-resolution velocity field. Using a frequency domain acoustic code (Pratt, 1999) over frequencies from 8 Hz to 24 Hz on two crossing profiles (45 and 20 km long), we detail how the limited refracted waves can constrain the velocity field above the depth of the turning waves (~1.5 km below seafloor). Several important features are resolved by the waveform velocity model that are not present in the initial travel-time model. In particular, a high velocity layer due to gas hydrates is imaged along the entire profile even where a characteristic BSR is not visible. The velocity increase in the gas hydrate layer is very small (< 100 m/s). In addition, a strong velocity increase of ~ 300 m/s exists below a deeper, gently dipping reflector along which discontinuous low-velocity zones, probably related to gas, are present. Velocity models are consistent at the crossing point between the two profiles. The depth limitation of the detailed MCS waveform tomography imaging could be extended by even longer streamers (e.g. 15 km) or by joint inversion with OBS data.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Critical Analysis of Different Methods to Retrieve Atmosphere Humidity Profiles from GNSS Radio Occultation Observations

NASA Astrophysics Data System (ADS)

Vespe, Francesco; Benedetto, Catia

2013-04-01

The huge amount of GPS Radio Occultation (RO) observations currently available thanks to space mission like COSMIC, CHAMP, GRACE, TERRASAR-X etc., have greatly encouraged the research of new algorithms suitable to extract humidity, temperature and pressure profiles of the atmosphere in a more and more precise way. For what concern the humidity profiles in these last years two different approaches have been widely proved and applied: the "Simple" and the 1DVAR methods. The Simple methods essentially determine dry refractivity profiles from temperature analysis profiles and hydrostatic equation. Then the dry refractivity is subtracted from RO refractivity to achieve the wet component. Finally from the wet refractivity is achieved humidity. The 1DVAR approach combines RO observations with profiles given by the background models with both the terms weighted with the inverse of covariance matrix. The advantage of "Simple" methods is that they are not affected by bias due to the background models. We have proposed in the past the BPV approach to retrieve humidity. Our approach can be classified among the "Simple" methods. The BPV approach works with dry atmospheric CIRA-Q models which depend on latitude, DoY and height. The dry CIRA-Q refractivity profile is selected estimating the involved parameters in a non linear least square fashion achieved by fitting RO observed bending angles through the stratosphere. The BPV as well as all the other "Simple" methods, has as drawback the unphysical occurrence of negative "humidity". Thus we propose to apply a modulated weighting of the fit residuals just to minimize the effects of this inconvenient. After a proper tuning of the approach, we plan to present the results of the validation.

Problem of the elimination of the refractional effects in Doppler positioning.

NASA Astrophysics Data System (ADS)

Gougoutoudis, I.

The influence of the tropospheric refraction on the Doppler positioning is discussed. It is found that the differences of coordinates resulting from the use of standard atmospheric parameters instead of real ones could amount to 0.60 m for single point positioning and 0.20 m for multilocation. The necessity of registration of the real meteorologic parameters at the Doppler station is confirmed.

Waveform inversion of acoustic waves for explosion yield estimation

DOE PAGES

Kim, K.; Rodgers, A. J.

2016-07-08

We present a new waveform inversion technique to estimate the energy of near-surface explosions using atmospheric acoustic waves. Conventional methods often employ air blast models based on a homogeneous atmosphere, where the acoustic wave propagation effects (e.g., refraction and diffraction) are not taken into account, and therefore, their accuracy decreases with increasing source-receiver distance. In this study, three-dimensional acoustic simulations are performed with a finite difference method in realistic atmospheres and topography, and the modeled acoustic Green's functions are incorporated into the waveform inversion for the acoustic source time functions. The strength of the acoustic source is related to explosionmore » yield based on a standard air blast model. The technique was applied to local explosions (<10 km) and provided reasonable yield estimates (<~30% error) in the presence of realistic topography and atmospheric structure. In conclusion, the presented method can be extended to explosions recorded at far distance provided proper meteorological specifications.« less

Waveform inversion of acoustic waves for explosion yield estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, K.; Rodgers, A. J.

We present a new waveform inversion technique to estimate the energy of near-surface explosions using atmospheric acoustic waves. Conventional methods often employ air blast models based on a homogeneous atmosphere, where the acoustic wave propagation effects (e.g., refraction and diffraction) are not taken into account, and therefore, their accuracy decreases with increasing source-receiver distance. In this study, three-dimensional acoustic simulations are performed with a finite difference method in realistic atmospheres and topography, and the modeled acoustic Green's functions are incorporated into the waveform inversion for the acoustic source time functions. The strength of the acoustic source is related to explosionmore » yield based on a standard air blast model. The technique was applied to local explosions (<10 km) and provided reasonable yield estimates (<~30% error) in the presence of realistic topography and atmospheric structure. In conclusion, the presented method can be extended to explosions recorded at far distance provided proper meteorological specifications.« less

Inverse opal photonic crystal of chalcogenide glass by solution processing.

PubMed

Kohoutek, Tomas; Orava, Jiri; Sawada, Tsutomu; Fudouzi, Hiroshi

2011-01-15

Chalcogenide opal and inverse opal photonic crystals were successfully fabricated by low-cost and low-temperature solution-based process, which is well developed in polymer films processing. Highly ordered silica colloidal crystal films were successfully infilled with nano-colloidal solution of the high refractive index As(30)S(70) chalcogenide glass by using spin-coating method. The silica/As-S opal film was etched in HF acid to dissolve the silica opal template and fabricate the inverse opal As-S photonic crystal. Both, the infilled silica/As-S opal film (Δn ~ 0.84 near λ=770 nm) and the inverse opal As-S photonic structure (Δn ~ 1.26 near λ=660 nm) had significantly enhanced reflectivity values and wider photonic bandgaps in comparison with the silica opal film template (Δn ~ 0.434 near λ=600 nm). The key aspects of opal film preparation by spin-coating of nano-colloidal chalcogenide glass solution are discussed. The solution fabricated "inorganic polymer" opal and the inverse opal structures exceed photonic properties of silica or any organic polymer opal film. The fabricated photonic structures are proposed for designing novel flexible colloidal crystal laser devices, photonic waveguides and chemical sensors. Copyright © 2010 Elsevier Inc. All rights reserved.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters.

PubMed

Manjappa, Rakesh; Makki S, Sharath; Kumar, Rajesh; Kanhirodan, Rajan

2015-02-01

Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at the inhomogeneities. Jacob's ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.

Human resources for refraction services in Central Nepal.

PubMed

Kandel, Himal; Murthy, G V S; Bascaran, Covadonga

2015-07-01

Uncorrected refractive error is a public health problem globally and in Nepal. Planning of refraction services is hampered by a paucity of data. This study was conducted to determine availability and distribution of human resources for refraction, their efficiency, the type and extent of their training; the current service provision of refraction services and the unmet need in human resources for refraction in Central Nepal. This was a descriptive cross-sectional study. All refraction facilities in the Central Region were identified through an Internet search and interviews of key informants from the professional bodies and parent organisations of primary eye centres. A stratified simple random sampling technique was used to select 50 per cent of refraction facilities. The selected facilities were visited for primary data collection. Face-to-face interviews were conducted with the managers and the refractionists available in the facilities using a semi-structured questionnaire. Data was collected in 29 centres. All the managers (n=29; response rate 100 per cent) and 50 refractionists (Response rate 65.8 per cent) were interviewed. Optometrists and ophthalmic assistants were the main providers of refraction services (n=70, 92.11 per cent). They were unevenly distributed across the region, highly concentrated around urban areas. The median number of refractions per refractionist per year was 3,600 (IQR: 2,400 - 6,000). Interviewed refractionists stated that clients' knowledge, attitude and practice related factors such as lack of awareness of the need for refraction services and/or availability of existing services were the major barriers to the output of refraction services. The total number of refractions carried out in the Central Region per year was 653,176. An additional 170 refractionists would be needed to meet the unmet need of 1,323,234 refractions. The study findings demand a major effort to develop appropriately trained personnel when planning refraction services in the Central Region and in Nepal as a whole. The equitable distribution of the refractionists, their community-outreach services and awareness raising activities should be emphasised. © 2015 The Authors. Clinical and Experimental Optometry © 2015 Optometry Australia.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manjappa, Rakesh; Makki S, Sharath; Kanhirodan, Rajan, E-mail: rajan@physics.iisc.ernet.in

2015-02-15

Purpose: Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. Methods: The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at themore » inhomogeneities. Jacob’s ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. Results: The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. Conclusions: The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.« less

Computational methods for inverse problems in geophysics: inversion of travel time observations

USGS Publications Warehouse

Pereyra, V.; Keller, H.B.; Lee, W.H.K.

1980-01-01

General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.

Diode Laser Pumped Alkali Vapor Lasers with Exciplex-Assisted Absorption

DTIC Science & Technology

2013-05-14

transfer agent that established the population inversion. The excitation source used in these initial studies was a pulsed optical parametric oscillator ...parametric oscillator . The lasers operated at 703.2 (Ne*), 912.5 (Ar*), 893.1 (Kr*) and 980.2 run (Xe*). Peak powers as high as 27kW/cm2 were observed...Larissa Glebova and Leonid B. Glebov. Ultra-low absorption and laser-induced heating of volume Bragg combiners recorded in photo-thermo- refractive

Single-molecule spectromicroscopy: a route towards sub-wavelength refractometry.

PubMed

Anikushina, T A; Gladush, M G; Gorshelev, A A; Naumov, A V

2015-01-01

We suggest a novel approach for spatially resolved probing of local fluctuations of the refractive index n in solids by means of single-molecule (SM) spectroscopy. It is based on the dependence T1(n) of the effective radiative lifetime T1 of dye centres in solids on n due to the local-field effects. Detection of SM zero-phonon lines at low temperatures gives the values of the SM natural spectral linewidth (which is inversely proportional to T1) and makes it possible to reveal the distribution of the local n values in solids. Here we demonstrate this possibility on the example of amorphous polyethylene and polycrystalline naphthalene doped with terrylene. In particular, we show that the obtained distributions of lifetime limited spectral linewidths of terrylene molecules embedded into these matrices are due to the spatial fluctuations of the refractive index local values.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

NASA Astrophysics Data System (ADS)

Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

2017-07-01

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Wavelength-dependent excess permittivity as indicator of kerosene in diesel oil.

PubMed

Kanyathare, Boniphace; Peiponen, Kai-Erik

2018-04-20

Adulteration of diesel oil by kerosene is a serious problem because of air pollution resulting from car exhaust gases. The objective of this study was to develop a relatively simple optical measurement and data analysis method to screen low-adulterated diesel oils. For this purpose, we introduce the utilization of refractive index measurement with a refractometer, scanning of visible-near-infrared transmittance, transmittance data inversion using the singly subtractive Kramers-Kronig relation, and exploitation of so-called wavelength-dependent relative excess permittivity. It is shown for three different diesel oil grades, adulterated with kerosene, that the excess permittivity is a powerful measure for screening fake diesel oils. The excess relative permittivity of such binary mixtures also reveals hidden spectral fingerprints that are neither visible in dispersion data alone nor in spectral transmittance measurements alone. We believe that the excess permittivity data are useful in the case of screening adulteration of diesel oil by kerosene and can further be explored for practical sensing solutions, e.g., in quality inspection of diesel oils in refineries.

On the isotropic Raman spectrum of Ar2 and how to benchmark ab initio calculations of small atomic clusters: Paradox lost.

PubMed

Chrysos, Michael; Dixneuf, Sophie; Rachet, Florent

2015-07-14

This is the long-overdue answer to the discrepancies observed between theory and experiment in Ar2 regarding both the isotropic Raman spectrum and the second refractivity virial coefficient, BR [Gaye et al., Phys. Rev. A 55, 3484 (1997)]. At the origin of this progress is the advent (posterior to 1997) of advanced computational methods for weakly interconnected neutral species at close separations. Here, we report agreement between the previously taken Raman measurements and quantum lineshapes now computed with the employ of large-scale CCSD or smartly constructed MP2 induced-polarizability data. By using these measurements as a benchmark tool, we assess the degree of performance of various other ab initio computed data for the mean polarizability α, and we show that an excellent agreement with the most recently measured value of BR is reached. We propose an even more refined model for α, which is solution of the inverse-scattering problem and whose lineshape matches exactly the measured spectrum over the entire frequency-shift range probed.

Inverse kinematic problem for a random gradient medium in geometric optics approximation

NASA Astrophysics Data System (ADS)

Petersen, N. V.

1990-03-01

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.

Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

NASA Technical Reports Server (NTRS)

Fymat, A. L.; Smith, C. B.

1979-01-01

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Atmospheric particulate analysis using angular light scattering

NASA Technical Reports Server (NTRS)

Hansen, M. Z.

1980-01-01

Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

Profile inversion in presence of ray bending

NASA Technical Reports Server (NTRS)

Wallio, H. A.; Grossi, M. D.

1972-01-01

Inversion of radio occultation data for planetary atmospheres and ionospheres has been performed using the seismological Herglotz-Wiechert method, as adapted by Phinney and Anderson to the radio-occultation case. Profile reconstruction performed in computer simulated experiments with this approach have been compared with the ones obtained with the straight-ray Abel transform. For a thin atmosphere and ionosphere, like the ones encountered on Mars, microwave occultation data can be inverted accurately with both methods. For a dense ionosphere like the sun's corona, ray bending of microwaves is severe, and recovered refractivity by the Herglotz-Wiechert method provides significant improvement over the straight-ray Abel transform: the error reduces from more than 60% to less than 20% at a height of 60,000 km above the base of the corona.

Retrievals of aerosol optical and microphysical properties from Imaging Polar Nephelometer scattering measurements

NASA Astrophysics Data System (ADS)

Reed Espinosa, W.; Remer, Lorraine A.; Dubovik, Oleg; Ziemba, Luke; Beyersdorf, Andreas; Orozco, Daniel; Schuster, Gregory; Lapyonok, Tatyana; Fuertes, David; Vanderlei Martins, J.

2017-03-01

A method for the retrieval of aerosol optical and microphysical properties from in situ light-scattering measurements is presented and the results are compared with existing measurement techniques. The Generalized Retrieval of Aerosol and Surface Properties (GRASP) is applied to airborne and laboratory measurements made by a novel polar nephelometer. This instrument, the Polarized Imaging Nephelometer (PI-Neph), is capable of making high-accuracy field measurements of phase function and degree of linear polarization, at three visible wavelengths, over a wide angular range of 3 to 177°. The resulting retrieval produces particle size distributions (PSDs) that agree, within experimental error, with measurements made by commercial optical particle counters (OPCs). Additionally, the retrieved real part of the refractive index is generally found to be within the predicted error of 0.02 from the expected values for three species of humidified salt particles, with a refractive index that is well established. The airborne measurements used in this work were made aboard the NASA DC-8 aircraft during the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) field campaign, and the inversion of this data represents the first aerosol retrievals of airborne polar nephelometer data. The results provide confidence in the real refractive index product, as well as in the retrieval's ability to accurately determine PSD, without assumptions about refractive index that are required by the majority of OPCs.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

[Multifocal intraocular lenses. A review].

PubMed

Auffarth, G U; Dick, H B

2001-02-01

Modern cataract surgery has developed tremendously during the past 10-15 years. Improved surgical techniques, as well as improved implant materials and designs, have enlarged patient profiles and indications for cataract surgery. This also created much higher expectations from the patients' site. The loss of accommodation is loss of quality of life for presbyopic and especially young pseudophakic patients. Therefore cataract surgery with multifocal IOL implantation is not only of academic interest, but reflects demands and expectations of our patients. Multifocal IOLs have been implanted since 1986, starting with 2-3 zone refractive and diffractive designs. Due to surgical techniques of that time MIOL decentration and surgically induced astigmatism were possible complications. In addition reduced contrast sensitivity and increased glare were common problems of MIOL because of their optical principles. New developments in this field in recent years such as the multizonal, progressive refractive MIOL in combination with improved surgical techniques have overcome those initial problems. Therefore, modern multifocal IOLs can be considered not only for correction of aphakia but also for refractive purposes.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Refractive errors in 3-6 year-old Chinese children: a very low prevalence of myopia?

PubMed

Lan, Weizhong; Zhao, Feng; Lin, Lixia; Li, Zhen; Zeng, Junwen; Yang, Zhikuan; Morgan, Ian G

2013-01-01

To examine the prevalence of refractive errors in children aged 3-6 years in China. Children were recruited for a trial of a home-based amblyopia screening kit in Guangzhou preschools, during which cycloplegic refractions were measured in both eyes of 2480 children. Cycloplegic refraction (from 3 to 4 drops of 1% cyclopentolate to ensure abolition of the light reflex) was measured by both autorefraction and retinoscopy. Refractive errors were defined as followed: myopia (at least -0.50 D in the worse eye), hyperopia (at least +2.00 D in the worse eye) and astigmatism (at least 1.50 D in the worse eye). Different definitions, as specified in the text, were also used to facilitate comparison with other studies. The mean spherical equivalent refractive error was at least +1.22 D for all ages and both genders. The prevalence of myopia for any definition at any age was at most 2.5%, and lower in most cases. In contrast, the prevalence of hyperopia was generally over 20%, and declined slightly with age. The prevalence of astigmatism was between 6% and 11%. There was very little change in refractive error with age over this age range. Previous reports of less hyperopic mean spherical equivalent refractive error, and more myopia and less hyperopia in children of this age may be due to problems with achieving adequate cycloplegia in children with dark irises. Using up to 4 drops of 1% cyclopentolate may be necessary to accurately measure refractive error in paediatric studies of such children. Our results suggest that children from all ethnic groups may follow a similar pattern of early refractive development, with little myopia and a hyperopic mean spherical equivalent over +1.00 D up to the age of 5-6 years in most conditions.

An assessment of some theoretical models used for the calculation of the refractive index of InXGa1-xAs

NASA Astrophysics Data System (ADS)

Engelbrecht, J. A. A.

2018-04-01

Theoretical models used for the determination of the refractive index of InXGa1-XAs are reviewed and compared. Attention is drawn to some problems experienced with some of the models. Models also extended to the mid-infrared region of the electromagnetic spectrum. Theoretical results in the mid-infrared region are then compared to previously published experimental results.

Optical systems in ergophthalmology

NASA Astrophysics Data System (ADS)

Kovalenko, Valentina; Besedovskaya, Valentina; Paloob, Tamara

1994-02-01

The important part of ergophthalmology is the problem of diagnosing and treatment of refraction errors, accommodation and visual disorders by means of the special optical systems. The using of our diagnostical approach helps to choose the right treatment strategy. Our therapeutical approach permits to normalize the muscle tonus and working capacity of eye accommodation apparatus and gives the possibility to obtain the stable positive results in treatment of the refraction amblyopia as well.

A progress report on the ARRA-funded geotechnical site characterization project

NASA Astrophysics Data System (ADS)

Martin, A. J.; Yong, A.; Stokoe, K.; Di Matteo, A.; Diehl, J.; Jack, S.

2011-12-01

For the past 18 months, the 2009 American Recovery and Reinvestment Act (ARRA) has funded geotechnical site characterizations at 189 seismographic station sites in California and the central U.S. This ongoing effort applies methods involving surface-wave techniques, which include the horizontal-to-vertical spectral ratio (HVSR) technique and one or more of the following: spectral analysis of surface wave (SASW), active and passive multi-channel analysis of surface wave (MASW) and passive array microtremor techniques. From this multi-method approach, shear-wave velocity profiles (VS) and the time-averaged shear-wave velocity of the upper 30 meters (VS30) are estimated for each site. To accommodate the variability in local conditions (e.g., rural and urban soil locales, as well as weathered and competent rock sites), conventional field procedures are often modified ad-hoc to fit the unanticipated complexity at each location. For the majority of sites (>80%), fundamental-mode Rayleigh wave dispersion-based techniques are deployed and where complex geology is encountered, multiple test locations are made. Due to the presence of high velocity layers, about five percent of the locations require multi-mode inversion of Rayleigh wave (MASW-based) data or 3-D array-based inversion of SASW dispersion data, in combination with shallow P-wave seismic refraction and/or HVSR results. Where a strong impedance contrast (i.e. soil over rock) exists at shallow depth (about 10% of sites), dominant higher modes limit the use of Rayleigh wave dispersion techniques. Here, use of the Love wave dispersion technique, along with seismic refraction and/or HVSR data, is required to model the presence of shallow bedrock. At a small percentage of the sites, surface wave techniques are found not suitable for stand-alone deployment and site characterization is limited to the use of the seismic refraction technique. A USGS Open File Report-describing the surface geology, VS profile and the calculated VS30 for each site-will be prepared after the completion of the project in November 2011.

An investigation of matched index of refraction technique and its application in optical measurements of fluid flow

NASA Astrophysics Data System (ADS)

Amini, Noushin; Hassan, Yassin A.

2012-12-01

Optical distortions caused by non-uniformities of the refractive index within the measurement volume is a major impediment for all laser diagnostic imaging techniques applied in experimental fluid dynamic studies. Matching the refractive indices of the working fluid and the test section walls and interfaces provides an effective solution to this problem. The experimental set-ups designed to be used along with laser imaging techniques are typically constructed of transparent solid materials. In this investigation, different types of aqueous salt solutions and various organic fluids are studied for refractive index matching with acrylic and fused quartz, which are commonly used in construction of the test sections. One aqueous CaCl2·2H2O solution (63 % by weight) and two organic fluids, Dibutyl Phthalate and P-Cymene, are suggested for refractive index matching with fused quartz and acrylic, respectively. Moreover, the temperature dependence of the refractive indices of these fluids is investigated, and the Thermooptic Constant is calculated for each fluid. Finally, the fluid viscosity for different shear rates is measured as a function of temperature and is applied to characterize the physical behavior of the proposed fluids.

On the controlled isotropic shrinkage induced fine-tuning of photo-luminescence in terbium ions embedded silica inverse opal films

NASA Astrophysics Data System (ADS)

Shrivastava, Vishnu Prasad; Kumar, Jitendra; Sivakumar, Sri

2017-12-01

Tb3+ embedded silica inverse opal structures with different photonic stop bands have been fabricated by annealing the SiO2-polystyrene spheres (diameter 390 nm) opal template at 320-650 oC. The PSB tuning realized in the wavelength range 498 - 600 nm is shown to depend on annealing temperature and impending isotropic shrinkage of silica matrix. The impact of wide PSB shift on four Tb3+ ion emission bands (blue, green, yellow, and red at 486, 545, 580, and 620 nm, respectively) corresponding to 5D4→7Fj (j = 6,5,4,3) transitions have been investigated. The effect amounts to significant suppression of emission bands at 586, 545 and 486 nm in inverse opals, obtained by annealing opal template at 350, 400, and 650 oC, respectively. Further, luminescence lifetime of Tb3+ ion 5D4 state increases with shrinkage induced in inverse opal progressively and get enhanced up to 2.3 times vis-à-vis reference silica. The changes in refractive index caused by thermal annealing of opal template is found to be responsible for the observed improvement in 5D4 state lifetime.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Crustal high-velocity anomaly at the East European Craton margin in SE Poland (TESZ) modelled by 3-D seismic tomography of refracted and reflected arrivals

NASA Astrophysics Data System (ADS)

Środa, Piotr; Dec, Monika

2016-04-01

The area of Trans-European Suture Zone in SE Poland represents a contact of major tectonic units of different consolidation age - from the Precambrian East European Craton, through Palaeozoic West European Platform to Cenozoic Carpathian orogen. The region was built by several phases of crustal accretion, which resulted in a complex collage of tectonic blocks. In 2000, this region was studied by several seismic wide-angle profiles of CELEBRATION 2000 experiment, providing a dense coverage of seismic data in SE Poland and allowing for detailed investigations of the crustal structure and properties in this area. Beneath the marginal part of the EEC, the 2-D modelling of in-line data form several CELEBRATION profiles revealed a prominent high P-wave velocity anomaly in the upper crust, with Vp of 6.7-7.1 km/s, starting at 10-16 km depth (e.g., Środa et al., 2006). Anomalously high velocities are observed in the area located approximately beneath Lublin trough, to the NE of Teisseyre-Tornquist Zone. Based on 3-D tomography of first arrivals of in- and off-line CELEBRATION 2000 recordings (Malinowski et al., 2008), elevated velocities are also reported in the same area and seem to continue to the SW, off the craton margin. Gravimetric modelling also revealed anomalously high density in the same region at similar depths. High seismic velocities and densities are interpreted as indicative for a pronounced mafic intrusion, possibly related to extensional processes at the EEC margin. Previous 3-D models of the high-velocity intrusion were based on first arrivals (crustal refractions) only. In this study, also off-line reflections (not modelled up to now) are used, in order to enlarge the data set and to better constrain the geometry and properties of the velocity anomaly. A code for 3-D joint tomographic inversion of refracted and reflected arrivals, with model parametrization allowing for velocity discontinuities was used (Rawlinson, 2007). With this approach, besides the refractions from the anomalous zone, also the off-line reflections from the top of the intrusion were used for inversion. Presented results provide new information about the depth and horizontal extent of the high-velocity intrusion. The model is also compared with other seismic studies of similar velocity anomalies observed at continental margins.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Evidence for Thin Oceanic Crust on the Extinct Aegir Ridge, Norwegian Basin, N.E. Atlantic Derived from Satellite Gravity Inversion

NASA Astrophysics Data System (ADS)

Greenhalgh, E. E.; Kusznir, N. J.

2006-12-01

Satellite gravity inversion incorporating a lithosphere thermal gravity correction has been used to map crustal thickness and lithosphere thinning factor for the N.E. Atlantic. The inversion of gravity data to determine crustal thickness incorporates a lithosphere thermal gravity anomaly correction for both oceanic and continental margin lithosphere. Predicted crustal thicknesses in the Norwegian Basin are between 7 and 4 km on the extinct Aegir oceanic ridge which ceased sea-floor spreading in the Oligocene. Crustal thickness estimates do not include a correction for sediment thickness and are upper bounds. Crustal thicknesses determined by gravity inversion for the Aegir Ridge are consistent with recent estimates derived using refraction seismology by Breivik et al. (2006). Failure to incorporate a lithosphere thermal gravity anomaly correction produces an over-estimate of crustal thickness. Oceanic crustal thicknesses within the Norwegian Basin are predicted by the gravity inversion to increase to 9-10 km eastwards towards the Norwegian (Moere) and westwards towards the Jan Mayen micro-continent, consistent with volcanic margin continental breakup at the end of the Palaeocene. The observation (from gravity inversion and seismic refraction studies) of thin oceanic crust produced by the Aegir ocean ridge in the Oligocene has implications for the temporal evolution of asthenosphere temperature under the N.E. Atlantic during the Tertiary. Thin Oligocene oceanic crust may imply cool (normal) asthenosphere temperatures during the Oligocene in contrast to elevated asthenosphere temperatures in the Palaeocene and Miocene-Recent as indicated by volcanic margin formation and the formation of Iceland respectively. Gravity inversion also predicts a region of thin oceanic crust to the west of the northern part of the Jan Mayen micro-continent and to the east of the thicker oceanic crust currently being formed at the Kolbeinsey Ridge. Thicker crust (c.f. ocean basins) is predicted for the Jan Mayen micro- continent south of Jan Mayen Island, with crust of the order of 20 km thickness extending southwards to connect with both the Faroes-Iceland Ridge and N.E. Iceland. Predicted crustal thicknesses under the Faroes- Iceland Ridge are approximately 25 km. The lithosphere thermal model used to predict the lithosphere thermal gravity anomaly correction may be conditioned using magnetic isochron data to provide the age of oceanic lithosphere. The resulting crustal thickness determination and the location of ocean-continent transition (OCT) are however sensitive to errors in the magnetic isochron data. An alternative method of inverting satellite gravity to give crustal thickness, incorporating a lithosphere thermal correction, has been used which does not use magnetic isochron data and provides an independent prediction of crustal thickness and OCT location. The crustal thickness estimates and OCT locations detailed above are robust to these sensitivity tests.

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein. PMID:23043260

First Calderón Prize

NASA Astrophysics Data System (ADS)

Rundell, William; Somersalo, Erkki

2008-07-01

The Inverse Problems International Association (IPIA) awarded the first Calderón Prize to Matti Lassas for his outstanding contributions to the field of inverse problems, especially in geometric inverse problems. The Calderón Prize is given to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined. The first Calderón Prize Committee consisted of Professors Adrian Nachman, Lassi Päivärinta, William Rundell (chair), and Michael Vogelius. William Rundell For the Calderón Prize Committee Prize ceremony The ceremony awarding the Calderón Prize. Matti Lassas is on the left. He and William Rundell are on the right. Photos by P Stefanov. Brief Biography of Matti Lassas Matti Lassas was born in 1969 in Helsinki, Finland, and studied at the University of Helsinki. He finished his Master's studies in 1992 in three years and earned his PhD in 1996. His PhD thesis, written under the supervision of Professor Erkki Somersalo was entitled `Non-selfadjoint inverse spectral problems and their applications to random bodies'. Already in his thesis, Matti demonstrated a remarkable command of different fields of mathematics, bringing together the spectral theory of operators, geometry of Riemannian surfaces, Maxwell's equations and stochastic analysis. He has continued to develop all of these branches in the framework of inverse problems, the most remarkable results perhaps being in the field of differential geometry and inverse problems. Matti has always been a very generous researcher, sharing his ideas with his numerous collaborators. He has authored over sixty scientific articles, among which a monograph on inverse boundary spectral problems with Alexander Kachalov and Yaroslav Kurylev and over forty articles in peer reviewed journals of the highest standards. To get an idea of the wide range of Matti's interests, it is enough to say that he also has three US patents on medical imaging applications. Matti is currently professor of mathematics at Helsinki University of Technology, where he has created his own line of research with young talented researchers around him. He is a central person in the Centre of Excellence in Inverse Problems Research of the Academy of Finland. Previously, Matti Lassas has won several awards in his home country, including the prestigious Vaisala price of the Finnish Academy of Science and Letters in 2004. He is a highly esteemed colleague, teacher and friend, and the Great Diving Beetle of the Finnish Inverse Problems Society (http://venda.uku.fi/research/FIPS/), an honorary title for a person who has no fear of the deep. Erkki Somersalo

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Global magnitude of visual impairment caused by uncorrected refractive errors in 2004

PubMed Central

Pascolini, Donatella; Mariotti, Silvio P; Pokharel, Gopal P

2008-01-01

Abstract Estimates of the prevalence of visual impairment caused by uncorrected refractive errors in 2004 have been determined at regional and global levels for people aged 5 years and over from recent published and unpublished surveys. The estimates were based on the prevalence of visual acuity of less than 6/18 in the better eye with the currently available refractive correction that could be improved to equal to or better than 6/18 by refraction or pinhole. A total of 153 million people (range of uncertainty: 123 million to 184 million) are estimated to be visually impaired from uncorrected refractive errors, of whom eight million are blind. This cause of visual impairment has been overlooked in previous estimates that were based on best-corrected vision. Combined with the 161 million people visually impaired estimated in 2002 according to best-corrected vision, 314 million people are visually impaired from all causes: uncorrected refractive errors become the main cause of low vision and the second cause of blindness. Uncorrected refractive errors can hamper performance at school, reduce employability and productivity, and generally impair quality of life. Yet the correction of refractive errors with appropriate spectacles is among the most cost-effective interventions in eye health care. The results presented in this paper help to unearth a formerly hidden problem of public health dimensions and promote policy development and implementation, programmatic decision-making and corrective interventions, as well as stimulate research. PMID:18235892

Strange Horizons: Teaching Usual and Unusual Atmospheric Effects using APOD

NASA Astrophysics Data System (ADS)

Wilson, Teresa

2015-01-01

Unusual Sun and moonsets are not only photogenic -- they are educational. Images appearing on the Astronomy Picture of the Day (APOD) that demonstrate dramatic examples of the green flash, the Moon illusion, Fata Morgana, and the Etruscan vase effect are discussed in terms of how they demonstrate atmospheric refraction, chromatic aberration, and temperature inversions. A lesson plan is given for undergraduate classrooms as well as estimates of how each effect might alter the perceived time of a common sunset.

Nature and Role of Subducting Sediments on the Megathrust and Forearc Evolution in the 2004 Great Sumatra Earthquake Rupture Zone: Results from Full Waveform Inversion of Long Offset Seismic Data

NASA Astrophysics Data System (ADS)

Singh, S. C.; Qin, Y.

2015-12-01

On active accretionary margins, the nature of incoming sediments defines the locking mechanism on the megathrust, and the development and evolution of the accretionary wedge. Drilling is the most direct method to characterise the nature of these sediments, but the drilling is very expensive, and provide information at only a few locations. In north Sumatra, an IODP drilling is programmed to take place in July-August 2016. We have performed seismic full waveform inversion of 12 km long offset seismic reflection data acquired by WesternGeco in 2006 over a 35 km zone near the subduction front in the 2004 earthquake rupture zone area that provide detailed quantitative information on the characteristics of the incoming sediments. We first downward continue the surface streamer data to the seafloor, which removes the effect of deep water (~5 km) and brings out the refraction arrivals as the first arrivals. We carry out travel time tomography, and then performed full waveform inversion of seismic refraction data followed by the full waveform inversion of reflection data providing detailed (10-20 m) velocity structure. The sediments in this area are 3-5 km thick where the P-wave velocity increases from 1.6 km/s near the seafloor to more than 4.5 km/s above the oceanic crust. The high velocity of sediments above the basement suggests that the sediments are highly compacted, strengthened the coupling near the subduction front, which might have been responsible for 2004 earthquake rupture propagation up to the subduction front, enhancing the tsunami. We also find several thin velocity layers within the sediments, which might be due to high pore-pressure fluid or free gas. These layers might be responsible for the formation of pseudo-decollement within the forearc sediments that acts as a conveyer belt between highly compacted subducting lower sediments and accreted sediments above. The presence of well intact sediments on the accretionary prism supports this interpretation. Our results provide first hand information about the sediments properties, which will be ground toothed by drilling.

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

NASA Astrophysics Data System (ADS)

Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro

2007-06-01

These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this flourishing time, it is necessary to carefully analyse the current status of inverse problems for further development. Thus we have opened with the panel discussion entitled `Future of Inverse Problems' with panelists: Professors J Cheng, H W Engl, V Isakov, R Kress, J-K Seo, G Uhlmann and the commentator: Elaine Longden-Chapman from IOP Publishing. The aims of the panel discussion were to examine the current research status from various viewpoints, to discuss how we can overcome any difficulties and how we can promote young researchers and open new possibilities for inverse problems such as industrial linkages. As one output, the panel discussion has triggered the organization of the Inverse Problems International Association (IPIA) which has led to its first international congress in the summer of 2007. Another remarkable outcome of the conference is, of course, the present volume: this is the very high quality online proceedings volume of Journal of Physics: Conference Series. Readers can see in these proceedings very well written tutorial lecture notes, and very high quality original research and review papers all of which show what was achieved by the time the conference was held. The electronic publication of the proceedings is a new way of publicizing the achievement of the conference. It has the advantage of wide circulation and cost reduction. We believe this is a most efficient method for our needs and purposes. We would like to take this opportunity to acknowledge all the people who helped to organize the conference. Guest Editors Jin Cheng, Fudan University, Shanghai, China Yuusuke Iso, Kyoto University, Kyoto, Japan Gen Nakamura, Hokkaido University, Sapporo, Japan Masahiro Yamamoto, University of Tokyo, Tokyo, Japan

Information Content and Sensitivity of the 3β+2α Lidar Measurement System for Microphysical Retrievals

NASA Astrophysics Data System (ADS)

Burton, S. P.; Liu, X.; Chemyakin, E.; Hostetler, C. A.; Stamnes, S.; Moore, R.; Sawamura, P.; Ferrare, R. A.; Knobelspiesse, K. D.

2015-12-01

There is considerable interest in retrieving aerosol effective radius, number concentration and refractive index from lidar measurements of extinction and backscatter at several wavelengths. The 3 backscatter + 2 extinction (3β+2α) combination is particularly important since the planned NASA Aerosol-Clouds-Ecosystem (ACE) mission recommends this combination of measurements. The 2nd-generation NASA Langley airborne High Spectral Resolution Lidar (HSRL-2) has been making 3β+2α measurements since 2012. Here we develop a deeper understanding of the information content and sensitivities of the 3β+2α system in terms of aerosol microphysical parameters of interest. We determine best case results using a retrieval-free methodology. We calculate information content and uncertainty metrics from Optimal Estimation techniques using only a simplified forward model look-up table, with no explicit inversion. Simplifications include spherical particles, mono-modal log-normal size distributions, and wavelength-independent refractive indices. Since we only use the forward model with no retrieval, our results are applicable as a best case for all existing retrievals. Retrieval-dependent errors due to mismatch between the assumptions and true atmospheric aerosols are not included. The sensitivity metrics allow for identifying (1) information content of the measurements versus a priori information; (2) best-case error bars on the retrieved parameters; and (3) potential sources of cross-talk or "compensating" errors wherein different retrieval parameters are not independently captured by the measurements. These results suggest that even in the best case, this retrieval system is underdetermined. Recommendations are given for addressing cross-talk between effective radius and number concentration. A potential solution to the under-determination problem is a combined active (lidar) and passive (polarimeter) retrieval, which is the subject of a new funded NASA project by our team.

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

Suppression of Air Refractive Index Variations in High-Resolution Interferometry

PubMed Central

Lazar, Josef; Číp, Ondřej; Čížek, Martin; Hrabina, Jan; Buchta, Zdeněk

2011-01-01

The influence of the refractive index of air has proven to be a major problem on the road to improvement of the uncertainty in interferometric displacement measurements. We propose an approach with two counter-measuring interferometers acting as a combination of tracking refractometer and a displacement interferometer referencing the wavelength of the laser source to a mechanical standard made of a material with ultra-low thermal expansion. This technique combines length measurement within a specified range with measurement of the refractive index fluctuations in one axis. Errors caused by different position of the interferometer laser beam and air sensors are thus eliminated. The method has been experimentally tested in comparison with the indirect measurement of the refractive index of air in a thermal controlled environment. Over a 1 K temperature range an agreement on the level of 5 × 10−8 has been achieved. PMID:22164036

Refractive errors in medical students in Singapore.

PubMed

Woo, W W; Lim, K A; Yang, H; Lim, X Y; Liew, F; Lee, Y S; Saw, S M

2004-10-01

Refractive errors are becoming more of a problem in many societies, with prevalence rates of myopia in many Asian urban countries reaching epidemic proportions. This study aims to determine the prevalence rates of various refractive errors in Singapore medical students. 157 second year medical students (aged 19-23 years) in Singapore were examined. Refractive error measurements were determined using a stand-alone autorefractor. Additional demographical data was obtained via questionnaires filled in by the students. The prevalence rate of myopia in Singapore medical students was 89.8 percent (Spherical equivalence (SE) at least -0.50 D). Hyperopia was present in 1.3 percent (SE more than +0.50 D) of the participants and the overall astigmatism prevalence rate was 82.2 percent (Cylinder at least 0.50 D). Prevalence rates of myopia and astigmatism in second year Singapore medical students are one of the highest in the world.

Enhanced contrast ratio and viewing angle of polymer-stabilized liquid crystal via refractive index matching between liquid crystal and polymer network.

PubMed

Lee, Ji-Hoon; Lee, Jung Jin; Lim, Young Jin; Kundu, Sudarshan; Kang, Shin-Woong; Lee, Seung Hee

2013-11-04

Long standing electro-optic problems of a polymer-dispersed liquid crystal (PDLC) such as low contrast ratio and transmittances decrease in oblique viewing angle have been challenged with a mixture of dual frequency liquid crystal (DFLC) and reactive mesogen (RM). The DFLC and RM molecules were vertically aligned and then photo-polymerized using a UV light. At scattering state under 50 kHz electric field, DFLC was switched to planar state, giving greater extraordinary refractive index than the normal PDLC cell. Consequently, the scattering intensity and the contrast ratio were increased compared to the conventional PDLC cell. At transparent state under 1 kHz electric field, the extraordinary refractive index of DFLC was simultaneously matched with the refractive index of vertically aligned RM so that the light scattering in oblique viewing angles was minimized, giving rise to high transmittance in all viewing angles.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Computing the total atmospheric refraction for real-time optical imaging sensor simulation

NASA Astrophysics Data System (ADS)

Olson, Richard F.

2015-05-01

Fast and accurate computation of light path deviation due to atmospheric refraction is an important requirement for real-time simulation of optical imaging sensor systems. A large body of existing literature covers various methods for application of Snell's Law to the light path ray tracing problem. This paper provides a discussion of the adaptation to real time simulation of atmospheric refraction ray tracing techniques used in mid-1980's LOWTRAN releases. The refraction ray trace algorithm published in a LOWTRAN-6 technical report by Kneizys (et. al.) has been coded in MATLAB for development, and in C-language for simulation use. To this published algorithm we have added tuning parameters for variable path segment lengths, and extensions for Earth grazing and exoatmospheric "near Earth" ray paths. Model atmosphere properties used to exercise the refraction algorithm were obtained from tables published in another LOWTRAN-6 related report. The LOWTRAN-6 based refraction model is applicable to atmospheric propagation at wavelengths in the IR and visible bands of the electromagnetic spectrum. It has been used during the past two years by engineers at the U.S. Army Aviation and Missile Research, Development and Engineering Center (AMRDEC) in support of several advanced imaging sensor simulations. Recently, a faster (but sufficiently accurate) method using Gauss-Chebyshev Quadrature integration for evaluating the refraction integral was adopted.

Prevalence of refractive errors among school children in gondar town, northwest ethiopia.

PubMed

Yared, Assefa Wolde; Belaynew, Wasie Taye; Destaye, Shiferaw; Ayanaw, Tsegaw; Zelalem, Eshete

2012-10-01

Many children with poor vision due to refractive error remain undiagnosed and perform poorly in school. The situation is worse in the Sub-Saharan Africa, including Ethiopia, and current information is lacking. The objective of this study is to determine the prevalence of refractive error among children enrolled in elementary schools in Gondar town, Ethiopia. This was a cross-sectional study of 1852 students in 8 elementary schools. Subjects were selected by multistage random sampling. The study parameters were visual acuity (VA) evaluation and ocular examination. VA was measured by staff optometrists with the Snellen E-chart while students with subnormal vision were examined using pinhole, retinoscopy evaluation and subjective refraction by ophthalmologists. The study cohort was comprised of 45.8% males and 54.2% females from 8 randomly selected elementary schools with a response rate of 93%. Refractive errors in either eye were present in 174 (9.4%) children. Of these, myopia was diagnosed in 55 (31.6%) children in the right and left eyes followed by hyperopia in 46 (26.4%) and 39 (22.4%) in the right and left eyes respectively. Low myopia was the most common refractive error in 61 (49.2%) and 68 (50%) children for the right and left eyes respectively. Refractive error among children is a common problem in Gondar town and needs to be assessed at every health evaluation of school children for timely treatment.

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Prevalence and pattern of refractive errors among primary school children in Al Hassa , Saudi Arabia.

PubMed

Al Wadaani, Fahd Abdullah; Amin, Tarek Tawfik; Ali, Ayub; Khan, Atuar Rahman

2012-11-11

Some 12.8 million in the age group 5-15 years are visually impaired from uncorrected or inadequately corrected refractive errors. In Saudi Arabia, the size of this public health problem is not well defined especially among primary schoolchildren. The purpose of this cross-sectional study was to assess the prevalence and pattern of refractive errors among primary school children in Al Hassa, Saudi Arabia.  A total of 2246 Saudi primary school children aged 6 to 14 years of both genders were selected using multistage sampling method form 30 primary schools located in the three different areas of Al Hassa. School children were interviewed to collect demographics and vision data using a special data collection form followed by screening for refractive errors by trained optometrists within the school premises using a standardized protocol. Assessment of visual acuity and ocular motility evaluation were carried out and cover-uncover test was performed. Children detected with defective vision were referred for further examination employing subjective refraction with auto refractometer and objective refraction using streak retinoscopy after 1% cyclopentolate. Of the screened school children (N=2002), the overall prevalence of refractive errors was 13.7% (n=274), higher among females (Odds ratio, OR=1.39, P=0.012) and significantly more among students of rural residence (OR=2.40, P=0.001). The prevalence of refractive errors was disproportionately more among those aged 12-14 years (OR=9.02, P=0.001). Only 9.4% of students with poor vision were wore spectacles for correction. Myopia was the most commonly encountered refractive error among both genders (65.7% of the total errors encountered). Uncorrected refractive errors affected a sizable portion of primary school children in Al Hassa, Saudi Arabia. Primary schoolchildren especially females, rural and older children represents high risk group for refractive errors for which the included children were unaware.

Prevalence and Pattern of Refractive Errors among Primary School Children in Al Hassa, Saudi Arabia

PubMed Central

Wadaani, Fahd Abdullah Al; Amin, Tarek Tawfik; Ali, Ayub; Khan, Ataur Rahman

2013-01-01

Some 12.8 million in the age group 5–15 years are visually impaired from uncorrected or inadequately corrected refractive errors. In Saudi Arabia, the size of this public health problem is not well defined especially among primary schoolchildren. The purpose of this cross-sectional study was to assess the prevalence and pattern of refractive errors among primary school children in Al Hassa, Saudi Arabia. A total of 2246 Saudi primary school children aged 6 to 14 years of both genders were selected using multistage sampling method form 30 primary schools located in the three different areas of Al Hassa. School children were interviewed to collect demographics and vision data using a special data collection form followed by screening for refractive errors by trained optometrists within the school premises using a standardized protocol. Assessment of visual acuity and ocular motility evaluation were carried out and cover-uncover test was performed. Children detected with defective vision were referred for further examination employing subjective refraction with auto refractometer and objective refraction using streak retinoscopy after 1% cyclopentolate. Of the screened school children (N=2002), the overall prevalence of refractive errors was 13.7% (n=274), higher among females (Odds ratio, OR=1.39, P=0.012) and significantly more among students of rural residence (OR=2.40, P=0.001). The prevalence of refractive errors was disproportionately more among those aged 12-14 years (OR=9.02, P=0.001). Only 9.4% of students with poor vision were wore spectacles for correction. Myopia was the most commonly encountered refractive error among both genders (65.7% of the total errors encountered). Uncorrected refractive errors affected a sizable portion of primary school children in Al Hassa, Saudi Arabia. Primary schoolchildren especially females, rural and older children represents high risk group for refractive errors for which the included children were unaware. PMID:23283044

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

[Qualitative analysis of the evaluation indicators and their related parameters of ametropic state].

PubMed

Ren, Zeqin

2016-01-01

To investigate the theoretical basis and practical limitations of the existing calculation formulas in the evaluation of ametropic state. The evaluation indicators and their calculation parameters of ametropia were analyzed by using the reduced schematic model eye, the paraxial imaging principle, and the dimension laws. The existing formulas resulted from the reduced object vergence of object distance and image distance relation. Regarding the two measurement indicators of the existing formulas, diopter was misused for refractive power. "Ametropia degree" was a non-standard diction. Both of them were not suitable as the evaluation indicators. The outcomes of the existing formulas and their related plus or minus sign rules showed refractive corrections instead of refractive errors proper. For refractive errors, there was no suitable evaluation indicator. In the evaluation of ametropic state, there are fundamental problems in the existing formulas resulting from the reduced object vergence. The measurement indicators and their dimensional units are confused and misused. The calculation results refer to the refractive corrections only. The evaluation indicators for ametropia need to be further discussed.

Acoustic Inversion in Optoacoustic Tomography: A Review

PubMed Central

Rosenthal, Amir; Ntziachristos, Vasilis; Razansky, Daniel

2013-01-01

Optoacoustic tomography enables volumetric imaging with optical contrast in biological tissue at depths beyond the optical mean free path by the use of optical excitation and acoustic detection. The hybrid nature of optoacoustic tomography gives rise to two distinct inverse problems: The optical inverse problem, related to the propagation of the excitation light in tissue, and the acoustic inverse problem, which deals with the propagation and detection of the generated acoustic waves. Since the two inverse problems have different physical underpinnings and are governed by different types of equations, they are often treated independently as unrelated problems. From an imaging standpoint, the acoustic inverse problem relates to forming an image from the measured acoustic data, whereas the optical inverse problem relates to quantifying the formed image. This review focuses on the acoustic aspects of optoacoustic tomography, specifically acoustic reconstruction algorithms and imaging-system practicalities. As these two aspects are intimately linked, and no silver bullet exists in the path towards high-performance imaging, we adopt a holistic approach in our review and discuss the many links between the two aspects. Four classes of reconstruction algorithms are reviewed: time-domain (so called back-projection) formulae, frequency-domain formulae, time-reversal algorithms, and model-based algorithms. These algorithms are discussed in the context of the various acoustic detectors and detection surfaces which are commonly used in experimental studies. We further discuss the effects of non-ideal imaging scenarios on the quality of reconstruction and review methods that can mitigate these effects. Namely, we consider the cases of finite detector aperture, limited-view tomography, spatial under-sampling of the acoustic signals, and acoustic heterogeneities and losses. PMID:24772060

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Extreme Brightness Temperatures and Refractive Substructure in 3C273 with RadioAstron

NASA Astrophysics Data System (ADS)

Johnson, Michael D.; Kovalev, Yuri Y.; Gwinn, Carl R.; Gurvits, Leonid I.; Narayan, Ramesh; Macquart, Jean-Pierre; Jauncey, David L.; Voitsik, Peter A.; Anderson, James M.; Sokolovsky, Kirill V.; Lisakov, Mikhail M.

2016-03-01

Earth-space interferometry with RadioAstron provides the highest direct angular resolution ever achieved in astronomy at any wavelength. RadioAstron detections of the classic quasar 3C 273 on interferometric baselines up to 171,000 km suggest brightness temperatures exceeding expected limits from the “inverse-Compton catastrophe” by two orders of magnitude. We show that at 18 cm, these estimates most likely arise from refractive substructure introduced by scattering in the interstellar medium. We use the scattering properties to estimate an intrinsic brightness temperature of 7× {10}12 {{K}}, which is consistent with expected theoretical limits, but which is ˜15 times lower than estimates that neglect substructure. At 6.2 cm, the substructure influences the measured values appreciably but gives an estimated brightness temperature that is comparable to models that do not account for the substructure. At 1.35 {{cm}}, the substructure does not affect the extremely high inferred brightness temperatures, in excess of {10}13 {{K}}. We also demonstrate that for a source having a Gaussian surface brightness profile, a single long-baseline estimate of refractive substructure determines an absolute minimum brightness temperature, if the scattering properties along a given line of sight are known, and that this minimum accurately approximates the apparent brightness temperature over a wide range of total flux densities.

A new local GPS water vapor tomography imaging technique using spectral functions w.r.t space and time: initial tests and results for the Tahiti Island case (French Polynesia)

NASA Astrophysics Data System (ADS)

Sichoix, L.; Barriot, J.; Fadil, A.; Ortega, P.

2009-12-01

In this study, we present the initial tests and validation results performed on a newly-developed GPS water vapor tomography inversion code based on a spectral approach tailored to coarse networks of GPS stations. Our work is mainly motivated by the lack of dense GPS coverage in Tahiti Island. Firstly, we use the GAMIT software to estimate the tropospheric slant wet delays (SWD) from a single GPS ground-based receiver to each visible satellite. SWD values are our model input. Secondly, the refractivity along ray paths is written as 3D Zernike radial and spherical harmonic series as well as sinusoidal time series and then inserted into the Radon transform linking slant delays and refractivity. This approach is in contrast with usual previous approaches where the atmosphere is divided into voxels (3D pixels). These approaches may exhibit instabilities as a voxel is crossed by more than one ray. Thirdly, we overcome the ill-posedness of the Radon transform by adding a priori constraints in the form of a full covariance matrix of the atmospheric refractivity taking into account the transport and mixing processes in the atmosphere.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Prevalence of the refractive errors by age and gender: the Mashhad eye study of Iran.

PubMed

Ostadimoghaddam, Hadi; Fotouhi, Akbar; Hashemi, Hassan; Yekta, Abbasali; Heravian, Javad; Rezvan, Farhad; Ghadimi, Hamidreza; Rezvan, Bijan; Khabazkhoob, Mehdi

2011-11-01

Refractive errors are a common eye problem. Considering the low number of population-based studies in Iran in this regard, we decided to determine the prevalence rates of myopia and hyperopia in a population in Mashhad, Iran. Cross-sectional population-based study. Random cluster sampling. Of 4453 selected individuals from the urban population of Mashhad, 70.4% participated. Refractive error was determined using manifest (age > 15 years) and cycloplegic refraction (age ≤ 15 years). Myopia was defined as a spherical equivalent of -0.5 diopter or worse. An spherical equivalent of +0.5 diopter or worse for non-cycloplegic refraction and an spherical equivalent of +2 diopter or worse for cycloplegic refraction was used to define hyperopia. Prevalence of refractive errors. The prevalence of myopia and hyperopia in individuals ≤ 15 years old was 3.64% (95% CI: 2.19-5.09) and 27.4% (95% CI: 23.72-31.09), respectively. The same measurements for subjects > 15 years of age was 22.36% (95% CI: 20.06-24.66) and 34.21% (95% CI: 31.57-36.85), respectively. Myopia was found to increase with age in individuals ≤ 15 years and decrease with age in individuals > 15 years of age. The rate of hyperopia showed a significant increase with age in individuals > 15 years. The prevalence of astigmatism was 25.64% (95% CI: 23.76-27.51). In children and the elderly, hyperopia is the most prevalent refractive error. After hyperopia, astigmatism is also of importance in older ages. Age is the most important demographic factor associated with different types of refractive errors. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Quantification of Nanoscale Density Fluctuations in Biological Cells/Tissues: Inverse Participation Ratio (IPR) Analysis of Transmission Electron Microscopy Images and Implications for Early-Stage Cancer Detection

NASA Astrophysics Data System (ADS)

Pradhan, Prabhakar; Damania, Dhwanil; Joshi, Hrushikesh; Taflove, Allen; Roy, Hemant; Dravid, Vinayak; Backman, Vadim

2010-03-01

We report a study of the nanoscale mass density fluctuations of biological cells and tissues by quantifying their nanoscale light-localization properties. Transmission electron microscope (TEM) images of human cells and tissues are used to construct corresponding effective disordered optical lattices. Light-localization properties are studied by statistical analysis of the inverse participation ratio (IPR) of the eigenfunctions of these optical lattices at the nanoscales. Our results indicate elevation of the nanoscale disorder strength (e.g., refractive index fluctuations) in early carcinogenesis. Importantly, our results demonstrate that the increase in the nanoscale disorder represents the earliest structural alteration in cells undergoing carcinogenesis known to-date. Potential applications of the technique for early stage cancer detection will be discussed.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Analytic semigroups: Applications to inverse problems for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rebnord, D. A.

1990-01-01

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

Refractive errors in children with autism in a developing country.

PubMed

Ezegwui, I R; Lawrence, L; Aghaji, A E; Okoye, O I; Okoye, O; Onwasigwe, E N; Ebigbo, P O

2014-01-01

In a resource-limited country visual problems of mentally challenged individuals are often neglected. The present study aims to study refractive errors in children diagnosed with autism in a developing country. Ophthalmic examination was carried out on children diagnosed with autism attending a school for the mentally challenged in Enugu, Nigeria between December 2009 and May 2010. Visual acuity was assessed using Lea symbols. Anterior and posterior segments were examined. Cycloplegic refraction was performed. Data was entered on the protocol prepared for the study and analyzed using Statistical Package for the Social Sciences version 17 (Chicago IL, USA). A total of 21 children with autism were enrolled in the school; 18 of whom were examined giving coverage of 85.7%. The age range was 5-15 years, with a mean of 10.28 years (standard deviation ± 3.20). There were 13 boys and 5 girls. One child had bilateral temporal pallor of the disc and one had bilateral maculopathy with diffuse chorioretinal atrophy. Refraction revealed 4 children (22.2%) had astigmatism and 2 children (11.1%) had hypermetropia. Significant refractive error mainly astigmatism was noted in the children with autism. Identifying refractive errors in these children early and providing appropriate corrective lenses may help optimize their visual functioning and impact their activities of daily life in a positive way.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Gravity inversion of a fault by Particle swarm optimization (PSO).

PubMed

Toushmalani, Reza

2013-01-01

Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult optimization problems. The technique proved to work efficiently when tested to a number of models.

The Inverse Problem in Jet Acoustics

NASA Technical Reports Server (NTRS)

Wooddruff, S. L.; Hussaini, M. Y.

2001-01-01

The inverse problem for jet acoustics, or the determination of noise sources from far-field pressure information, is proposed as a tool for understanding the generation of noise by turbulence and for the improved prediction of jet noise. An idealized version of the problem is investigated first to establish the extent to which information about the noise sources may be determined from far-field pressure data and to determine how a well-posed inverse problem may be set up. Then a version of the industry-standard MGB code is used to predict a jet noise source spectrum from experimental noise data.

Reflecting anastigmatic optical systems: a retrospective

NASA Astrophysics Data System (ADS)

Rakich, Andrew

2017-11-01

Reflecting anastigmatic optical systems hold several inherent advantages over refracting equivalents; such as compactness, absence of color, high "refractive efficiency", wide bandwidth, and size-scalability to enormous apertures. Such advantages have led to these systems becoming, increasingly since their first deliberate development in 1905, the "go-to" solution for various classes of optical design problem. This paper describes in broad terms the history of the development of this class of optical system, with an emphasis on the early history.

The Inverted Snow Globe Shadow

NASA Astrophysics Data System (ADS)

Ribeiro, Jair Lúcio Prados

2015-01-01

Our high school optics course finishes with an assignment that students usually appreciate. They must take pictures of everyday situations representing optical phenomena such as reflection, refraction, or dispersion, and post them on Instagram.1 When the photos were presented to the class, one student revealed an intriguing photo, similar to Fig. 1, showing a snow globe exposed to sunlight and its inverted shadow. This paper offers an explanation of the problem, which occurs due to light refraction from the globe.

Determining index of refraction from polarimetric hyperspectral radiance measurements

NASA Astrophysics Data System (ADS)

Martin, Jacob A.; Gross, Kevin C.

2015-09-01

Polarimetric hyperspectral imaging (P-HSI) combines two of the most common remote sensing modalities. This work leverages the combination of these techniques to improve material classification. Classifying and identifying materials requires parameters which are invariant to changing viewing conditions, and most often a material's reflectivity or emissivity is used. Measuring these most often requires assumptions be made about the material and atmospheric conditions. Combining both polarimetric and hyperspectral imaging, we propose a method to remotely estimate the index of refraction of a material. In general, this is an underdetermined problem because both the real and imaginary components of index of refraction are unknown at every spectral point. By modeling the spectral variation of the index of refraction using a few parameters, however, the problem can be made overdetermined. A number of different functions can be used to describe this spectral variation, and some are discussed here. Reducing the number of spectral parameters to fit allows us to add parameters which estimate atmospheric downwelling radiance and transmittance. Additionally, the object temperature is added as a fit parameter. The set of these parameters that best replicate the measured data is then found using a bounded Nelder-Mead simplex search algorithm. Other search algorithms are also examined and discussed. Results show that this technique has promise but also some limitations, which are the subject of ongoing work.

Inverse kinematics problem in robotics using neural networks

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.; Lawrence, Charles

1992-01-01

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

NASA Astrophysics Data System (ADS)

Fedele, Micaela; Vernia, Cecilia

2017-10-01

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Model of Atmospheric Links on Optical Communications from High Altitude

NASA Technical Reports Server (NTRS)

Subich, Christopher

2004-01-01

Optical communication links have the potential to solve many of the problems of current radio and microwave links to satellites and high-altitude aircraft. The higher frequency involved in optical systems allows for significantly greater signal bandwidth, and thus information transfer rate, in excess of 10 Gbps, and the highly directional nature of laser-based signals eliminates the need for frequency-division multiplexing seen in radio and microwave links today. The atmosphere, however, distorts an optical signal differently than a microwave signal. While the ionosphere is one of the most significant sources of noise and distortion in a microwave or radio signal, the lower atmosphere affects an optical signal more significantly. Refractive index fluctuations, primarily caused by changes in atmospheric temperature and density, distort the incoming signal in both deterministic and nondeterministic ways. Additionally, suspended particles, such as those in haze or rain, further corrupt the transmitted signal. To model many of the atmospheric effects on the propagating beam, we use simulations based on the beam-propagation method. This method, developed both for simulation of signals in waveguides and propagation in atmospheric turbulence, separates the propagation into a diffraction and refraction problem. The diffraction step is an exact solution, within the limits of numerical precision, to the problem of propagation in free space, and the refraction step models the refractive index variances over a segment of the propagation path. By applying refraction for a segment of the propagation path, then diffracting over that same segment, this method forms a good approximation to true propagation through the atmospheric medium. Iterating over small segments of the total propagation path gives a good approximation to the problem of propagation over the entire path. Parameters in this model, such as initial beam profile and atmospheric constants, are easily modified in a simulation such as this, which allows for the rapid analysis of different propagation scenarios. Therefore, this method allows the development of a near-optimal system design for a wide range of situations, typical of what would be seen in different atmospheric conditions over a receiving ground station. A simulation framework based upon this model was developed in FORTRAN, and for moderate grid sizes and propagation distances these simulations are computable in reasonable time on a standard workstation. This presentation will discuss results thus far.

Parametric study of beam refraction problems across laser anemometer windows

NASA Technical Reports Server (NTRS)

Owen, A. K.

1986-01-01

The experimenter is often required to view flows through a window with a different index of refraction than either the medium being observed or the medium that the laser anemometer is immersed in. The refraction that occurs at the window surfaces may lead to undesirable changes in probe volume position or beam crossing angle and can lead to partial or complete beam uncrossing. This report describes the results of a parametric study of this problem using a ray tracing technique to predict these changes. The windows studied were a flat plate and a simple cyclinder. For the flat-plate study: (1) surface thickness, (2) beam crossing angle, (3) bisecting line - surface normal angle, and (4) incoming beam plane surface orientation were varied. For the cylindrical window additional parameters were also varied: (1) probe volume immersion, (2) probe volume off-radial position, and (3) probe volume position out of the R-theta plane of the lens. A number of empirical correlations were deduced to aid the interested reader in determining the movement, uncrossing, and change in crossing angle for a particular situation.

A parametric study of the beam refraction problems across laser anemometer windows

NASA Technical Reports Server (NTRS)

Owen, Albert K.

1986-01-01

The experimenter is often required to view flows through a window with a different index of refraction than either the medium being observed or the medium that the laser anemometer is immersed in. The refraction that occurs at the window surfaces may lead to undesirable changes in probe volume position or beam crossing angle and can lead to partial or complete beam uncrossing. This report describes the results of a parametric study of this problem using a ray tracing technique to predict these changes. The windows studied were a flat plate and a simple cylinder. For the flat-plate study: (1) surface thickness, (2) beam crossing angle, (3) bisecting line - surface normal angle, and (4) incoming beam plane surface orientation were varied. For the cylindrical window additional parameters were also varied: (1) probe volume immersion, (2) probe volume off-radial position, and (3) probe volume position out of the r-theta plane of the lens. A number of empirical correlations were deduced to aid the reader in determining the movement, uncrossing, and change in crossing angle for a particular situations.

Computational structures for robotic computations

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chang, P. R.

1987-01-01

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.

A Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

PubMed Central

Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrell J; Wang, Dafang F; Steffen, Michael; Brooks, Dana H; van Dam, Peter M; Macleod, Rob S

2012-01-01

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems. PMID:22254301

The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography.

PubMed

Dushaw, Brian D; Sagen, Hanne

2017-12-01

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

Refractive Errors in 3–6 Year-Old Chinese Children: A Very Low Prevalence of Myopia?

PubMed Central

Lin, Lixia; Li, Zhen; Zeng, Junwen; Yang, Zhikuan; Morgan, Ian G.

2013-01-01

Purpose To examine the prevalence of refractive errors in children aged 3–6 years in China. Methods Children were recruited for a trial of a home-based amblyopia screening kit in Guangzhou preschools, during which cycloplegic refractions were measured in both eyes of 2480 children. Cycloplegic refraction (from 3 to 4 drops of 1% cyclopentolate to ensure abolition of the light reflex) was measured by both autorefraction and retinoscopy. Refractive errors were defined as followed: myopia (at least −0.50 D in the worse eye), hyperopia (at least +2.00 D in the worse eye) and astigmatism (at least 1.50 D in the worse eye). Different definitions, as specified in the text, were also used to facilitate comparison with other studies. Results The mean spherical equivalent refractive error was at least +1.22 D for all ages and both genders. The prevalence of myopia for any definition at any age was at most 2.5%, and lower in most cases. In contrast, the prevalence of hyperopia was generally over 20%, and declined slightly with age. The prevalence of astigmatism was between 6% and 11%. There was very little change in refractive error with age over this age range. Conclusions Previous reports of less hyperopic mean spherical equivalent refractive error, and more myopia and less hyperopia in children of this age may be due to problems with achieving adequate cycloplegia in children with dark irises. Using up to 4 drops of 1% cyclopentolate may be necessary to accurately measure refractive error in paediatric studies of such children. Our results suggest that children from all ethnic groups may follow a similar pattern of early refractive development, with little myopia and a hyperopic mean spherical equivalent over +1.00 D up to the age of 5–6 yearsin most conditions. PMID:24205064

Joint Geophysical Inversion With Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelievre, P. G.; Bijani, R.; Farquharson, C. G.

2015-12-01

Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem is essentially a geometry inversion, which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

Time-reversal and Bayesian inversion

NASA Astrophysics Data System (ADS)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Prevalence of Refractive Errors Among School Children in Gondar Town, Northwest Ethiopia

PubMed Central

Yared, Assefa Wolde; Belaynew, Wasie Taye; Destaye, Shiferaw; Ayanaw, Tsegaw; Zelalem, Eshete

2012-01-01

Purpose: Many children with poor vision due to refractive error remain undiagnosed and perform poorly in school. The situation is worse in the Sub-Saharan Africa, including Ethiopia, and current information is lacking. The objective of this study is to determine the prevalence of refractive error among children enrolled in elementary schools in Gondar town, Ethiopia. Materials and Methods: This was a cross-sectional study of 1852 students in 8 elementary schools. Subjects were selected by multistage random sampling. The study parameters were visual acuity (VA) evaluation and ocular examination. VA was measured by staff optometrists with the Snellen E-chart while students with subnormal vision were examined using pinhole, retinoscopy evaluation and subjective refraction by ophthalmologists. Results: The study cohort was comprised of 45.8% males and 54.2% females from 8 randomly selected elementary schools with a response rate of 93%. Refractive errors in either eye were present in 174 (9.4%) children. Of these, myopia was diagnosed in 55 (31.6%) children in the right and left eyes followed by hyperopia in 46 (26.4%) and 39 (22.4%) in the right and left eyes respectively. Low myopia was the most common refractive error in 61 (49.2%) and 68 (50%) children for the right and left eyes respectively. Conclusions: Refractive error among children is a common problem in Gondar town and needs to be assessed at every health evaluation of school children for timely treatment. PMID:23248538

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

NASA Astrophysics Data System (ADS)

Uhlmann, Gunther

2008-07-01

This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology, Finland), Masahiro Yamamoto (University of Tokyo, Japan), Gunther Uhlmann (University of Washington) and Jun Zou (Chinese University of Hong Kong). IPIA is a recently formed organization that intends to promote the field of inverse problem at all levels. See http://www.inverse-problems.net/. IPIA awarded the first Calderón prize at the opening of the conference to Matti Lassas (see first article in the Proceedings). There was also a general meeting of IPIA during the workshop. This was probably the largest conference ever on IP with 350 registered participants. The program consisted of 18 invited speakers and the Calderón Prize Lecture given by Matti Lassas. Another integral part of the program was the more than 60 mini-symposia that covered a broad spectrum of the theory and applications of inverse problems, focusing on recent developments in medical imaging, seismic exploration, remote sensing, industrial applications, numerical and regularization methods in inverse problems. Another important related topic was image processing in particular the advances which have allowed for significant enhancement of widely used imaging techniques. For more details on the program see the web page: http://www.pims.math.ca/science/2007/07aip. These proceedings reflect the broad spectrum of topics covered in AIP 2007. The conference and these proceedings would not have happened without the contributions of many people. I thank all my fellow organizers, the invited speakers, the speakers and organizers of mini-symposia for making this an exciting and vibrant event. I also thank PIMS, NSF and MITACS for their generous financial support. I take this opportunity to thank the PIMS staff, particularly Ken Leung, for making the local arrangements. Also thanks are due to Stephen McDowall for his help in preparing the schedule of the conference and Xiaosheng Li for the help in preparing these proceedings. I also would like to thank the contributors of this volume and the referees. Finally, many thanks are due to Graham Douglas and Elaine Longden-Chapman for suggesting publication in Journal of Physics: Conference Series.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

Experimental Determination of Infrared Extinction Coefficients of Interplanetary Dust Particles

NASA Technical Reports Server (NTRS)

Spann, J. F., Jr.; Abbas, M. M.

1998-01-01

This technique is based on irradiating a single isolated charged dust particle suspended in balance by an electric field, and measuring the scattered radiation as a function of angle. The observed scattered intensity profile at a specific wavelength obtained for a dust particle of known composition is compared with Mie theory calculations, and the variable parameters relating to the particle size and complex refractive index are adjusted for a best fit between the two profiles. This leads to a simultaneous determination of the particle radius, the complex refractive index, and the scattering and extinction coefficients. The results of these experiments can be utilized to examine the IRAS and DIRBE (Diffuse Infrared Background Experiment) infrared data sets in order to determine the dust particle physical characteristics and distributions by using infrared models and inversion techniques. This technique may also be employed for investigation of the rotational bursting phenomena whereby large size cosmic and interplanetary particles are believed to fragment into smaller dust particles.

3D crustal model of the US and Canada East Coast rifted margin

NASA Astrophysics Data System (ADS)

Dowla, N.; Bird, D. E.; Murphy, M. A.

2017-12-01

We integrate seismic reflection and refraction data with gravity and magnetic data to generate a continent-scale 3D crustal model of the US and Canada East Coast, extending north from the Straits of Florida to Newfoundland, and east from the Appalachian Mountains to the Central Atlantic Ocean. The model includes five layers separated by four horizons: sea surface, topography, crystalline basement, and Moho. We tested magnetic depth-to-source techniques to improve the basement morphology, from published sources, beneath the continental Triassic rift basins and outboard to the Jurassic ocean floor. A laterally varying density grid was then produced for the resultant sedimentary rock layer thickness based on an exponential decay function that approximates sedimentary compaction. Using constant density values for the remaining layers, we calculated an isostatically compensated Moho. The following structural inversion results of the Moho, controlled by seismic refraction depths, advances our understanding of rift-to-drift crustal geometries, and provides a regional context for additional studies.

An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength

NASA Astrophysics Data System (ADS)

Millard, R. C.; Seaver, G.

1990-12-01

A 27-term index of refraction algorithm for pure and sea waters has been developed using four experimental data sets of differing accuracies. They cover the range 500-700 nm in wavelength, 0-30°C in temperature, 0-40 psu in salinity, and 0-11,000 db in pressure. The index of refraction algorithm has an accuracy that varies from 0.4 ppm for pure water at atmospheric pressure to 80 ppm at high pressures, but preserves the accuracy of each original data set. This algorithm is a significant improvement over existing descriptions as it is in analytical form with a better and more carefully defined accuracy. A salinometer algorithm with the same uncertainty has been created by numerically inverting the index algorithm using the Newton-Raphson method. The 27-term index algorithm was used to generate a pseudo-data set at the sodium D wavelength (589.26 nm) from which a 6-term densitometer algorithm was constructed. The densitometer algorithm also produces salinity as an intermediate step in the salinity inversion. The densitometer residuals have a standard deviation of 0.049 kg m -3 which is not accurate enough for most oceanographic applications. However, the densitometer algorithm was used to explore the sensitivity of density from this technique to temperature and pressure uncertainties. To achieve a deep ocean densitometer of 0.001 kg m -3 accuracy would require the index of refraction to have an accuracy of 0.3 ppm, the temperature an accuracy of 0.01°C and the pressure 1 db. Our assessment of the currently available index of refraction measurements finds that only the data for fresh water at atmospheric pressure produce an algorithm satisfactory for oceanographic use (density to 0.4 ppm). The data base for the algorithm at higher pressures and various salinities requires an order of magnitude or better improvement in index measurement accuracy before the resultant density accuracy will be comparable to the currently available oceanographic algorithm.

Two-way WKB Approximation Applied to GPR - COST Action TU1208

NASA Astrophysics Data System (ADS)

Prokopovich, Igor; Popov, Alexei; Marciniak, Marian; Pajewski, Lara

2016-04-01

The main goal of subsurface radio wave probing consists in reconstruction of the shape and the electrical properties of buried objects in material media. For this purpose the knowledge of the laws of EM pulse excitation and propagation in non-uniform subsurface medium is required, as well as the methods and algorithms of solving the inverse problem. Two ways of treating this problem exist. On the one hand, one can describe EM wave propagation by solving the Maxwell's equations with finite difference methods implemented in computer codes. However, when solving inverse problems, pure numerical algorithms require huge amount of calculation and, as a consequence, long calculation time. In this respect, more promising are analytical approaches. Here, we apply couple wave theory ("two-way WKB" approximation) to the problem of subsurface wave propagation. The derived formulas can be used in GPR design and for fast data processing of the experimental data. We start from the 1D model problem of GPR probing. Classical WKB method [1] allows one to describe wave propagation through non-uniform media with slowly varying dielectric permittivity. A principal shortcoming of this approximation is that it does not take into account backward reflection from permittivity gradients. Consequently, WKB method as such can not be used for the purposes of GPR sounding. An extension of this approximation consists in solving two coupled WKB-type equations by iterations. This approach properly describes backward reflections and provides good accuracy in a wide frequency range [2]. In our previous work [3] a time-domain counterpart of the Bremmer-Brekhovkikh approximation has been derived and applied to a 1D inverse problem of subsurface medium probing by an ultra-wide band EM pulse. In order to convert this approach into a practical GPR algorithm, a more realistic model is required: 2D or 3D propagation from a localized source with the effects of wave divergence and refraction taken into account. In this work we study bistatic EM pulse probing of a horizontally layered medium in a 2D case. Coupled WKB equations set describing both forward and backward waves are derived and solved analytically. The comparison of our semi-analytical solutions with numerical calculations by gprMax software [4] demonstrates a good agreement, being hundreds of times faster than the letter. Our numerical results explain the protracted return pulses in the low-frequency GPR data. As an example, we discuss the experimental data obtained during the GPR mission in search of a big fragment of Chelyabinsk meteorite under a thick silt layer at the bottom of Chebarcul' Lake [5]. Acknowledgement The Authors are grateful to the European Cooperation in Science and Technology (www.cost.eu) facilitating this work by a Short-Term Scientific Missions (STSM) within the framework of the Action TU1208 "Civil engineering applications of Ground Penetrating Radar" (www.GPRadar.eu). References 1. H. Bremmer "Propagation of electromagnetic waves", in Handbuch der Physik, S. Flugge, Ed. Berlin-Goettingen-Heidelberg: Springer, 1958, pp. 423-639 2. L.M. Brekhovskikh, Waves in Stratified Media (in Russian). Moscow: USSR Academy of Sciences, 1957. 3. V.A.Vinogradov, V.V. Kopeikin, A.V. Popov, "An Approximate Solution of 1D Inverse Problem", in Proc. 10th Internat. Conf. on GPR, 21-24 June, 2004, Delft, The Netherlands 4. A. Giannopoulos, "Modelling ground penetrating radar by GprMax", Construction and Building Materials, vol. 19, no. 10, pp. 755-762, 2005, doi: 10.1016/j.conbuildmat.2005.06.007 5. V. V. Kopeikin , V. D. Kuznetsov, P. A. Morozov, A. V. Popov et al., "Ground penetrating radar investigation of the supposed fall site of a fragment of the Chelyabinsk meteorite in Lake Chebarkul'", Geochemistry International, vol. 51, no. 7, pp. 575-582, 2013, doi: 10.1134/S0016702913070112

Refractive Index of Alkali Halides and Its Wavelength and Temperature Derivatives.

DTIC Science & Technology

1975-05-01

of CoBr . . . .......... 236 82. Comparison of Dispersion Equations Proposed for CsBr ... . 237 83. Recommmded Values on the Refractive Index and Its... discovery of empirical relationships which enable us to calculate dn/dT data at 293 K for some ma- terials on which no data are available. In the data...or in handbooks. In the present work, however, this problem 160 was solved by our empirical discoveries by which the unknown parameters of Eq. (19) for

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

DOE PAGES

Butler, Troy; Graham, L.; Estep, D.; ...

2015-02-03

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in amore » shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.« less

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Time-lapse joint inversion of geophysical data with automatic joint constraints and dynamic attributes

NASA Astrophysics Data System (ADS)

Rittgers, J. B.; Revil, A.; Mooney, M. A.; Karaoulis, M.; Wodajo, L.; Hickey, C. J.

2016-12-01

Joint inversion and time-lapse inversion techniques of geophysical data are often implemented in an attempt to improve imaging of complex subsurface structures and dynamic processes by minimizing negative effects of random and uncorrelated spatial and temporal noise in the data. We focus on the structural cross-gradient (SCG) approach (enforcing recovered models to exhibit similar spatial structures) in combination with time-lapse inversion constraints applied to surface-based electrical resistivity and seismic traveltime refraction data. The combination of both techniques is justified by the underlying petrophysical models. We investigate the benefits and trade-offs of SCG and time-lapse constraints. Using a synthetic case study, we show that a combined joint time-lapse inversion approach provides an overall improvement in final recovered models. Additionally, we introduce a new approach to reweighting SCG constraints based on an iteratively updated normalized ratio of model sensitivity distributions at each time-step. We refer to the new technique as the Automatic Joint Constraints (AJC) approach. The relevance of the new joint time-lapse inversion process is demonstrated on the synthetic example. Then, these approaches are applied to real time-lapse monitoring field data collected during a quarter-scale earthen embankment induced-piping failure test. The use of time-lapse joint inversion is justified by the fact that a change of porosity drives concomitant changes in seismic velocities (through its effect on the bulk and shear moduli) and resistivities (through its influence upon the formation factor). Combined with the definition of attributes (i.e. specific characteristics) of the evolving target associated with piping, our approach allows localizing the position of the preferential flow path associated with internal erosion. This is not the case using other approaches.

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

PubMed Central

Van Regenmortel, Marc H. V.

2018-01-01

Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly rational design process. This is why the complexity of the human immune system prevents us from rationally designing an HIV vaccine by solving inverse problems. PMID:29387066

Unidirectional complex grating assisted couplers

NASA Astrophysics Data System (ADS)

Greenberg, Maxim; Orenstein, Meir

2004-08-01

We present a novel concept which enables the realization of unidirectional and irreversible grating assisted couplers by using gain-loss modulated medium to eliminate the reversibility. Employing a matched periodic modulation of both refractive index and loss (gain) we achieve a unidirectional energy transfer between the modes of the coupler which translates to light transmission from one waveguide to another while disabling the inverse transmission. The importance of self coupling coefficients is explored as well and a feasible implementation, where the real and imaginary perturbations are implemented in different waveguides is presented.

On Sagnac frequency splitting in a solid-state ring Raman laser.

PubMed

Liang, Wei; Savchenkov, Anatoliy; Ilchenko, Vladimir; Griffith, Robert; De Cuir, Edwin; Kim, Steven; Matsko, Andrey; Maleki, Lute

2017-11-15

We report on an accurate measurement of the frequency splitting of an optical rotating ring microcavity made out of calcium fluoride. By measuring the frequencies of the clockwise and counter-clockwise coherent Raman emissions confined in the cavity modes, we show that the frequency splitting is inversely proportional to the refractive index of the cavity host material. The measurement has an accuracy of 1% and unambiguously confirms the classical theoretical prediction based on special theory of relativity. This Letter also demonstrates the usefulness of the ring Raman microlaser for rotation measurements.

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Refractive indices of superlattices made of III-V semiconductor compounds and their solid solutions and semiconductor waveguide laser structures

NASA Astrophysics Data System (ADS)

Unger, K.

1988-11-01

An analysis is made of the theoretical problems encountered in precision calculations of refractive indices of semiconductor materials arising in connection with the use of superlattices as active layers in double-heterostructure lasers and in connection with the use of the impurity-induced disordering effect, i.e., the ability to transform selectively a superlattice into a corresponding solid solution. This can be done by diffusion or ion implantation. A review is given of calculations of refractive indices based on the knowledge of the energy band structure and the role of disorder is considered particularly. An anomaly observed in the (InAl)As system is considered. It is shown that the local field effects and exciton transitions are important. A reasonable approach is clearly a direct calculation of the difference between the refractive indices of superlattices based on compounds and of those based on their solid solutions.

Solution of Radiative Transfer Equation with a Continuous and Stochastic Varying Refractive Index by Legendre Transform Method

PubMed Central

Gantri, M.

2014-01-01

The present paper gives a new computational framework within which radiative transfer in a varying refractive index biological tissue can be studied. In our previous works, Legendre transform was used as an innovative view to handle the angular derivative terms in the case of uniform refractive index spherical medium. In biomedical optics, our analysis can be considered as a forward problem solution in a diffuse optical tomography imaging scheme. We consider a rectangular biological tissue-like domain with spatially varying refractive index submitted to a near infrared continuous light source. Interaction of radiation with the biological material into the medium is handled by a radiative transfer model. In the studied situation, the model displays two angular redistribution terms that are treated with Legendre integral transform. The model is used to study a possible detection of abnormalities in a general biological tissue. The effect of the embedded nonhomogeneous objects on the transmitted signal is studied. Particularly, detection of targets of localized heterogeneous inclusions within the tissue is discussed. Results show that models accounting for variation of refractive index can yield useful predictions about the target and the location of abnormal inclusions within the tissue. PMID:25013454

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Application of 3D full waveform inversion on real marine data sets

NASA Astrophysics Data System (ADS)

Plessix, Rene-Edouard

2010-05-01

Full waveform inversion (FWI) was proposed more than 25 years. Over the last ten years, several real 2D examples have been published showing the potential and the difficulties of this approach. The application of acoustic FWI to sizeable real 3D data sets became possible a few year ago thanks to the increase of computer power. The developments in seismic acquisition are also an enabler to FWI that works best with wide aperture data sets and low frequencies. In this way, the Ocean Bottom Seismometer (OBS) or Ocean Bottom Cable (OBC) data sets are well suited since they often contain long offsets, wide azimuth and low frequencies. In this presentation, I will describe the results we obtained by inverting a deep-water OBS data set from the Gulf of Mexico. The data set contains offsets up to 17 km. A classic multiscale FWI was applied starting at 2 Hz. FWI helps to reveal shallow gas accumulations that were difficult to capture with classic reflection traveltime inversion. The presence of these gas accumulations was also supported by a visco-acoustic FWI and an inversion for the quality factor. This result illustrates the power of FWI to image the shallow structures where diving waves propagate. Detecting these shallow velocity anomalies is not only important for imaging but also for hazard analysis, for instance, during a well planning. Analysis of the isotropic FWI results showed that some of the reflected energy was not correctly interpreted, since after pre-stack migration the common image gathers were not flat. In fact, FWI tries to interpret both reflected and refracted energy. Since the sediments in the Gulf of Mexico are anisotropic, the reflected and refracted waves may travel with a different velocity. We then carried out a VTI (Vertical Transversely Isotropic) FWI with a fixed ratio between the NMO (Normal MoveOut) velocity and the horizontal velocity. This ratio was found by traveltime inversion and is spatially varying. Migrating with the velocity found by VTI FWI led to a better image even for the sediments beneath the salt at 6 km depth. This improvement at those depths however strongly depends on the accuracy of the initial model since FWI works in a (non-linear) migration mode at that depth with this acquisition. Depending on the permission to publish, I may also discuss some results obtained with a more traditional narrow azimuth streamer data sets.

East Pacific Rise axial structure from a joint tomographic inversion of traveltimes picked on downward continued and standard shot gathers collected by 3D MCS surveying

NASA Astrophysics Data System (ADS)

Newman, Kori; Nedimović, Mladen; Delescluse, Matthias; Menke, William; Canales, J. Pablo; Carbotte, Suzanne; Carton, Helene; Mutter, John

2010-05-01

We present traveltime tomographic models along closely spaced (~250 m), strike-parallel profiles that flank the axis of the East Pacific Rise at 9°41' - 9°57' N. The data were collected during a 3D (multi-streamer) multichannel seismic (MCS) survey of the ridge. Four 6-km long hydrophone streamers were towed by the ship along three along-axis sail lines, yielding twelve possible profiles over which to compute tomographic models. Based on the relative location between source-receiver midpoints and targeted subsurface structures, we have chosen to compute models for four of those lines. MCS data provide for a high density of seismic ray paths with which to constrain the model. Potentially, travel times for ~250,000 source-receiver pairs can be picked over the 30 km length of each model. However, such data density does not enhance the model resolution, so, for computational efficiency, the data are decimated so that ~15,000 picks per profile are used. Downward continuation of the shot gathers simulates an experimental geometry in which the sources and receivers are positioned just above the sea floor. This allows the shallowest sampling refracted arrivals to be picked and incorporated into the inversion whereas they would otherwise not be usable with traditional first-arrival travel-time tomographic techniques. Some of the far-offset deep-penetrating 2B refractions cannot be picked on the downward continued gathers due to signal processing artifacts. For this reason, we run a joint inversion by also including 2B traveltime picks from standard shot gathers. Uppermost velocity structure (seismic layer 2A thickness and velocity) is primarily constrained from 1D inversion of the nearest offset (<500 m) source-receiver travel-time picks for each downward continued shot gather. Deeper velocities are then computed in a joint 2D inversion that uses all picks from standard and downward continued shot gathers and incorporates the 1D results into the starting model. The resulting velocity models extend ~1 km into the crust. Preliminary results show thicker layer 2A and faster layer 2A velocities at fourth order ridge segment boundaries. Additionally, layer 2A thickens north of 9° 52' N, which is consistent with earlier investigations of this ridge segment. Slower layer 2B velocities are resolved in the vicinity of documented hydrothermal vent fields. We anticipate that additional analyses of the results will yield further insight into fine scale variations in near-axis mid-ocean ridge structure.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

Compact 3D photonic crystals sensing platform with 45 degree angle polished fibers

NASA Astrophysics Data System (ADS)

Guo, Yuqing; Chen, Lu; Zhu, Jiali; Ni, Haibin; Xia, Wei; Wang, Ming

2017-07-01

Three dimensional photonic crystals are a kind of promising sensing materials in biology and chemistry. A compact structure, consists of planner colloidal crystals and 45 degree angle polished fiber, is proposed as a platform for accurate, fast, reliable three dimensional photonic crystals sensing in practice. This structure show advantages in compact size for integration and it is ease for large scale manufacture. Reflectivity of the 45 degree angle polished surface with and without a layer of Ag film are simulated by FDTD simulation. Refractive index sensing properties as well as mode distribution of this structure consists of both polystyrene opal and silica inverse opal film is investigated, and an experimental demonstration of silica inverse opal film is performed, which shows a sensitivity of 733 nm/RIU. Different kinds of three dimensional photonic crystals can also be applied in this structure for particular purpose.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre

PubMed Central

Turitsyn, Sergei K.; Bednyakova, Anastasia E.; Fedoruk, Mikhail P.; Papernyi, Serguei B.; Clements, Wallace R.L.

2015-01-01

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics. PMID:26345290

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

NASA Astrophysics Data System (ADS)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

The inverse Wiener polarity index problem for chemical trees.

PubMed

Du, Zhibin; Ali, Akbar

2018-01-01

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

Propagation in and scattering from a matched metamaterial having a zero index of refraction.

PubMed

Ziolkowski, Richard W

2004-10-01

Planar metamaterials that exhibit a zero index of refraction have been realized experimentally by several research groups. Their existence stimulated the present investigation, which details the properties of a passive, dispersive metamaterial that is matched to free space and has an index of refraction equal to zero. Thus, unlike previous zero-index investigations, both the permittivity and permeability are zero here at a specified frequency. One-, two-, and three-dimensional source problems are treated analytically. The one- and two-dimensional source problem results are confirmed numerically with finite difference time domain (FDTD) simulations. The FDTD simulator is also used to treat the corresponding one- and two-dimensional scattering problems. It is shown that in both the source and scattering configurations the electromagnetic fields in a matched zero-index medium take on a static character in space, yet remain dynamic in time, in such a manner that the underlying physics remains associated with propagating fields. Zero phase variation at various points in the zero-index medium is demonstrated once steady-state conditions are obtained. These behaviors are used to illustrate why a zero-index metamaterial, such as a zero-index electromagnetic band-gap structured medium, significantly narrows the far-field pattern associated with an antenna located within it. They are also used to show how a matched zero-index slab could be used to transform curved wave fronts into planar ones.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Reasons For Not Performing Keratorefractive Surgery in Patients Seeking Refractive Surgery in a Hospital-Based Cohort in “Yemen”

PubMed Central

Bamashmus, Mahfouth A.; Saleh, Mahmoud F.; Awadalla, Mohamed A.

2010-01-01

Background: To determine and analyze the reasons why keratorefractive surgery, laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK) were not performed in patients who presented for refractive surgery consultation. Materials and Methods: A retrospective observational study was performed between January 2006 and December 2007 in the Yemen Magrabi Hospital. The case records of 2,091 consecutive new patients who presented for refractive surgery were reviewed. Information from the pre-operative ophthalmic examination, such as refractive error, corneal topography and visual acuity, were analyzed. The reasons for not performing LASIK and PRK in the cases that were rejected were recorded and analyzed. Results: In this cohort, 1,660 (79.4%) patients were advised to have LASIK or PRK from the 2,091 patients examined. LASIK and PRK were not advised in 431 (21%) patients. The most common reasons for not performing the surgery were high myopia >-11.00 Diopters (19%), keratoconus (18%), suboptimal central corneal thickness (15%), cataract (12%) and keratoconus suspect (forme fruste keratoconus) (10%). Conclusion: Patients who requested keratorefractive surgery have a variety of problems and warrant comprehensive attention to selection criteria on the part of the surgeon. Corneal topographies and pachymetry of refractive surgery candidates need to be read cautiously. High-refractive error, keratoconus and insufficient corneal thickness were found to be the leading reasons for not performing keratorefractive surgery in this study. PMID:21180437

VUV thin films, chapter 7

NASA Technical Reports Server (NTRS)

Zukic, Muamer; Torr, Douglas G.

1993-01-01

The application of thin film technology to the vacuum ultraviolet (VUV) wavelength region from 120 nm to 230 nm has not been fully exploited in the past because of absorption effects which complicate the accurate determination of the optical functions of dielectric materials. The problem therefore reduces to that of determining the real and imaginary parts of a complex optical function, namely the frequency dependent refractive index n and extinction coefficient k. We discuss techniques for the inverse retrieval of n and k for dielectric materials at VUV wavelengths from measurements of their reflectance and transmittance. Suitable substrate and film materials are identified for application in the VUV. Such applications include coatings for the fabrication of narrow and broadband filters and beamsplitters. The availability of such devices open the VUV regime to high resolution photometry, interferometry and polarimetry both for space based and laboratory applications. This chapter deals with the optics of absorbing multilayers, the determination of the optical functions for several useful materials, and the design of VUV multilayer stacks as applied to the design of narrow and broadband reflection and transmission filters and beamsplitters. Experimental techniques are discussed briefly, and several examples of the optical functions derived for selected materials are presented.

Performance impact of mutation operators of a subpopulation-based genetic algorithm for multi-robot task allocation problems.

PubMed

Liu, Chun; Kroll, Andreas

2016-01-01

Multi-robot task allocation determines the task sequence and distribution for a group of robots in multi-robot systems, which is one of constrained combinatorial optimization problems and more complex in case of cooperative tasks because they introduce additional spatial and temporal constraints. To solve multi-robot task allocation problems with cooperative tasks efficiently, a subpopulation-based genetic algorithm, a crossover-free genetic algorithm employing mutation operators and elitism selection in each subpopulation, is developed in this paper. Moreover, the impact of mutation operators (swap, insertion, inversion, displacement, and their various combinations) is analyzed when solving several industrial plant inspection problems. The experimental results show that: (1) the proposed genetic algorithm can obtain better solutions than the tested binary tournament genetic algorithm with partially mapped crossover; (2) inversion mutation performs better than other tested mutation operators when solving problems without cooperative tasks, and the swap-inversion combination performs better than other tested mutation operators/combinations when solving problems with cooperative tasks. As it is difficult to produce all desired effects with a single mutation operator, using multiple mutation operators (including both inversion and swap) is suggested when solving similar combinatorial optimization problems.

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

The inverse electroencephalography pipeline

NASA Astrophysics Data System (ADS)

Weinstein, David Michael

The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.

IPDO-2007: Inverse Problems, Design and Optimization Symposium

DTIC Science & Technology

2007-08-01

Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

Broadband All-angle Negative Refraction by Optimized Phononic Crystals.

PubMed

Li, Yang Fan; Meng, Fei; Zhou, Shiwei; Lu, Ming-Hui; Huang, Xiaodong

2017-08-07

All-angle negative refraction (AANR) of phononic crystals and its frequency range are dependent on mechanical properties of constituent materials and their spatial distribution. So far, it is impossible to achieve the maximum operation frequency range of AANR theoretically. In this paper, we will present a numerical approach for designing a two-dimensional phononic crystal with broadband AANR without negative index. Through analyzing the mechanism of AANR, a topology optimization problem aiming at broadband AANR is established and solved by bi-directional evolutionary structural optimization method. The optimal steel/air phononic crystal exhibits a record AANR range over 20% and its refractive properties and focusing effects are further investigated. The results demonstrate the multifunctionality of a flat phononic slab including superlensing effect near upper AANR frequencies and self-collimation at lower AANR frequencies.

Holographic interferometry applied to the measurement of displacements of the interior points of transparent bodies.

PubMed

Sciammarella, C A; Gilbert, J A

1976-09-01

Utilizing the light scattering property of transparent media, holographic interferometry is applied to the measurement of displacement at the interior planes of three dimensional bodies. The use of a double beam illumination and the introduction of a fictitious displacement make it feasible to obtain information corresponding to components of displacement projected on the scattering plane. When the proposed techniques are invoked, it is possible to eliminate the use of a matching index of refraction fluid in many problems involving symmetrically loaded prismatic bodies. Scattered light holographic interferometry is limited in its use to small changes in the index of refraction and to low values of relative retardation. In spite of these restrictions, a large number of technical problems in both statics and dynamics can be solved.

Critical Zone structure inferred from multiscale near surface geophysical and hydrological data across hillslopes at the Eel River CZO

NASA Astrophysics Data System (ADS)

Lee, S. S.; Rempe, D. M.; Holbrook, W. S.; Schmidt, L.; Hahm, W. J.; Dietrich, W. E.

2017-12-01

Except for boreholes and road cut, landslide, and quarry exposures, the subsurface structure of the critical zone (CZ) of weathered bedrock is relatively invisible and unmapped, yet this structure controls the short and long term fluxes of water and solutes. Non-invasive geophysical methods such as seismic refraction are widely applied to image the structure of the CZ at the hillslope scale. However, interpretations of such data are often limited due to heterogeneity and anisotropy contributed from fracturing, moisture content, and mineralogy on the seismic signal. We develop a quantitative framework for using seismic refraction tomography from intersecting geophysical surveys and hydrologic data obtained at the Eel River Critical Zone Observatory (ERCZO) in Northern California to help quantify the nature of subsurface structure across multiple hillslopes of varying topography in the area. To enhance our understanding of modeled velocity gradients and boundaries in relation to lithological properties, we compare refraction tomography results with borehole logs of nuclear magnetic resonance (NMR), gamma and neutron density, standard penetration testing, and observation drilling logs. We also incorporate laboratory scale rock characterization including mineralogical and elemental analyses as well as porosity and density measurements made via pycnometry, helium and mercury porosimetry, and laboratory scale NMR. We evaluate the sensitivity of seismically inferred saprolite-weathered bedrock and weathered-unweathered bedrock boundaries to various velocity and inversion parameters in relation with other macro scale processes such as gravitational and tectonic forces in influencing weathered bedrock velocities. Together, our sensitivity analyses and multi-method data comparison provide insight into the interpretation of seismic refraction tomography for the quantification of CZ structure and hydrologic dynamics.

Nonlinear Programming shallow tomography improves deep structure imaging

NASA Astrophysics Data System (ADS)

Li, J.; Morozov, I.

2004-05-01

In areas with strong variations in topography or near-surface lithology, conventional seismic data processing methods do not produce clear images, neither shallow nor deep. The conventional reflection data processing methods do not resolve stacking velocities at very shallow depth; however, refraction tomography can be used to obtain the near-surface velocities. We use Nonlinear Programming (NP) via known velocity and depth in points from shallow boreholes and outcrop as well as derivation of slowness as constraint conditions to gain accurate shallow velocities. We apply this method to a 2D reflection survey shot across the Flame Mountain, a typical mountain with high gas reserve volume in Western China, by PetroChina and BGP in 1990s. The area has a highly rugged topography with strong variations of lithology near the surface. Over its hillside, the quality of reflection data is very good, but on the mountain ridge, reflection quality is poorer. Because of strong noise, only the first breaks are clear in the records, with velocities varying by more than 3 times in the near offsets. Because this region contains a steep cliff and an overthrust fold, it is very difficult to find a standard refraction horizon, therefore, GLI refractive statics conventional field and residual statics do not result in a good image. Our processing approach includes: 1) The Herglotz-Wiechert method to derive a starting velocity model which is better than horizontal velocity model; 2) using shallow boreholes and geological data, construct smoothness constraints on the velocity field as well as; 3) perform tomographic velocity inversion by NP algorithm; 4) by using the resulting accurate shallow velocities, derive the statics to correct the seismic data for the complex near-surface velocity variations. The result indicates that shallow refraction tomography can greatly improve deep seismic images in complex surface conditions.

A preprocessing strategy for helioseismic inversions

NASA Astrophysics Data System (ADS)

Christensen-Dalsgaard, J.; Thompson, M. J.

1993-05-01

Helioseismic inversion in general involves considerable computational expense, due to the large number of modes that is typically considered. This is true in particular of the widely used optimally localized averages (OLA) inversion methods, which require the inversion of one or more matrices whose order is the number of modes in the set. However, the number of practically independent pieces of information that a large helioseismic mode set contains is very much less than the number of modes, suggesting that the set might first be reduced before the expensive inversion is performed. We demonstrate with a model problem that by first performing a singular value decomposition the original problem may be transformed into a much smaller one, reducing considerably the cost of the OLA inversion and with no significant loss of information.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Refractive errors among patients attending the ophthalmology department of a medical college in North-East India

PubMed Central

Natung, Tanie; Taye, Trishna; Lyngdoh, Laura Amanda; Dkhar, Begonia; Hajong, Ranendra

2017-01-01

Purpose: To determine the magnitude and pattern of refractive errors among patients attending the ophthalmology department of a new medical college in North-East India. Materials and Methods: A prospective study of the new patients (age ≥5 years), who were phakic and whose unaided visual acuities were worse than 20/20 but improved with pinhole, was done. Complete ophthalmic examination and refraction with appropriate cycloplegia for age were done for the 4582 eligible patients. Spherical equivalents (SE) of refractive errors of the right eyes were used for analysis. Results: Of the 4582 eligible patients, 2546 patients had refractive errors (55.56%). The proportion of emmetropia (SE − 0.50–+0.50 diopter sphere [DS]), myopia (SE <−0.50 DS), high myopia (SE >−5.0 DS), and hypermetropia (>+0.50 DS for adults and >+2.0 DS for children) were 53.1%, 27.4%, 2.6%, and 16.9%, respectively. The proportion of hyperopia increased till 59 years and then decreased with age (P = 0.000). The proportion of myopia and high myopia decreased significantly with age after 39 years (P = 0.000 and P = 0.004, respectively). Of the 1510 patients with astigmatism, 17% had with-the-rule (WTR), 23.4% had against-the-rule (ATR), and 19% had oblique astigmatisms. The proportion of WTR and ATR astigmatisms significantly decreased (P = 0.000) and increased (P = 0.000) with age, respectively. Conclusions: This study has provided the magnitude and pattern of refractive errors in the study population. It will serve as the initial step for conducting community-based studies on the prevalence of refractive errors in this part of the country since such data are lacking from this region. Moreover, this study will help the primary care physicians to have an overview of the magnitude and pattern of refractive errors presenting to a health-care center as refractive error is an established and significant public health problem worldwide. PMID:29417005

Refractive errors among patients attending the ophthalmology department of a medical college in North-East India.

PubMed

Natung, Tanie; Taye, Trishna; Lyngdoh, Laura Amanda; Dkhar, Begonia; Hajong, Ranendra

2017-01-01

To determine the magnitude and pattern of refractive errors among patients attending the ophthalmology department of a new medical college in North-East India. A prospective study of the new patients (age ≥5 years), who were phakic and whose unaided visual acuities were worse than 20/20 but improved with pinhole, was done. Complete ophthalmic examination and refraction with appropriate cycloplegia for age were done for the 4582 eligible patients. Spherical equivalents (SE) of refractive errors of the right eyes were used for analysis. Of the 4582 eligible patients, 2546 patients had refractive errors (55.56%). The proportion of emmetropia (SE - 0.50-+0.50 diopter sphere [DS]), myopia (SE <-0.50 DS), high myopia (SE >-5.0 DS), and hypermetropia (>+0.50 DS for adults and >+2.0 DS for children) were 53.1%, 27.4%, 2.6%, and 16.9%, respectively. The proportion of hyperopia increased till 59 years and then decreased with age ( P = 0.000). The proportion of myopia and high myopia decreased significantly with age after 39 years ( P = 0.000 and P = 0.004, respectively). Of the 1510 patients with astigmatism, 17% had with-the-rule (WTR), 23.4% had against-the-rule (ATR), and 19% had oblique astigmatisms. The proportion of WTR and ATR astigmatisms significantly decreased ( P = 0.000) and increased ( P = 0.000) with age, respectively. This study has provided the magnitude and pattern of refractive errors in the study population. It will serve as the initial step for conducting community-based studies on the prevalence of refractive errors in this part of the country since such data are lacking from this region. Moreover, this study will help the primary care physicians to have an overview of the magnitude and pattern of refractive errors presenting to a health-care center as refractive error is an established and significant public health problem worldwide.

Performance of a Quintuple-GEM Based RICHDetector Prototype

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blatnik, Marie; Dehmelt, Klaus; Deshpande, Abhay

2015-12-17

Cerenkov technology is often the optimal choice for particle identification in high energy particle collision applications. Typically, the most challenging regime is at high pseudorapidity (forward) where particle identification must perform well at high laboratory momenta. For the upcoming electron ion collider (EIC), the physics goals require hadron (π, K, p) identification up to ~50 GeV/c. In this region Cerenkov ring-imaging (RICH) is the most viable solution. The speed of light in a radiator medium is inversely proportional to the refractive index. Hence, for particle identification (PID) reaching out to high momenta a small index of refraction is required. Unfortunately,more » the lowest indices of refraction also result in the lowest light yield ([(dNγ)/dx] ∝ sin2(θC)) driving up the radiator length and thereby the overall detector cost. In this paper we report on a successful test of a compact RICH detector (1 meter radiator) capable of delivering in excess of 10 photoelectrons per ring with a low index radiator gas (CF4). The detector concept is a natural extension of the PHENIX hadron-blind detector (HBD) achieved by adding focusing capability at low wavelength and adequate gain for high efficiency detection of single-electron induced avalanches. Our results indicate that this technology is indeed a viable choice in the forward direction of the EIC. The setup and results are described within.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE PAGES

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

2017-10-29

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Final Report: Resolving and Discriminating Overlapping Anomalies from Multiple Objects in Cluttered Environments

DTIC Science & Technology

2015-12-15

UXO community . NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Irma Shamatava 0.50 0.50 1 Resolving and Discriminating...Distinguishing an object of interest from innocuous items is the main problem that the UXO community is facing currently. This inverse problem...innocuous items is the main problem that the UXO community is facing currently. This inverse problem demands fast and accurate representation of

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yun; Zhang, Yin

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as smallmore » as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.« less

Data analysis and calibration for a bulk-refractive-index-compensated surface plasmon resonance affinity sensor

NASA Astrophysics Data System (ADS)

Chinowsky, Timothy M.; Yee, Sinclair S.

2002-02-01

Surface plasmon resonance (SPR) affinity sensing, the problem of bulk refractive index (RI) interference in SPR sensing, and a sensor developed to overcome this problem are briefly reviewed. The sensor uses a design based on Texas Instruments' Spreeta SPR sensor to simultaneously measure both bulk and surface RI. The bulk RI measurement is then used to compensate the surface measurement and remove the effects of bulk RI interference. To achieve accurate compensation, robust data analysis and calibration techniques are necessary. Simple linear data analysis techniques derived from measurements of the sensor response were found to provide a versatile, low noise method for extracting measurements of bulk and surface refractive index from the raw sensor data. Automatic calibration using RI gradients was used to correct the linear estimates, enabling the sensor to produce accurate data even when the sensor has a complicated nonlinear response which varies with time. The calibration procedure is described, and the factors influencing calibration accuracy are discussed. Data analysis and calibration principles are illustrated with an experiment in which sucrose and detergent solutions are used to produce changes in bulk and surface RI, respectively.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Viscoelastic material inversion using Sierra-SD and ROL

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis

2014-11-01

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

PubMed Central

Louis, A. K.

2006-01-01

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts. PMID:23165060

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

NASA Astrophysics Data System (ADS)

Marinoni, Marianna; Delay, Frederick; Ackerer, Philippe; Riva, Monica; Guadagnini, Alberto

2016-08-01

We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A. In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy's law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg-Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

Coupling of Large Amplitude Inversion with Other States

NASA Astrophysics Data System (ADS)

Pearson, John; Yu, Shanshan

2016-06-01

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

An approach to quantum-computational hydrologic inverse analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Inverse opal photonic crystals with photonic band gaps in the visible and near-infrared

NASA Astrophysics Data System (ADS)

Jarvis, Brandon C.; Gilleland, Cody L.; Renfro, Tim; Gutierrez, Jose; Parikh, Kunjal; Glosser, R.; Landon, Preston B.

2005-08-01

Colloidal silica spheres with 200nm, 250nm, and 290nm diameters were self-assembled with single crystal crystallites 4-5mm wide and 10-15mm long. Larger spheres with diameters between 1000-2300nm were self-assembled with single crystal crystallites up to 1.5mm wide and 2mm long. The silica opals self-assembled vertically along the [100] direction of the face centered cubic lattice resulting in self-templated opals. Inverse opal photonic crystals with a partial band gap possessing a maximum in the near infrared at 3.8μm were constructed from opal templates composed of 2300nm diameter spheres with chalcogenide Ge33As12Se55 (AMTIR-1), a transparent glass in the near infrared with high refractive index. Inverse gold and gold/ polypropylene composite photonic crystals were fabricated from synthetic opal templates composed of 200-290nm silica spheres. The reflectance spectra and electrical conductance of the resulting structures is presented. Gold was infiltrated into opal templates as gold chloride and heat converted to metallic gold. Opals partially infiltrated with gold were co-infiltrated with polypropylene plastic for mechanical support prior to removal of the silica template with hydrofluoric acid.

Development of a refractive error quality of life scale for Thai adults (the REQ-Thai).

PubMed

Sukhawarn, Roongthip; Wiratchai, Nonglak; Tatsanavivat, Pyatat; Pitiyanuwat, Somwung; Kanato, Manop; Srivannaboon, Sabong; Guyatt, Gordon H

2011-08-01

To develop a scale for measuring refractive error quality of life (QOL) for Thai adults. The full survey comprised 424 respondents from 5 medical centers in Bangkok and from 3 medical centers in Chiangmai, Songkla and KhonKaen provinces. Participants were emmetropes and persons with refractive correction with visual acuity of 20/30 or better An item reduction process was employed by combining 3 methods-expert opinion, impact method and item-total correlation methods. The classical reliability testing and the validity testing including convergent, discriminative and construct validity was performed. The developed questionnaire comprised 87 items in 6 dimensions: 1) quality of vision, 2) visual function, 3) social function, 4) psychological function, 5) symptoms and 6) refractive correction problems. It is the 5-level Likert scale type. The Cronbach's Alpha coefficients of its dimensions ranged from 0.756 to 0. 979. All validity testing were shown to be valid. The construct validity was validated by the confirmatory factor analysis. A short version questionnaire comprised 48 items with good reliability and validity was also developed. This is the first validated instrument for measuring refractive error quality of life for Thai adults that was developed with strong research methodology and large sample size.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

DTIC Science & Technology

1988-09-14

Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

Green Color Purification in Tb(3+) Ions through Silica Inverse Opal Heterostructure.

PubMed

Shrivastava, Vishnu Prasad; Sivakumar, Sri; Kumar, Jitendra

2015-06-10

The ordered SiO2:Tb(3+) inverse opal heterostructure films are fabricated through polystyrene spheres hetero-opal template using the convective self-assembly method to examine their potential for color purification. Their optical properties and photoluminescence have been investigated and compared with individual single inverse opals and reference (SiO2:Tb(3+) powder). The heterostructures are shown to possess two broad photonic stop bands separated by an effective pass band, causing suppression of blue, orange, and red emission bands corresponding to (5)D4 → (7)F(j); j = 6, 4, 3 transitions, respectively and an enhancement of green emission (i.e., (5)D4 → (7)F5). Although the suppression of various emission occurs because of its overlap with the photonic band gaps (PSBs), the enhancement of green radiation is observed because of its location matching with the pass band region. The Commission International de l'Eclairage (CIE) chromaticity coordinates of the emission spectrum of the heterostructure based on polystyrene sphere of 390 and 500 nm diameter are x = 0.2936, y = 0.6512 and lie closest to those of standard green color (wavelength 545 nm). In addition, a significant increase observed in luminescence lifetime for (5)D4 level of terbium in inverse opal heterostructures vis-à-vis reference (SiO2:Tb(3+) powder) is attributed to the change in the effective refractive index.

Numerical modeling of thermal refraction inliquids in the transient regime.

PubMed

Kovsh, D; Hagan, D; Van Stryland, E

1999-04-12

We present the results of modeling of nanosecond pulse propagation in optically absorbing liquid media. Acoustic and electromagnetic wave equations must be solved simultaneously to model refractive index changes due to thermal expansion and/or electrostriction, which are highly transient phenomena on a nanosecond time scale. Although we consider situations with cylindrical symmetry and where the paraxial approximation is valid, this is still a computation-intensive problem, as beam propagation through optically thick media must be modeled. We compare the full solution of the acoustic wave equation with the approximation of instantaneous expansion (steady-state solution) and hence determine the regimes of validity of this approximation. We also find that the refractive index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulsewidth and the acoustic transit time exceeds a factor of unity.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Deconvolution using a neural network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehman, S.K.

1990-11-15

Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.

Genetics Home Reference: Koolen-de Vries syndrome

MedlinePlus

... of Koolen-de Vries syndrome , has undergone an inversion . An inversion involves two breaks in a chromosome; the resulting ... lineage have no health problems related to the inversion. However, genetic material can be lost or duplicated ...

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

Low dose reconstruction algorithm for differential phase contrast imaging.

PubMed

Wang, Zhentian; Huang, Zhifeng; Zhang, Li; Chen, Zhiqiang; Kang, Kejun; Yin, Hongxia; Wang, Zhenchang; Marco, Stampanoni

2011-01-01

Differential phase contrast imaging computed tomography (DPCI-CT) is a novel x-ray inspection method to reconstruct the distribution of refraction index rather than the attenuation coefficient in weakly absorbing samples. In this paper, we propose an iterative reconstruction algorithm for DPCI-CT which benefits from the new compressed sensing theory. We first realize a differential algebraic reconstruction technique (DART) by discretizing the projection process of the differential phase contrast imaging into a linear partial derivative matrix. In this way the compressed sensing reconstruction problem of DPCI reconstruction can be transformed to a resolved problem in the transmission imaging CT. Our algorithm has the potential to reconstruct the refraction index distribution of the sample from highly undersampled projection data. Thus it can significantly reduce the dose and inspection time. The proposed algorithm has been validated by numerical simulations and actual experiments.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Contact lenses and corrective flying spectacles in military aircrew--implications for flight safety.

PubMed

Partner, Andrew M; Scott, Robert A H; Shaw, Penny; Coker, William J

2005-07-01

Refractive devices used by aviators need to suit the aerospace environment or their failure can have serious implications. A relatively minor visual disability can result in loss of life and aircraft. We surveyed commonly occurring problems with the different types of refractive correction worn by Royal Air Force (RAF) aircrew over the previous 12 mo. We also asked if they had experienced any flight safety incidents (FSI) relating to their refractive correction. A retrospective anonymous questionnaire survey was given to 700 active aircrew occupationally graded as requiring corrective flying spectacles (CFS) or contact lenses (CL) for flying. 63% (443) of the questionnaires were completed. CL were worn by 53% of aircrew; 71% of them used daily disposable CL. CFS were worn by the remaining 47% of aircrew, 14% of whom used multifocal lenses. Of CFS wearers, 83% reported problems including misting, moving, discomfort, and conflict with helmet-mounted devices (HMD). CL-related ocular symptoms were reported in 67% of wearers including cloudy vision, dry eye, photophobia, red eyes, excessive mucus formation, CL movement, itching, and grittiness. No CL-related FSI were reported over the previous 12 mo compared with 5% CFS-related FSI (p < 0.001). The graded performance of CL for vision, comfort, handling, convenience, and overall satisfaction was significantly higher than for CFS. CFS are associated with problems in terms of comfort and safety. CL are well tolerated by aircrew, and deliver improved visual performance.

Are all children with visual impairment known to the eye clinic?

PubMed

Pilling, Rachel F; Outhwaite, Louise

2017-04-01

There is a growing body of evidence that children with special needs are more likely to have visual problems, be that visual impairment, visual processing problems or refractive error. While there is widespread provision of vision screening in mainstream schools, patchy provision exists in special schools. The aim of the study was to determine the unmet need and undiagnosed visual problems of children attending primary special schools in Bradford, England. Children attending special schools who were not currently under the care of the hospital eye service were identified. Assessments of visual function and refractive error were undertaken on site at the schools by an experienced orthoptist and/or paediatric ophthalmologist. A total of 157 children were identified as eligible for the study, with a mean age of 7.8 years (range 4-12 years). Of these, 33% of children were found to have visual impairment, as defined by WHO and six children were eligible for severe sight impairment certification. The study demonstrates significant unmet need or undiagnosed visual impairment in a high-risk population. It also highlights the poor uptake of hospital eye care for children identified with significant visual needs and suggests the importance of providing in-school assessment and support, including refractive correction, to fully realise the benefits of a visual assessment programme. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Shallow subsurface imaging of northern Cascadia margin using downward continued short-streamer data

NASA Astrophysics Data System (ADS)

Yelisetti, S.; Ghosal, D.; Spence, G.

2017-12-01

Since Eocene, the Juan de Fuca plate has been subducting beneath the North American plate, scrapping off sediments from the down going plate, accreting to the margin forming frontal accretionary wedge, Crescent terrane and the Pacific Rim terrane, which are separated by landward dipping Crescent thrust and Tofino faults. In 1989, the Geological Survey of Canada has acquired several multichannel seismic lines along the northern Cascadia margin to study the subduction zone processes and the formation and distribution of methane hydrates in the accreted sediment section. Seismic reflections and refractions are recorded on a 3.6 km streamer up to 14 s using 4 ms sample rate with 183 m near-offset. In this study, we present the migrated image of line 89-06 which indicate the top of the down-going plate and several landward dipping frontal thrusts. Additionally, a bottom simulating reflector (BSR) is identified over a 20 km distance at a depth of 250 m beneath the seafloor within the accretionary wedge sediments where the water depth is around 1500-2000 m. Preliminary velocity analyses corresponding to the BSR reflection using semblance method indicate high-velocity sediment with P-wave velocities of 2.0 km/s. To better constrain the velocity distribution of such shallow subsurface features, we have analyzed the refracted arrivals from the seaward part of the Tofino basin sediment section. Specifically, we have downward continued the shot and receiver gathers to the seafloor bringing the far offset refracted phases to near offset as first arrivals. Since the refractions are not well captured over the trench deposits due to large water depth ( 2500 m) and limited streamer length, the downward continued results do not show refracted arrivals very clearly at the near offset. In contrast, moving landward along the frontal slope with gradual decrease in water depth to 1300 m and less, the effect of downward continuation seems to be more prominent bringing the refracted phases to near offset more clearly as first arrivals. More detailed first arrival tomographic velocity analysis is currently underway using these downward continued datasets. The tomographic velocity model will then be used as a starting model for future full waveform inversion to obtain the high-resolution velocity and attenuation models of the accreted sediments.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Individual differences in children's understanding of inversion and arithmetical skill.

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables

NASA Astrophysics Data System (ADS)

Kamynin, V. L.; Bukharova, T. I.

2017-01-01

We prove the estimates of stability with respect to perturbations of input data for the solutions of inverse problems for degenerate parabolic equations with unbounded coefficients. An important feature of these estimates is that the constants in these estimates are written out explicitly by the input data of the problem.

New advances in amblyopia therapy II: refractive therapies.

PubMed

Kraus, Courtney L; Culican, Susan M

2018-06-05

The treatment of anisometropic or ametropic amblyopia has traditionally enjoyed a high treatment success rate. Early initiation and consistent use of spectacle correction can completely resolve amblyopia in a majority of patients. For those with anisometropic amblyopia that fail to improve with glasses wear alone, patching or atropine penalisation can lead to equalisation of visual acuity. However, successful treatment requires full-time compliance with refractive correction and this can be a challenge for a patient population that often has one eye with good acuity without correction. Other barriers for a select population with high anisometropic or ametropic amblyopia include rejection of glasses for various reasons including discomfort, behavioural or sensory problems, postural issues and visually significant aniseikonia. When consistent wear of optical correction proves difficult and patching/atropine remains a major obstacle, surgical correction of refractive error has proven success in achieving vision improvement. Acting as a means to achieve spectacle independence or reducing the overall needed refractive correction, refractive surgery can offer a unique treatment option for this patient population. Laser surgery, phakic intraocular lenses and clear lens exchange are three approaches to altering the refractive state of the eye. Each has documented success in improving vision, particularly in populations where glasses wear has not been possible. Surgical correction of refractive error has a risk profile greater than that of more traditional therapies. However, its use in a specific population offers the opportunity for improving visual acuity in children who otherwise have poor outcomes with glasses and patching/atropine alone. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Prevalence of refractive errors in children in India: a systematic review.

PubMed

Sheeladevi, Sethu; Seelam, Bharani; Nukella, Phanindra B; Modi, Aditi; Ali, Rahul; Keay, Lisa

2018-04-22

Uncorrected refractive error is an avoidable cause of visual impairment which affects children in India. The objective of this review is to estimate the prevalence of refractive errors in children ≤ 15 years of age. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines were followed in this review. A detailed literature search was performed to include all population and school-based studies published from India between January 1990 and January 2017, using the Cochrane Library, Medline and Embase. The quality of the included studies was assessed based on a critical appraisal tool developed for systematic reviews of prevalence studies. Four population-based studies and eight school-based studies were included. The overall prevalence of refractive error per 100 children was 8.0 (CI: 7.4-8.1) and in schools it was 10.8 (CI: 10.5-11.2). The population-based prevalence of myopia, hyperopia (≥ +2.00 D) and astigmatism was 5.3 per cent, 4.0 per cent and 5.4 per cent, respectively. Combined refractive error and myopia alone were higher in urban areas compared to rural areas (odds ratio [OR]: 2.27 [CI: 2.09-2.45]) and (OR: 2.12 [CI: 1.79-2.50]), respectively. The prevalence of combined refractive errors and myopia alone in schools was higher among girls than boys (OR: 1.2 [CI: 1.1-1.3] and OR: 1.1 [CI: 1.1-1.2]), respectively. However, hyperopia was more prevalent among boys than girls in schools (OR: 2.1 [CI: 1.8-2.4]). Refractive error in children in India is a major public health problem and requires concerted efforts from various stakeholders including the health care workforce, education professionals and parents, to manage this issue. © 2018 Optometry Australia.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

Elliptical concentrators.

PubMed

Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio

2006-10-10

Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

Fabrication and characterization of a planar gradient-index, plasma-enhanced chemical vapor deposition lens.

PubMed

Beltrami, D R; Love, J D; Durandet, A; Samo, A; Cogswell, C J

1997-10-01

A thin, one-dimensional, gradient-index slab lens with a parabolic profile was designed and fabricated in fluorine-doped silica by use of plasma-enhanced chemical vapor deposition in a Helicon plasma reactor. The refractive-index profile of the fabricated lens was determined by the application of an inversion technique to the values of modal effective index measured with a prism coupler. The periodic refocusing property of the lens and the independence of the wavelength were measured with the fluorescence of a specially doped, thin polymer layer spin-coated onto the surface of the lens.

Thermophysical properties of parahydrogen from the freezing liquid line to 5000 R for pressures to 10000 psia

NASA Technical Reports Server (NTRS)

Mccarty, R. D.; Weber, L. A.

1972-01-01

The tables include entropy, enthalpy, internal energy, density, volume, speed of sound, specific heat, thermal conductivity, viscosity, thermal diffusivity, Prandtl number, and the dielectric constant for 65 isobars. Quantities of special utility in heat transfer and thermodynamic calculations are also included in the isobaric tables. In addition to the isobaric tables, tables for the saturated vapor and liquid are given, which include all of the above properties, plus the surface tension. Tables for the P-T of the freezing liquid, index of refraction, and the derived Joule-Thomson inversion curve are also presented.

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Solving inversion problems with neural networks

NASA Technical Reports Server (NTRS)

Kamgar-Parsi, Behzad; Gualtieri, J. A.

1990-01-01

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Visual impairment and spectacle coverage rate in Baoshan district, China: population-based study

PubMed Central

2013-01-01

Background To investigate the prevalence and risk factors of visual impairment associated with refractive error and the unmet need for spectacles in a special suburban senior population in Baoshan District of Shanghai, one of several rural areas undergoing a transition from rural to urban area, where data of visual impairment are limited. Methods The study was a population based survey of 4545 Chinese aged (age: >60 years or older ) at Baoshan, Shanghai, in 2009. One copy of questionnaire was completed for each subject. Examinations included a standardized refraction and measurement of presenting and best corrected visual acuity (BCVA) as well as tonometry, slit lamp biomicroscopy, and fundus photography. Results The prevalence of mild (6/12 to 6/18), moderate (6/18 to 6/60) and severe visual impairment was 12.59%, 8.38% and 0.44%, respectively, and 5.26%, 3.06% and 0.09% with refractive correction. Visual impairment was associated with age, gender, education and career, but not insurance . The prevalence of correctable visual impairment was 5.81% (using 6/18 cutoff) and 13.18% (using 6/12 cutoff). Senior people and women were significantly at a higher risk of correctable visual impairment, while the well-educated on the contrary. The prevalence of undercorrected refractive error (improves by 2 or more lines with refraction) was 24.84%, and the proportion with undercorrected refractive error for mild, moderate , severe and no visual impairment was 61.54%, 67.98%, 60.00% and 14.10%, respectively. The spectacle coverage rate was 44.12%. Greater unmet need for spectacles was observed among elderly people, females, non-peasant, and subjects with less education and astigmatism only. Conclusions High prevalence of visual impairment, visual impairment alleviated by refractive correction, and low spectacle coverage existed among the senior population in Baoshan District of Shanghai. Education for the public of the importance of regular examination and appropriate and accessible refraction service might be helpful to solve the problem. PMID:23566106

Child Development and Refractive Errors in Preschool Children

PubMed Central

Ibironke, Josephine O.; Friedman, David S.; Repka, Michael X.; Katz, Joanne; Giordano, Lydia; Hawse, Patricia; Tielsch, James M.

2011-01-01

Purpose Many parents are concerned about their child's development. The purpose of this study is to determine if parental concerns about overall development are associated with significant refractive errors among urban preschool children. Methods A cross-sectional population-based study was conducted to evaluate the prevalence of ocular disorders in white and African American children 6 through 71 months of age in Baltimore, Maryland, United States. A comprehensive eye examination with cycloplegic refraction was performed. Parental concerns about development were measured with the Parents' Evaluation of Developmental Status screening tool. 2381 of 2546 eligible children (93.5%) completed the refraction and the parental interview. Results Parental concerns about development were present in 510 of the 2381 children evaluated (21.4%; 95% CI: 9.8% – 23.1%). The adjusted odds ratios [OR] of parental concerns with hyperopia (≥ 3.00D) was 1.26 (95% CI: 0.90 – 1.74), with myopia (≥ 1.00D) was 1.29 (95% CI: 0.83 – 2.03), with astigmatism (≥ 1.50D) was 1.44 (95% CI: 1.08 – 1.93) irrespective of the type of astigmatism, and with anisometropia ≥ 2.00D was 2.61 (95% CI: 1.07 – 6.34). The odds of parental concerns about development significantly increased in children older than 36 months with hyperopia ≥ 3.00D, astigmatism ≥ 1.50D, or anisometropia ≥ 2.00D. Conclusions Parental concerns about general developmental problems were associated with some types of refractive error, astigmatism ≥ 1.50D and anisometropia ≥ 2.00D in children ages 6 to 71 months. Parental concerns were also more likely in children older than 36 months of age with hypermetropia, astigmatism or anisometropia. Parental concerns were not associated with myopia. Due to the potential consequences of uncorrected refractive errors, children whose parents have expressed concerns regarding development should be referred for an eye examination with cycloplegic refraction to rule out significant refractive errors. PMID:21150680

Laser induced optical bleaching in Ge{sub 12}Sb{sub 25}S{sub 63} chalcogenide thin film

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naik, Ramakanta, E-mail: ramakanta.naik@gmail.com; Jena, S.; Sahoo, N. K.

2015-06-24

Photo induced effects of Ge{sub 12}Sb{sub 25}S{sub 63} films illuminated with 532 nm laser light is investigated from transmission spectra measured by FTIR spectroscopy. The material exhibit photo bleaching (PB) when exposed to band gap laser for a prolonged time in vacuum. The PB is ascribed to structural changes inside the film as well as surface photo oxidation. The amorphous nature of thin films was detected by X-ray diffraction. The chemical composition of the deposited thin films was examined by Energy Dispersive X-ray Analysis (EDAX). The refractive indices of the films were obtained from the transmission spectra based on inverse synthesismore » method, and the optical band gaps were derived from optical absorption spectra using the Tauc plot. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple–DiDomenico model. It was found that, the mechanism of the optical absorption follows the rule of the allowed non-direct transition. Raman spectra analysis also supports the optical changes.« less

Comparison of monomode KTiOPO4 waveguide formed by C3+ ion implantation and Rb+ ion exchange

NASA Astrophysics Data System (ADS)

Cui, Xiao-Jun; Wang, Liang-Ling

2017-02-01

In this work, we report on the formation and characterization of monomode KTiOPO4 waveguide at 1539 nm by 6.0 MeV C3+ ion implantation with the dose of 2×1015 ions/cm2 and Rb+-K+ ion exchange, respectively. The relative intensity of light as a function of effective refractive index of TM modes at 633 nm and 1539 nm for KTiOPO4 waveguide formed by two different methods were compared with the prism coupling technique. The refractive index (nz) profile for the ion implanted waveguide was reconstructed by reflectivity calculation method, and one for the ion exchanged waveguide was by inverse Wentzel-Kramers-Brillouin. The nuclear energy loss versus penetration depth of the C3+ ions implantation into KTiOPO4 was simulated using the Stopping Range of Ions in Matter software. The Rutherford Backscattering Spectrometry spectrum of KTiOPO4 waveguide was analyzed after ions exchanged. The results showed that monomode waveguide at 1539 nm can be formed by ion implantation and Rb+ -K+ ion exchange, respectively.

Wave propagation in pulsar magnetospheres - Refraction of rays in the open flux zone

NASA Technical Reports Server (NTRS)

Barnard, J. J.; Arons, J.

1986-01-01

The propagation of waves through a relativistically outflowing electron-positron plasma in a very strong dipolar magnetic field, conditions expected in pulsar magnetospheres, is investigated. Halmilton's equations is derived for the propagation of rays through a plasma which is inhomogeneous in density, magnetic field directions, and Lorentz factor. These equations are solved for rays propagating through the plasmas outflowing along the 'open' dipolar field lines in which the density decreases inversely as the radius cubed and in the case where gradients transverse to the radial direction exist. In the radial case, the effects of refraction on pulse profiles, spectrum, and polarization are examined, and the effects of a transverse gradient are indicated. Attention is given to models in which the observed broad bandwidth in the radio emission has its origin in a radius to frequency map. Models with broad-band emission at a single radius are also studied. These are compared to observations of pulse width and pulse component separation as a function of frequency. The origin of 'orthogonal modes' is discussed.

A proposed method for wind velocity measurement from space

NASA Technical Reports Server (NTRS)

Censor, D.; Levine, D. M.

1980-01-01

An investigation was made of the feasibility of making wind velocity measurements from space by monitoring the apparent change in the refractive index of the atmosphere induced by motion of the air. The physical principle is the same as that resulting in the phase changes measured in the Fizeau experiment. It is proposed that this phase change could be measured using a three cornered arrangement of satellite borne source and reflectors, around which two laser beams propagate in opposite directions. It is shown that even though the velocity of the satellites is much larger than the wind velocity, factors such as change in satellite position and Doppler shifts can be taken into account in a reasonable manner and the Fizeau phase measured. This phase measurement yields an average wind velocity along the ray path through the atmosphere. The method requires neither high accuracy for satellite position or velocity, nor precise knowledge of the refractive index or its gradient in the atmosphere. However, the method intrinsically yields wind velocity integrated along the ray path; hence to obtain higher spatial resolution, inversion techniques are required.

Ray propagation in oblate atmospheres. [for Jupiter

NASA Technical Reports Server (NTRS)

Hubbard, W. B.

1976-01-01

Phinney and Anderson's (1968) exact theory for the inversion of radio-occultation data for planetary atmospheres breaks down seriously when applied to occultations by oblate atmospheres because of departures from Bouguer's law. It has been proposed that this breakdown can be overcome by transforming the theory to a local spherical symmetry which osculates a ray's point of closest approach. The accuracy of this transformation procedure is assessed by evaluating the size of terms which are intrinsic to an oblate atmosphere and which are not eliminated by a local spherical approximation. The departures from Bouguer's law are analyzed, and it is shown that in the lowest-order deviation from that law, the plane of refraction is defined by the normal to the atmosphere at closest approach. In the next order, it is found that the oblateness of the atmosphere 'warps' the ray path out of a single plane, but the effect appears to be negligible for most purposes. It is concluded that there seems to be no source of serious error in making an approximation of local spherical symmetry with the refraction plane defined by the normal at closest approach.

Controlled thickness and dielectric constant titanium-doped SiO2 thin films on silicon by sol gel process

NASA Astrophysics Data System (ADS)

Liu, H. L.; Wang, S. S.; Zhou, Yan; Lam, Yee Loy; Chan, Yuen Chuen; Kam, Chan Hin

1997-08-01

In this paper, we report the preparation of crack-free relatively thick SiO2-TiO2 thin films on silicon substrates using the sol-gel spin-coating method. The influence of the process parameters on the quality of the film, such as the solution condition, the spin-coating speed, the heat treatment temperature and time, have been studied. We found that the cracking of the film could be avoided by selecting the right sol composition ratios, adding PVA to the sold and properly controlling the heat treatment. Most importantly, we discovered that by polishing the edges of the film after the deposition of each single layer, the number of such layers that deposited without crack formation could be substantially increased. The refractive index profile and thickness of the film have been determined using prism coupling technique and the inverse WKB method. The refractive index was found to depend on the content of TiO2 as well as the heat treatment condition. Using an AFM, the surface morphology of the film was found to be good.

Integrated Geophysical Investigation of Preferential Flow Paths at the Former Tyson Valley Powder Farm near Eureka, Missouri, May 2006

USGS Publications Warehouse

Burton, Bethany L.; Ball, Lyndsay B.; Stanton, Gregory P.; Hobza, Christopher M.

2009-01-01

In May 2006, the U.S. Geological Survey, in cooperation with the U.S. Army Corps of Engineers, conducted surface and borehole geophysical surveys at the former Tyson Valley Powder Farm near Eureka, Mo., to identify preferential pathways for potential contaminant transport along the bedrock surface and into dissolution-enhanced fractures. The Tyson Valley Powder Farm was formerly used as a munitions storage and disposal facility in the 1940s and 1950s, and the site at which the surveys were performed was a disposal area for munitions and waste solvents such as trichloroethylene and dichloroethylene. Direct-current resistivity and seismic refraction data were acquired on the surface; gamma, electromagnetic induction, and full waveform sonic logs were acquired in accessible boreholes. Through the combined interpretation of the seismic refraction tomographic and resistivity inversion results and borehole logs, inconsistencies in the bedrock surface were identified that may provide horizontal preferential flow paths for dense nonaqueous phase liquid contaminants. These results, interpreted and displayed in georeferenced three-dimensional space, should help to establish more effective monitoring and remediation strategies.

Anisometric C 60 Fullerene Colloids Assisted by Structure-Directing Agent

DOE Office of Scientific and Technical Information (OSTI.GOV)

Penterman, S.; Liddell Watson, Chekesha M.; Escobedo, Fernando A.

2016-08-05

Colloidal synthesis and assembly provide low cost, large area routes to mesoscale structures. In particular, shape-anisotropic particles may form crystalline, plastic crystalline, complex liquid crystalline and glassy phases. Arrangements in each order class have been used to generate photonic materials. For example, large photonic band gaps have been found for photonic crystals, hyperuniform photonic glasses, and also for plastic crystals at sufficient refractive index contrast. The latter structures support highly isotropic bandgaps that are desirable for free-form waveguides and LED out-coupling. Photonic glasses with optical gain lead to self-tuned lasing by the superposition of multiply scattered light. Typically, extrinsic mediamore » such as organic dyes, rare earths, lanthanides and quantum dots are used to impart optical gain in photonic solids. The present work advances fullerene microcrystals as a new materials platform for ‘active’ light emitting in colloid-based photonic crystals. Fullerenes support singlet excited states that recombine to produce a characteristic red photoluminescence. C 60 also has a high refractive index (n ~ 2.2) and transparency (> 560 nm) 9 so that inverse structures are not required.« less

Correlation of Geophysical and Geotechnical Methods for Sediment Mapping in Sungai Batu, Kedah

NASA Astrophysics Data System (ADS)

Zakaria, M. T.; Taib, A.; Saidin, M. M.; Saad, R.; Muztaza, N. M.; Masnan, S. S. K.

2018-04-01

Exploration geophysics is widely used to map the subsurface characteristics of a region, to understand the underlying rock structures and spatial distribution of rock units. 2-D resistivity and seismic refraction methods were conducted in Sungai Batu locality with objective to identify and map the sediment deposit with correlation of borehole record. 2-D resistivity data was acquire using ABEM SAS4000 system with Pole-dipole array and 2.5 m minimum electrode spacing while for seismic refraction ABEM MK8 seismograph was used to record the seismic data and 5 kg sledgehammer used as a seismic source with geophones interval of 5 m spacing. The inversion model of 2-D resistivity result shows that, the resistivity values <100 Ωm was interpreted as saturated zone with while high resistivity values >500 Ωm as the hard layer for this study area. The seismic result indicates that the velocity values <2000 m/s represent as the highly-weathered soil consists of clay and sand while high velocity values >3600 m/s interpreted as the hard layer in this locality.

Inverse problems and coherence

NASA Astrophysics Data System (ADS)

Baltes, H. P.; Ferwerda, H. A.

1981-03-01

A summary of current inverse problems of statistical optics is presented together with a short guide to the pertinent review-type literature. The retrieval of structural information from the far-zone degree of coherence and the average intensity distribution of radiation scattered by a superposition of random and periodic scatterers is discussed.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

SIAM conference on inverse problems: Geophysical applications. Final technical report

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1995-12-31

This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devotedmore » to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.« less

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Inverse problem of the vibrational band gap of periodically supported beam

NASA Astrophysics Data System (ADS)

Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei

2017-04-01

The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.

Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

NASA Astrophysics Data System (ADS)

Xia, Jake Jiqing

The electromagnetic inverse scattering problems concerned in this thesis are to find unknown inhomogeneous permittivity and conductivity profiles in a medium from the scattering data. Both analytical and numerical methods are studied in the thesis. The inverse methods can be applied to geophysical medium probing, non-destructive testing, medical imaging, optical waveguide synthesis and material characterization. An introduction is given in Chapter 1. The first part of the thesis presents inhomogeneous media probing. The Riccati equation approach is discussed in Chapter 2 for a one-dimensional planar profile inversion problem. Two types of the Riccati equations are derived and distinguished. New renormalized formulae based inverting one specific type of the Riccati equation are derived. Relations between the inverse methods of Green's function, the Riccati equation and the Gel'fand-Levitan-Marchenko (GLM) theory are studied. In Chapter 3, the renormalized source-type integral equation (STIE) approach is formulated for inversion of cylindrically inhomogeneous permittivity and conductivity profiles. The advantages of the renormalized STIE approach are demonstrated in numerical examples. The cylindrical profile inversion problem has an application for borehole inversion. In Chapter 4 the renormalized STIE approach is extended to a planar case where the two background media are different. Numerical results have shown fast convergence. This formulation is applied to inversion of the underground soil moisture profiles in remote sensing. The second part of the thesis presents the synthesis problem of inhomogeneous dielectric waveguides using the electromagnetic inverse methods. As a particular example, the rational function representation of reflection coefficients in the GLM theory is used. The GLM method is reviewed in Chapter 5. Relations between modal structures and transverse reflection coefficients of an inhomogeneous medium are established in Chapter 6. A stratified medium model is used to derive the guidance condition and the reflection coefficient. Results obtained in Chapter 6 provide the physical foundation for applying the inverse methods for the waveguide design problem. In Chapter 7, a global guidance condition for continuously varying medium is derived using the Riccati equation. It is further shown that the discrete modes in an inhomogeneous medium have the same wave vectors as the poles of the transverse reflection coefficient. An example of synthesizing an inhomogeneous dielectric waveguide using a rational reflection coefficient is presented. A summary of the thesis is given in Chapter 8. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Geophysical approaches to inverse problems: A methodological comparison. Part 1: A Posteriori approach

NASA Technical Reports Server (NTRS)

Seidman, T. I.; Munteanu, M. J.

1979-01-01

The relationships of a variety of general computational methods (and variances) for treating illposed problems such as geophysical inverse problems are considered. Differences in approach and interpretation based on varying assumptions as to, e.g., the nature of measurement uncertainties are discussed along with the factors to be considered in selecting an approach. The reliability of the results of such computation is addressed.

Layer Stripping Solutions of Inverse Seismic Problems.

DTIC Science & Technology

1985-03-21

problems--more so than has generally been recognized. The subject of this thesis is the theoretical development of the . layer-stripping methodology , and...medium varies sharply at each interface, which would be expected to cause difficulties for the algorithm, since it was designed for a smoothy varying... methodology was applied in a novel way. The inverse problem considered in this chapter was that of reconstructing a layered medium from measurement of its

Hydromagnetic conditions near the core-mantle boundary

NASA Technical Reports Server (NTRS)

Backus, George E.

1995-01-01

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

The Relationship Between Non-Symbolic Multiplication and Division in Childhood

PubMed Central

McCrink, Koleen; Shafto, Patrick; Barth, Hilary

2016-01-01

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b − b = a). The current study examines children’s ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8 * 4 / 4) or did not (e.g., 8 * 4 / 2). Children’s performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a * b / b structure, suggesting they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems. PMID:26880261

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Corneal refractive power and eccentricity in the 40- to 64-year-old population of Shahroud, Iran.

PubMed

Asgari, Soheila; Hashemi, Hassan; Mehravaran, Shiva; Khabazkhoob, Mehdi; Emamian, Mohammad Hassan; Jafarzadehpur, Ebrahim; Shariati, Mohammad; Fotouhi, Akbar

2013-01-01

To determine the normal corneal curvature, power, and eccentricity in an Iranian population and their determinants. This report is part of a population-based study conducted in 2009. Of the 5190 participants of the study, Pentacam data from 8532 eyes of 4266 people who met the inclusion criteria for this analysis were used. For each eye, we extracted minimum and maximum keratometry readings, the average of the 2 readings (mean-K), the difference between these 2 parameters (keratometric astigmatism), and corneal eccentricity. The average mean-K, keratometric astigmatism, and eccentricity were 43.73 ± 2.47, 0.90 ± 0.93, and 0.27 ± 0.63 diopter, respectively. Mean-K was directly correlated with age; inversely correlated with body mass index, axial length, white-to-white corneal diameter, and anterior chamber depth; increased at higher amounts of myopia; and was higher in women compared with men. Keratometric astigmatism was significantly higher in women, increased at higher amount of refractive error, but showed no association with other variables. Eccentricity was correlated indirectly with age and white-to-white corneal diameter, and directly with axial length. It increased with myopia. Compared with other studies, the mean corneal power and eccentricity values were lower in this Iranian population sample. Our findings may have implications for clinical interventions, especially refractive surgery. Further studies can identify the causes of such differences in the shape and size of the cornea, which may also be attributable to the choice of the measuring device.

UV-Vis-IR spectral complex refractive indices and optical properties of brown carbon aerosol from biomass burning

NASA Astrophysics Data System (ADS)

Sumlin, Benjamin J.; Heinson, Yuli W.; Shetty, Nishit; Pandey, Apoorva; Pattison, Robert S.; Baker, Stephen; Hao, Wei Min; Chakrabarty, Rajan K.

2018-02-01

Constraining the complex refractive indices, optical properties and size of brown carbon (BrC) aerosols is a vital endeavor for improving climate models and satellite retrieval algorithms. Smoldering wildfires are the largest source of primary BrC, and fuel parameters such as moisture content, source depth, geographic origin, and fuel packing density could influence the properties of the emitted aerosol. We measured in situ spectral (375-1047 nm) optical properties of BrC aerosols emitted from smoldering combustion of Boreal and Indonesian peatlands across a range of these fuel parameters. Inverse Lorenz-Mie algorithms used these optical measurements along with simultaneously measured particle size distributions to retrieve the aerosol complex refractive indices (m = n + iκ). Our results show that the real part n is constrained between 1.5 and 1.7 with no obvious functionality in wavelength (λ), moisture content, source depth, or geographic origin. With increasing λ from 375 to 532 nm, κ decreased from 0.014 to 0.003, with corresponding increase in single scattering albedo (SSA) from 0.93 to 0.99. The spectral variability of κ follows the Kramers-Kronig dispersion relation for a damped harmonic oscillator. For λ ≥ 532 nm, both κ and SSA showed no spectral dependency. We discuss differences between this study and previous work. The imaginary part κ was sensitive to changes in FPD, and we hypothesize mechanisms that might help explain this observation.

Inverse scattering and refraction corrected reflection for breast cancer imaging

NASA Astrophysics Data System (ADS)

Wiskin, J.; Borup, D.; Johnson, S.; Berggren, M.; Robinson, D.; Smith, J.; Chen, J.; Parisky, Y.; Klock, John

2010-03-01

Reflection ultrasound (US) has been utilized as an adjunct imaging modality for over 30 years. TechniScan, Inc. has developed unique, transmission and concomitant reflection algorithms which are used to reconstruct images from data gathered during a tomographic breast scanning process called Warm Bath Ultrasound (WBU™). The transmission algorithm yields high resolution, 3D, attenuation and speed of sound (SOS) images. The reflection algorithm is based on canonical ray tracing utilizing refraction correction via the SOS and attenuation reconstructions. The refraction correction reflection algorithm allows 360 degree compounding resulting in the reflection image. The requisite data are collected when scanning the entire breast in a 33° C water bath, on average in 8 minutes. This presentation explains how the data are collected and processed by the 3D transmission and reflection imaging mode algorithms. The processing is carried out using two NVIDIA® Tesla™ GPU processors, accessing data on a 4-TeraByte RAID. The WBU™ images are displayed in a DICOM viewer that allows registration of all three modalities. Several representative cases are presented to demonstrate potential diagnostic capability including: a cyst, fibroadenoma, and a carcinoma. WBU™ images (SOS, attenuation, and reflection modalities) are shown along with their respective mammograms and standard ultrasound images. In addition, anatomical studies are shown comparing WBU™ images and MRI images of a cadaver breast. This innovative technology is designed to provide additional tools in the armamentarium for diagnosis of breast disease.

Seismic Wave Amplification in Las Vegas: Site Characterization Measurements and Response Models

NASA Astrophysics Data System (ADS)

Louie, J. N.; Anderson, J. G.; Luke, B.; Snelson, C.; Taylor, W.; Rodgers, A.; McCallen, D.; Tkalcic, H.; Wagoner, J.

2004-12-01

As part of a multidisciplinary effort to understand seismic wave amplification in Las Vegas Valley, we conducted geotechnical and seismic refraction field studies, geologic and lithologic interpretation, and geophysical model building. Frequency-dependent amplifications (site response) and peak ground motions strongly correlate with site conditions as characterized by the models. The models include basin depths and velocities, which also correlate against ground motions. Preliminary geologic models were constructed from detailed geologic and fault mapping, logs of over 500 wells penetrating greater than 200 m depth, gravity-inversion results from the USGS, and USDA soil maps. Valley-wide refraction studies we conducted in 2002 and 2003 were inverted for constraints on basin geometry, and deep basin and basement P velocities with some 3-d control to depths of 5 km. Surface-wave studies during 2002-2004 characterized more than 75 sites within the Valley for shear velocity to depths exceeding 100 m, including all the legacy sites where nuclear-blast ground motions were recorded. The SASW and refraction-microtremor surface-surveying techniques proved to provide complementary, and coordinating Rayleigh dispersion-curve data at a dozen sites. Borehole geotechnical studies at a half-dozen sites confirmed the shear-velocity profiles that we derived from surface-wave studies. We then correlated all the geotechnical data against a detailed stratigraphic model, derived from drilling logs, to create a Valley-wide model for shallow site conditions. This well-log-based model predicts site measurements better than do models based solely on geologic or soil mapping.

Two color interferometric electron density measurement in an axially blown arc

NASA Astrophysics Data System (ADS)

Stoller, Patrick; Carstensen, Jan; Galletti, Bernardo; Doiron, Charles; Sokolov, Alexey; Salzmann, René; Simon, Sandor; Jabs, Philipp

2016-09-01

High voltage circuit breakers protect the power grid by interrupting the current in case of a short circuit. To do so an arc is ignited between two contacts as they separate; transonic gas flow is used to cool and ultimately extinguish the arc at a current-zero crossing of the alternating current. A detailed understanding of the arc interruption process is needed to improve circuit breaker design. The conductivity of the partially ionized gas remaining after the current-zero crossing, a key parameter in determining whether the arc will be interrupted or not, is a function of the electron density. The electron density, in turn, is a function of the detailed dynamics of the arc cooling process, which does not necessarily occur under local thermodynamic equilibrium (LTE) conditions. In this work, we measure the spatially resolved line-integrated index of refraction in a near-current-zero arc stabilized in an axial flow of synthetic air with two nanosecond pulsed lasers at wavelengths of 532 nm and 671 nm. Generating a stable, cylindrically symmetric arc enables us to determine the three-dimensional index of refraction distribution using Abel inversion. Due to the wavelength dependence of the component of the index of refraction related to the free electrons, the information at two different wavelengths can be used to determine the electron density. This information allows us to determine how important it is to take into account non-equilibrium effects for accurate modeling of the physics of decaying arcs.

Modeling of light propagation in the human neck for diagnoses of thyroid cancers by diffuse optical tomography.

PubMed

Fujii, H; Yamada, Y; Kobayashi, K; Watanabe, M; Hoshi, Y

2017-05-01

Diffuse optical tomography using near-infrared light in a wavelength range from 700 to 1000 nm has the potential to enable non-invasive diagnoses of thyroid cancers; some of which are difficult to detect by conventional methods such as ultrasound tomography. Diffuse optical tomography needs to be based on a physically accurate model of light propagation in the neck, because it reconstructs tomographic images of the optical properties in the human neck by inverse analysis. Our objective here was to investigate the effects of three factors on light propagation in the neck using the 2D time-dependent radiative transfer equation: (1) the presence of the trachea, (2) the refractive-index mismatch at the trachea-tissue interface, and (3) the effect of neck organs other than the trachea (spine, spinal cord, and blood vessels). There was a significant influence of reflection and refraction at the trachea-tissue interface on the light intensities in the region between the trachea and the front of the neck surface. Organs other than the trachea showed little effect on the light intensities measured at the front of the neck surface although these organs affected the light intensities locally. These results indicated the necessity of modeling the refractive-index mismatch at the trachea-tissue interface and the possibility of modeling other neck organs simply as a homogeneous medium when the source and detectors were far from large blood vessels. Copyright © 2016 John Wiley & Sons, Ltd.

Constraints on the Velocity Structure and Accommodation of Shortening in the Atlas Mountains (Morocco) from Travel-Time Inversion of Refraction/Wide Angle Reflection Seismic Data

NASA Astrophysics Data System (ADS)

Ayarza, P.; Carbonell, R.; Palomeras, I.; Levander, A.; Teixell, A.; Zelt, C. A.; Kchikach, A.

2013-12-01

The Atlas Mountains are an intra-continental Cenozoic orogenic belt located at the southern edge of the diffuse plate boundary zone separating Africa and Europe. Its western part, the Moroccan Atlas, has long been under the scope of geoscientists investigating the origin of its high topography, locally exceeding 4000 m. Geological studies indicate that this mountain belt has experienced low to moderate shortening (<24% from balanced sections) and that topography and shortening do not keep a direct relationship. Forward modelling of the SIMA (Seismic Imaging of the Moroccan Atlas) refraction/wide angle reflection seismic data suggests that the total orogenic shortening, is resolved at depth with a Moho offset and a limited lower crust duplication that defines a 40 km-deep root in the northern part of the central High Atlas. However, the shortening accomodated by this feature (50 km) exceeds that estimated with surface data, and the position of the root appears to the north of the highest topography. In order to achieve a better definition of the crust/mantle boundary and to outline a tectonic model more coherent with surface data, we have used the RAYINVR code to carry out travel-time inversion of the SIMA data set. Inversion results depict a small shift to the south of the crustal root, formerly positioned in the northern part of the High Atlas, and define a thrusted mantle wedge. A limited crustal imbrication also appears in the Middle Atlas. The new velocity model implies complex ray trajectories but provides a better travel-time fit between the observed and the calculated data. Also, the amount of shortening implied by the this model is in agreement with that estimated from geological cross-sections. The final crustal thickness, as yet not exceeding 40 km in the root zone and less than 35 km elsewhere, still implies the need of a significant contribution from the mantle to support the topography of the Atlas mountains

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ciraolo, Giulio, E-mail: g.ciraolo@math.unipa.it; Gargano, Francesco, E-mail: gargano@math.unipa.it; Sciacca, Vincenzo, E-mail: sciacca@math.unipa.it

2013-08-01

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

Inverse problems in the modeling of vibrations of flexible beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Powers, R. K.; Rosen, I. G.

1987-01-01

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

Topographic profiling and refractive-index analysis by use of differential interference contrast with bright-field intensity and atomic force imaging.

PubMed

Axelrod, Noel; Radko, Anna; Lewis, Aaron; Ben-Yosef, Nissim

2004-04-10

A methodology is described for phase restoration of an object function from differential interference contrast (DIC) images. The methodology involves collecting a set of DIC images in the same plane with different bias retardation between the two illuminating light components produced by a Wollaston prism. These images, together with one conventional bright-field image, allows for reduction of the phase deconvolution restoration problem from a highly complex nonlinear mathematical formulation to a set of linear equations that can be applied to resolve the phase for images with a relatively large number of pixels. Additionally, under certain conditions, an on-line atomic force imaging system that does not interfere with the standard DIC illumination modes resolves uncertainties in large topographical variations that generally lead to a basic problem in DIC imaging, i.e., phase unwrapping. Furthermore, the availability of confocal detection allows for a three-dimensional reconstruction with high accuracy of the refractive-index measurement of the object that is to be imaged. This has been applied to reconstruction of the refractive index of an arrayed waveguide in a region in which a defect in the sample is present. The results of this paper highlight the synergism of far-field microscopies integrated with scanned probe microscopies and restoration algorithms for phase reconstruction.

Candidates to replace R-12 as a radiator gas in Cherenkov detectors

NASA Astrophysics Data System (ADS)

Harvey, Allan H.; Paulechka, Eugene; Egan, Patrick F.

2018-06-01

Dichlorodifluoromethane (R-12) has been widely used as a radiator gas in pressure threshold Cherenkov detectors for high-energy particle physics. However, that compound is becoming unavailable due to the Montreal Protocol. To find a replacement with suitably high refractive index, we use a combination of theory and experiment to examine the polarizability and refractivity of several non-ozone-depleting compounds. Our measurements show that the fourth-generation refrigerants R-1234yf (2,3,3,3-tetrafluoropropene) and R-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) have sufficient refractivity to replace R-12 in this application. If the slight flammability of these compounds is a problem, two nonflammable alternatives are R-218 (octafluoropropane), which has a high Global Warming Potential, and R-13I1 (trifluoroiodomethane), which has low Ozone Depletion Potential and Global Warming Potential but may not be sufficiently inert.

Extraordinary-mode refractive-index change produced by the linear electro-optic effect in LiNbO3 and reverse-poled LiNbO3

NASA Astrophysics Data System (ADS)

Boyd, Joseph T.; Servizzi, Anthony J.; Sriram, S.; Kingsley, Stuart A.

1995-07-01

To examine aspects of an integrated photonic electric-field sensor, we calculate electro-optically induced refractive-index change in regular and reverse-poled LiNbO3. Specifically, for y-propagating extraordinary modes, we determine how index change depends on electric-field magnitude and direction. To accomplish this, changes in index-ellipsoid shape and orientation are found by the use of a numerical eigenvalue procedure to diagonalize the impermeability tensor; then, refractive index is calculated by the use of a vector reference-frame transformation and a small perturbation approximation. A general formula is inferred from calculations for specific field directions. Electro-optic coefficients for reverse-poled LiNbO3 are obtained by application of a tensor reference-frame transformation to those of LiNbO3. The index-calculation procedure has utility beyond the problem that is considered.

Refining Sunrise/set Prediction Models by Accounting for the Effects of Refraction

NASA Astrophysics Data System (ADS)

Wilson, Teresa; Bartlett, Jennifer L.

2016-01-01

Current atmospheric models used to predict the times of sunrise and sunset have an error of one to four minutes at mid-latitudes (0° - 55° N/S). At higher latitudes, slight changes in refraction may cause significant discrepancies, including determining even whether the Sun appears to rise or set. While different components of refraction are known, how they affect predictions of sunrise/set has not yet been quantified. A better understanding of the contributions from temperature profile, pressure, humidity, and aerosols, could significantly improve the standard prediction. Because sunrise/set times and meteorological data from multiple locations will be necessary for a thorough investigation of the problem, we will collect this data using smartphones as part of a citizen science project. This analysis will lead to more complete models that will provide more accurate times for navigators and outdoorsman alike.

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

ERIC Educational Resources Information Center

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

Mechanisms of the anomalous Pockels effect in bulk water

NASA Astrophysics Data System (ADS)

Yukita, Shunpei; Suzuki, Yuto; Shiokawa, Naoyuki; Kobayashi, Takayoshi; Tokunaga, Eiji

2018-04-01

The "anomalous" Pockels effect is a phenomenon that a light beam passing between two electrodes in an aqueous electrolyte solution is deflected by an AC voltage applied between the electrodes: the deflection angle is proportional to the voltage such that the incident beam alternately changes its direction. This phenomenon, the Pockels effect in bulk water, apparently contradicts what is believed in nonlinear optics, i.e., macroscopic inversion symmetry should be broken for the second-order nonlinear optical effect to occur such as the first-order electro-optic effect, i.e., the Pockels effect. To clarify the underlying mechanism, the dependence of the effect on the electrode material is investigated to find that the Pockels coefficient with Pt electrodes is two orders of magnitude smaller than with indium tin oxide (ITO) electrodes. It is experimentally confirmed that the Pockels effect of interfacial water in the electric double layer (EDL) on these electrodes shows an electrode dependence similar to the effect in bulk water while the effects depend on the frequency of the AC voltage such that the interfacial signal decreases with frequency but the bulk signal increases with frequency up to 221 Hz. These experimental results lead to a conclusion that the beam deflection is caused by the refractive index gradient in the bulk water region, which is formed transiently by the Pockels effect of interfacial water in the EDL when an AC electric field is applied. The refractive index gradient is caused by the diffuse layer spreading into the bulk region to work as a breaking factor of inversion symmetry of bulk water due to its charge-biased ionic distribution. This mechanism does not contradict the principle of nonlinear optics.

Application and Limitations of GPS Radio Occultation (GPS-RO) Data for Atmospheric Boundary Layer Height Detection over the Arctic.

NASA Astrophysics Data System (ADS)

Ganeshan, M.; Wu, D. L.

2014-12-01

Due to recent changes in the Arctic environment, it is important to monitor the atmospheric boundary layer (ABL) properties over the Arctic Ocean, especially to explore the variability in ABL clouds (such as sensitivity and feedback to sea ice loss). For example, radiosonde and satellite observations of the Arctic ABL height (and low-cloud cover) have recently suggested a positive response to sea ice loss during October that may not occur during the melt season (June-September). Owing to its high vertical and spatiotemporal resolution, an independent ABL height detection algorithm using GPS Radio Occultation (GPS-RO) refractivity in the Arctic is explored. Similar GPS-RO algorithms developed previously typically define the level of the most negative moisture gradient as the ABL height. This definition is favorable for subtropical oceans where a stratocumulus-topped ABL is often capped by a layer of sharp moisture lapse rate (coincident with the temperature inversion). The Arctic Ocean is also characterized by stratocumulus cloud cover, however, the specific humidity does not frequently decrease in the ABL capping inversion. The use of GPS-RO refractivity for ABL height retrieval therefore becomes more complex. During winter months (December-February), when the total precipitable water in the troposphere is a minimum, a fairly straightforward algorithm for ABL height retrieval is developed. The applicability and limitations of this method for other seasons (Spring, Summer, Fall) is determined. The seasonal, interannual and spatial variability in the GPS-derived ABL height over the Arctic Ocean, as well as its relation to the underlying surface (ice vs. water), is investigated. The GPS-RO profiles are also explored for the evidence of low-level moisture transport in the cold Arctic environment.

Estimating uncertainty of Full Waveform Inversion with Ensemble-based methods

NASA Astrophysics Data System (ADS)

Thurin, J.; Brossier, R.; Métivier, L.

2017-12-01

Uncertainty estimation is one key feature of tomographic applications for robust interpretation. However, this information is often missing in the frame of large scale linearized inversions, and only the results at convergence are shown, despite the ill-posed nature of the problem. This issue is common in the Full Waveform Inversion community.While few methodologies have already been proposed in the literature, standard FWI workflows do not include any systematic uncertainty quantifications methods yet, but often try to assess the result's quality through cross-comparison with other results from seismic or comparison with other geophysical data. With the development of large seismic networks/surveys, the increase in computational power and the more and more systematic application of FWI, it is crucial to tackle this problem and to propose robust and affordable workflows, in order to address the uncertainty quantification problem faced for near surface targets, crustal exploration, as well as regional and global scales.In this work (Thurin et al., 2017a,b), we propose an approach which takes advantage of the Ensemble Transform Kalman Filter (ETKF) proposed by Bishop et al., (2001), in order to estimate a low-rank approximation of the posterior covariance matrix of the FWI problem, allowing us to evaluate some uncertainty information of the solution. Instead of solving the FWI problem through a Bayesian inversion with the ETKF, we chose to combine a conventional FWI, based on local optimization, and the ETKF strategies. This scheme allows combining the efficiency of local optimization for solving large scale inverse problems and make the sampling of the local solution space possible thanks to its embarrassingly parallel property. References:Bishop, C. H., Etherton, B. J. and Majumdar, S. J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), 420-436.Thurin, J., Brossier, R. and Métivier, L. 2017,a.: Ensemble-Based Uncertainty Estimation in Full Waveform Inversion. 79th EAGE Conference and Exhibition 2017, (12 - 15 June, 2017)Thurin, J., Brossier, R. and Métivier, L. 2017,b.: An Ensemble-Transform Kalman Filter - Full Waveform Inversion scheme for Uncertainty estimation; SEG Technical Program Expanded Abstracts 2012