Fourier transform of the multicenter product of 1s hydrogenic orbitals and Coulomb or Yukawa potentials and the analytically reduced form for subsequent integrals that include plane waves

NASA Technical Reports Server (NTRS)

Straton, Jack C.

1989-01-01

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.

Electromagnetic pulse propagation in dispersive planar dielectrics.

PubMed

Moten, K; Durney, C H; Stockham, T G

1989-01-01

The responses of a plane-wave pulse train irradiating a lossy dispersive dielectric half-space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half-space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time-averaged specific absorption rate (SAR) for pulse-train propagation is shown to be the sum of the time-averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier-frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse-train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectral point of view.

Modulated Fourier Transform Raman Fiber-Optic Spectroscopy

NASA Technical Reports Server (NTRS)

Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)

2000-01-01

A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

A fractional Fourier transform analysis of the scattering of ultrasonic waves.

PubMed

Tant, Katherine M M; Mulholland, Anthony J; Langer, Matthias; Gachagan, Anthony

2015-03-08

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time-frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time-frequency domain framework to assist in flaw identification and classification.

Study of Lamb Waves for Non-Destructive Testing Behind Screens

NASA Astrophysics Data System (ADS)

Kauffmann, P.; Ploix, M.-A.; Chaix, J.-F.; Gueudré, C.; Corneloup, G.; Baqué, F. AF(; )

2018-01-01

The inspection and control of sodium-cooled fast reactors (SFR) is a major issue for the nuclear industry. Ultrasonic solutions are under study because of the opacity of liquid sodium. In this paper, the use of leaky Lamb waves is considered for non-destructive testing (NDT) on parallel and immersed structures assimilated as plates. The first phase of our approach involved studying the propagation properties of leaky Lamb waves. Equations that model the propagation of Lamb waves in an immersed plate were solved numerically. The phase velocity can be experimentally measured using a two dimensional Fourier transform. The group velocity can be experimentally measured using a short-time Fourier transform technique. Attenuation of leaky Lamb waves is mostly due to the re-emission of energy into the surrounding fluid, and it can be measured by these two techniques.

Optical generation of millimeter-wave pulses using a fiber Bragg grating in a fiber-optics system.

PubMed

Ye, Qing; Qu, Ronghui; Fang, Zujie

2007-04-10

A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Book review: Nonlinear ocean waves and the inverse scattering transform

USGS Publications Warehouse

Geist, Eric L.

2011-01-01

Nonlinear Ocean Waves and the Inverse Scattering Transform is a comprehensive examination of ocean waves built upon the theory of nonlinear Fourier analysis. The renowned author, Alfred R. Osborne, is perhaps best known for the discovery of internal solitons in the Andaman Sea during the 1970s. In this book, he provides an extensive treatment of nonlinear water waves based on a nonlinear spectral theory known as the inverse scattering transform. The writing is exceptional throughout the book, which is particularly useful in explaining some of the more difficult mathematical concepts.  Review info: Nonlinear Ocean Waves and the Inverse Scattering Transform. By Alfred R. Osborne, 2010. ISBN: 978-125286299, 917 pp.

Retina as Reciprocal Spatial Fourier Transform Space Implies ``Wave-transformation'' Functions, String Theory, the Inappropriate Uncertainty Principle, and Predicts ``Quarked'' Protons.

NASA Astrophysics Data System (ADS)

Mc Leod, Roger David; Mc Leod, David M.

2007-10-01

Vision, via transform space: ``Nature behaves in a reciprocal way;' also, Rect x pressure-input sense-reports as Sinc p, indicating brain interprets reciprocal ``p'' space as object space. Use Mott's and Sneddon's Wave Mechanics and Its Applications. Wave transformation functions are strings of positron, electron, proton, and neutron; uncertainty is a semantic artifact. Neutrino-string de Broglie-Schr"odinger wave-function models for electron, positron, suggest three-quark models for protons, neutrons. Variably vibrating neutrino-quills of this model, with appropriate mass-energy, can be a vertical proton string, quills leftward; thread string circumferentially, forming three interlinked circles with ``overpasses''. Diameters are 2:1:2, center circle has quills radially outward; call it a down quark, charge --1/3, charge 2/3 for outward quills, the up quarks of outer circles. String overlap summations are nodes; nodes also far left and right. Strong nuclear forces may be --px. ``Dislodging" positron with neutrino switches quark-circle configuration to 1:2:1, `downers' outside. Unstable neutron charge is 0. Atoms build. With scale factors, retinal/vision's, and quantum mechanics,' spatial Fourier transforms/inverses are equivalent.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.

PubMed

Tang, Heng-He; Liu, Pu-Kun

2015-09-07

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

A fractional Fourier transform analysis of the scattering of ultrasonic waves

PubMed Central

Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

2015-01-01

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.

1974-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Two-dimensional linear and nonlinear Talbot effect from rogue waves.

PubMed

Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng

2015-03-01

We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.

Investigations of the functional states of dendritic cells under different conditioned microenvironments by Fourier transformed infrared spectroscopy.

PubMed

Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu

2014-01-10

Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P < 0.05 or 0.01). The expression levels of NF-kappa B (NF-κB) in dendritic cells were also specifically inhibited by tumor-derived factors (P < 0.05 or 0.01). Moreover, the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.

High resolution wavenumber analysis for investigation of arterial pulse wave propagation

NASA Astrophysics Data System (ADS)

Hasegawa, Hideyuki; Sato, Masakazu; Irie, Takasuke

2016-07-01

The propagation of the pulse wave along the artery is relatively fast (several m/s), and a high-temporal resolution is required to measure pulse wave velocity (PWV) in a regional segment of the artery. High-frame-rate ultrasound enables the measurement of the regional PWV. In analyses of wave propagation phenomena, the direction and propagation speed are generally identified in the frequency-wavenumber space using the two-dimensional Fourier transform. However, the wavelength of the pulse wave is very long (1 m at a propagation velocity of 10 m/s and a temporal frequency of 10 Hz) compared with a typical lateral field of view of 40 mm in ultrasound imaging. Therefore, PWV cannot be identified in the frequency-wavenumber space owing to the low resolution of the two-dimensional Fourier transform. In the present study, PWV was visualized in the wavenumber domain using phases of arterial wall acceleration waveforms measured by high-frame-rate ultrasound.

Iterative wave-front reconstruction in the Fourier domain.

PubMed

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

GIFTS SM EDU Radiometric and Spectral Calibrations

NASA Technical Reports Server (NTRS)

Tian, J.; Reisse, R. a.; Johnson, D. G.; Gazarik, J. J.

2007-01-01

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiance using a Fourier transform spectrometer (FTS). The GIFTS instrument gathers measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration. The calibration procedures can be subdivided into three categories: the pre-calibration stage, the calibration stage, and finally, the post-calibration stage. Detailed derivations for each stage are presented in this paper.

The soliton transform and a possible application to nonlinear Alfven waves in space

NASA Technical Reports Server (NTRS)

Hada, T.; Hamilton, R. L.; Kennel, C. F.

1993-01-01

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Microcomputer Simulation of a Fourier Approach to Optical Wave Propagation

DTIC Science & Technology

1992-06-01

and transformed input in transform domain). 44 Figure 21. SHFTOUTPUT1 ( inverse transform of product of Bessel filter and transformed input). . . . 44...Figure 22. SHFT OUTPUT2 ( inverse transform of product of ,derivative filter and transformed input).. 45 Figure 23. •tIFT OUTPUT (sum of SHFTOUTPUT1...52 Figure 33. SHFT OUTPUT1 at time slice 1 ( inverse transform of product of Bessel filter and transformed input) .... ............. ... 53

Application of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

a 2d Model of Ultrasonic Testing for Cracks Near a Nonplanar Surface

NASA Astrophysics Data System (ADS)

Westlund, Jonathan; Boström, Anders

2010-02-01

2D P-SV elastic wave scattering by a crack near a non-planar surface is investigated. The wave scattering problem is solved in the frequency domain using a combination of the boundary element method (BEM) for the back surface displacement and a Fourier series expansion of the crack opening displacement (COD). The model accounts for the action of the transmitting and receiving ultrasonic contact probes, and the time traces are obtained by applying an inverse temporal Fourier transform.

Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite-Gaussian beams

NASA Astrophysics Data System (ADS)

Chen, Y. F.; Chang, C. C.; Lee, C. Y.; Tung, J. C.; Liang, H. C.; Huang, K. F.

2018-01-01

Theoretical wave functions are analytically derived to characterize the propagation evolution of the Hermite-Gaussian (HG) beams transformed by a single-lens astigmatic mode converter with arbitrary angle. The derived wave functions are related to the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula is systematically validated by using an off-axis diode-pumped solid-state laser to generate various high-order HG beams for mode conversions. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical analyses can be used not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.

Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

PubMed

Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

2005-11-01

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

Fourier transform infrared and Raman spectroscopic characterization of homogeneous solution concentration gradients near a container wall at different temperatures

NASA Technical Reports Server (NTRS)

Loo, B. H.; Burns, D. H.; Lee, Y. G. L.; Emerson, M. T.

1991-01-01

Fourier transform infrared (FTIR) and Raman spectroscopic techniques were used to study the solution concentration gradient in succino nitrile-rich and water-rich homogeneous solutions. The spectroscopic data shows significant concentration dependency. Although FTIR-attenuated total reflectance could not yield surface spectra since the evanescent infrared wave penetrated deep into the bulk solution, it showed that water-rich clusters were decreased at higher temperatures. This result is consistent with the calorimetric results reported earlier.

The Application of MP-FTS to Aperture Synthesis

NASA Astrophysics Data System (ADS)

Hattori, M.; Ohta, I. S.; Matsuo, H.; Shibata, Y.

2000-12-01

The application of the Martin-Puplett type Fourier transform spectrometer to aperture synthesis is considered. The configuration of the mirrors and beam splitters and the fundamental mathematical elements of the system are summarized. We show that the system can measure spectrally resolved spatial distribution of the Stokes parameters of sources as interfered signals. An original Martin-Puplett type Fourier transform spectrometer that can be applied to aperture synthesis in mm and sub-mm wave bands has been constructed. The preliminary results of our laboratory experiments are reported.

A compact LWIR hyperspectral system employing a microbolometer array and a variable gap Fabry-Perot interferometer employed as a Fourier transform spectrometer

NASA Astrophysics Data System (ADS)

Lucey, Paul G.; Hinrichs, John L.; Akagi, Jason

2012-06-01

A prototype long wave infrared Fourier transform spectral imaging system using a wedged Fabry-Perot interferometer and a microbolometer array was designed and built. The instrument can be used at both short (cm) and long standoff ranges (infinity focus). Signal to noise ratios are in the several hundred range for 30 C targets. The sensor is compact, fitting in a volume about 12 x12 x 4 inches.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

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

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

Measurements of Wave Power in Wave Energy Converter Effectiveness Evaluation

NASA Astrophysics Data System (ADS)

Berins, J.; Berins, J.; Kalnacs, A.

2017-08-01

The article is devoted to the technical solution of alternative budget measuring equipment of the water surface gravity wave oscillation and the theoretical justification of the calculated oscillation power. This solution combines technologies such as lasers, WEB-camera image digital processing, interpolation of defined function at irregular intervals, volatility of discrete Fourier transformation for calculating the spectrum.

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

PubMed

Guizal, Brahim; Barchiesi, Dominique; Felbacq, Didier

2003-12-01

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Fourier analysis of surface plasmon waves launched from single nanohole and nanohole arrays: unraveling tip-induced effects.

PubMed

Chang, Y C; Chu, J Y; Wang, T J; Lin, M W; Yeh, J T; Wang, J K

2008-01-21

The authors report the investigation of surface plasmon waves (SPW) generated by single nanohole and nanohole arrays. Scattering-type scanning near-field microscopy is used to directly observe near-field distribution. The images after Fourier transformation display characteristic patterns that match with the derived analytic formula. The correspondence helps to identify the role of the scanning tip in generating SPW, making possible of the removal of this tip-induced effect. This study provides a means to perform in-depth investigation on surface plasmon polaritons.

Full-wave and half-wave rectification in second-order motion perception

NASA Technical Reports Server (NTRS)

Solomon, J. A.; Sperling, G.

1994-01-01

Microbalanced stimuli are dynamic displays which do not stimulate motion mechanisms that apply standard (Fourier-energy or autocorrelational) motion analysis directly to the visual signal. In order to extract motion information from microbalanced stimuli, Chubb and Sperling [(1988) Journal of the Optical Society of America, 5, 1986-2006] proposed that the human visual system performs a rectifying transformation on the visual signal prior to standard motion analysis. The current research employs two novel types of microbalanced stimuli: half-wave stimuli preserve motion information following half-wave rectification (with a threshold) but lose motion information following full-wave rectification; full-wave stimuli preserve motion information following full-wave rectification but lose motion information following half-wave rectification. Additionally, Fourier stimuli, ordinary square-wave gratings, were used to stimulate standard motion mechanisms. Psychometric functions (direction discrimination vs stimulus contrast) were obtained for each type of stimulus when presented alone, and when masked by each of the other stimuli (presented as moving masks and also as nonmoving, counterphase-flickering masks). RESULTS: given sufficient contrast, all three types of stimulus convey motion. However, only one-third of the population can perceive the motion of the half-wave stimulus. Observers are able to process the motion information contained in the Fourier stimulus slightly more efficiently than the information in the full-wave stimulus but are much less efficient in processing half-wave motion information. Moving masks are more effective than counterphase masks at hampering direction discrimination, indicating that some of the masking effect is interference between motion mechanisms, and some occurs at earlier stages. When either full-wave and Fourier or half-wave and Fourier gratings are presented simultaneously, there is a wide range of relative contrasts within which the motion directions of both gratings are easily determinable. Conversely, when half-wave and full-wave gratings are combined, the direction of only one of these gratings can be determined with high accuracy. CONCLUSIONS: the results indicate that three motion computations are carried out, any two in parallel: one standard ("first order") and two non-Fourier ("second-order") computations that employ full-wave and half-wave rectification.

SIR-B ocean-wave enhancement with fast Fourier transform techniques

NASA Technical Reports Server (NTRS)

Tilley, David G.

1987-01-01

Shuttle Imaging Radar (SIR-B) imagery is Fourier filtered to remove the estimated system-transfer function, reduce speckle noise, and produce ocean scenes with a gray scale that is proportional to wave height. The SIR-B system response to speckled scenes of uniform surfaces yields an estimate of the stationary wavenumber response of the imaging radar, modeled by the 15 even terms of an eighth-order two-dimensional polynomial. Speckle can also be used to estimate the dynamic wavenumber response of the system due to surface motion during the aperture synthesis period, modeled with a single adaptive parameter describing an exponential correlation along track. A Fourier filter can then be devised to correct for the wavenumber response of the remote sensor and scene correlation, with subsequent subtraction of an estimate of the speckle noise component. A linearized velocity bunching model, combined with a surface tilt and hydrodynamic model, is incorporated in the Fourier filter to derive estimates of wave height from the radar intensities corresponding to individual picture elements.

Noise-band factor analysis of cancer Fourier transform infrared evanescent-wave fiber optical (FTIR-FEW) spectra

NASA Astrophysics Data System (ADS)

Sukuta, Sydney; Bruch, Reinhard F.

2002-05-01

The goal of this study is to test the feasibility of using noise factor/eigenvector bands as general clinical analytical tools for diagnoses. We developed a new technique, Noise Band Factor Cluster Analysis (NBFCA), to diagnose benign tumors via their Fourier transform IR fiber optic evanescent wave spectral data for the first time. The middle IR region of human normal skin tissue and benign and melanoma tumors, were analyzed using this new diagnostic technique. Our results are not in full-agreement with pathological classifications hence there is a possibility that our approaches could complement or improve these traditional classification schemes. Moreover, the use of NBFCA make it much easier to delineate class boundaries hence this method provides results with much higher certainty.

Fourier transform infrared evanescent wave (FTIR-FEW) spectroscopy of tissue

NASA Astrophysics Data System (ADS)

Bruch, Reinhard F.; Sukuta, Sydney; Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Butvina, Leonid N.

1997-05-01

A new Fourier transform infrared fiberoptic evanescent wave (FTIR-FEW) spectroscopy method has been developed for tissue diagnostics in the middle infrared (MIR) wavelength range (3 to 20 micrometers). Specific novel fiberoptical chemical and biological sensors have been studied and used for spectroscopic diagnostic purposes. These nontoxic and nonhygroscopic fiber sensors are characterized by (1) low optical losses (0.05 to 0.2 dB/m at about 10 micrometer) and (2) high flexibility. Our new fiber optical devices can be utilized with standard commercially available Fourier transform spectrometers including attenuated total reflection (ATR) techniques. They are in particular ideally suited for noninvasive, fast, direct, sensitive investigations of in vivo and ex vivo medical diagnostics applications. Here we present data on IR spectra of skin tissue in vivo for various cases of melanoma and nevus in the range of 1480 - 1800 cm-1. The interpretation of the spectra of healthy and different stages of tumor and cancer skin tissue clearly indicates that this technique can be used for precancer and cancer diagnostics. This technique can be designed for real-time and on-line computer modeling and analysis of tissue changes.

Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy

NASA Astrophysics Data System (ADS)

Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks

2016-06-01

Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.

A hybrid method for transient wave propagation in a multilayered solid

NASA Astrophysics Data System (ADS)

Tian, Jiayong; Xie, Zhoumin

2009-08-01

We present a hybrid method for the evaluation of transient elastic-wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace-Fourier domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of generalized-ray group integrals. Each generalized-ray group integral containing Kth power of reverberation matrix R represents the set of K-times reflections and refractions of source waves arriving at receivers in the multilayered solid, which was computed by fast inverse Laplace transform (FILT) and fast Fourier transform (FFT) algorithms. However, the calculation burden and low precision of FILT-FFT algorithm limit the application of reverberation matrix method. In this paper, we expand each of generalized-ray group integrals into the sum of a series of generalized-ray integrals, each of which is accurately evaluated by Cagniard-De Hoop method in the theory of generalized ray. The numerical examples demonstrate that the proposed method makes it possible to calculate the early-time transient response in the complex multilayered-solid configuration efficiently.

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

Traveling waves and their tails in locally resonant granular systems

DOE PAGES

Xu, H.; Kevrekidis, P. G.; Stefanov, A.

2015-04-22

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely themore » avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.« less

Traveling waves and their tails in locally resonant granular systems

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

Xu, H.; Kevrekidis, P. G.; Stefanov, A.

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely themore » avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.« less

Propagation characteristics of optical fiber structures with arbitrary shape and index variation

NASA Technical Reports Server (NTRS)

Manshadi, F.

1990-01-01

The application of the scalar wave-fast Fourier transform (SW-FFT) technique to the computation of the propagation characteristics of some complex optical fiber structures is presented. The SW-FFT technique is based on the numerical solution of the scalar wave equation by a forward-marching fast Fourier transform method. This solution yields the spatial configuration of the fields as well as its modal characteristics in and around the guiding structure. The following are treated by the SW-FFT method: analysis of coupled optical fibers and computation of their odd and even modes and coupling length; the solution of tapered optical waveguides (transitions) and the study of the effect of the slope of the taper on mode conversion; and the analysis of branching optical fibers and demonstration of their mode-filtering and/or power-dividing properties.

Far-infrared Fourier Transform Spectroscopy Measurements of Mn12-acetate.

NASA Astrophysics Data System (ADS)

Tu, Jiufeng; Suzuki, Yoko; Mertes, K. M.; Sarachik, M. P.; Agladze, N. I.; Sievers, A. J.; Rumberger, E. M.; Hendrickson, D. N.; Christou, G.

2004-03-01

The transmission spectra of both powder samples and assemblies of single crystals of Mn_12-acetate were measured in the far infrared region (2.0 - 20 cm-1) using a Fourier transform technique. The energies of the observed aborption lines agree with those obtained by Mukhin et al. [1] using the backwards wave oscillator technique. The temperature dependence of the aborption lines, as well as the presence of additional absorption lines, will be discussed. [1] A. A. Mukhin, V. D. Travkin, A. K. Zvesdin, A. Caneschi, D. Gatteschi and R. Sessoli, Physica B 284-288 (2000) 1221-1222

Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements

NASA Technical Reports Server (NTRS)

Lait, Leslie R.; Stanford, John L.

1988-01-01

A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.

Quantitative damage imaging using Lamb wave diffraction tomography

NASA Astrophysics Data System (ADS)

Zhang, Hai-Yan; Ruan, Min; Zhu, Wen-Fa; Chai, Xiao-Dong

2016-12-01

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated numerically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern (SDP) of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional (1D) Fourier transform of the scattered projection and two-dimensional (2D) spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode (TMDT) and reflection mode diffraction tomography (RMDT), respectively. The reconstructed results of the two projections for a non-converted S0 scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11474195, 11274226, 11674214, and 51478258).

Investigation of the phase velocities of guided acoustic waves in soft porous layers.

PubMed

Boeckx, L; Leclaire, P; Khurana, P; Glorieux, C; Lauriks, W; Allard, J F

2005-02-01

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.

Molecular recognition in gas sensing: Results from acoustic wave and in-situ FTIR measurements

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

Hierlemann, A.; Ricco, A.J.; Bodenhoefer, K.

Surface acoustic wave (SAW) measurements were combined with direct, in-situ molecular spectroscopy to understand the interactions of surface-confined sensing films with gas-phase analytes. This was accomplished by collecting Fourier-transform infrared external-reflectance spectra (FTIR-ERS) on operating SAW devices during dosing of their specifically coated surfaces with key analytes.

On the asymptotic evolution of finite energy Airy wave functions.

PubMed

Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S

2015-06-15

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Cosine beamforming

NASA Astrophysics Data System (ADS)

Ruigrok, Elmer; Wapenaar, Kees

2014-05-01

In various application areas, e.g., seismology, astronomy and geodesy, arrays of sensors are used to characterize incoming wavefields due to distant sources. Beamforming is a general term for phased-adjusted summations over the different array elements, for untangling the directionality and elevation angle of the incoming waves. For characterizing noise sources, beamforming is conventionally applied with a temporal Fourier and a 2D spatial Fourier transform, possibly with additional weights. These transforms become aliased for higher frequencies and sparser array-element distributions. As a partial remedy, we derive a kernel for beamforming crosscorrelated data and call it cosine beamforming (CBF). By applying beamforming not directly to the data, but to crosscorrelated data, the sampling is effectively increased. We show that CBF, due to this better sampling, suffers less from aliasing and yields higher resolution than conventional beamforming. As a flip-side of the coin, the CBF output shows more smearing for spherical waves than conventional beamforming.

Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms.

PubMed

Trillo, C; Doval, A F; López-Vázquez, J C

2010-07-05

Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Lagueux, P.; Farley, V.; Marcotte, F.; Chamberland, M.

2009-09-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Farley, V.; Lagueux, P.; Marcotte, F.; Chamberland, M.

2009-05-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Finite mode analysis through harmonic waveguides

PubMed

Alieva; Wolf

2000-08-01

The mode analysis of signals in a multimodal shallow harmonic waveguide whose eigenfrequencies are equally spaced and finite can be performed by an optoelectronic device, of which the optical part uses the guide to sample the wave field at a number of sensors along its axis and the electronic part computes their fast Fourier transform. We illustrate this process with the Kravchuk transform.

Compression and R-wave detection of ECG/VCG data

NASA Technical Reports Server (NTRS)

Hayden, W. L.; Conover, M. F.; Bennett, W. P.

1972-01-01

Application of information theory to eliminate redundant part of electrocardiogram or vectorcardiogram is described. Operation of medical equipment to obtain three dimensional study of patient is discussed. Use of fast Fourier transform to accomplish data compression is explained.

Radar cross-section reduction based on an iterative fast Fourier transform optimized metasurface

NASA Astrophysics Data System (ADS)

Song, Yi-Chuan; Ding, Jun; Guo, Chen-Jiang; Ren, Yu-Hui; Zhang, Jia-Kai

2016-07-01

A novel polarization insensitive metasurface with over 25 dB monostatic radar cross-section (RCS) reduction is introduced. The proposed metasurface is comprised of carefully arranged unit cells with spatially varied dimension, which enables approximate uniform diffusion of incoming electromagnetic (EM) energy and reduces the threat from bistatic radar system. An iterative fast Fourier transform (FFT) method for conventional antenna array pattern synthesis is innovatively applied to find the best unit cell geometry parameter arrangement. Finally, a metasurface sample is fabricated and tested to validate RCS reduction behavior predicted by full wave simulation software Ansys HFSSTM and marvelous agreement is observed.

Fiber-optic evanescent-wave spectroscopy for fast multicomponent analysis of human blood

NASA Astrophysics Data System (ADS)

Simhi, Ronit; Gotshal, Yaron; Bunimovich, David; Katzir, Abraham; Sela, Ben-Ami

1996-07-01

A spectral analysis of human blood serum was undertaken by fiber-optic evanescent-wave spectroscopy (FEWS) by the use of a Fourier-transform infrared spectrometer. A special cell for the FEWS measurements was designed and built that incorporates an IR-transmitting silver halide fiber and a means for introducing the blood-serum sample. Further improvements in analysis were obtained by the adoption of multivariate calibration techniques that are already used in clinical chemistry. The partial least-squares algorithm was used to calculate the concentrations of cholesterol, total protein, urea, and uric acid in human blood serum. The estimated prediction errors obtained (in percent from the average value) were 6% for total protein, 15% for cholesterol, 30% for urea, and 30% for uric acid. These results were compared with another independent prediction method that used a neural-network model. This model yielded estimated prediction errors of 8.8% for total protein, 25% for cholesterol, and 21% for uric acid. spectroscopy, fiber-optic evanescent-wave spectroscopy, Fourier-transform infrared spectrometer, blood, multivariate calibration, neural networks.

Hyper-spectral imaging of aircraft exhaust plumes

NASA Astrophysics Data System (ADS)

Bowen, Spencer; Bradley, Kenneth; Gross, Kevin; Perram, Glen; Marciniak, Michael

2008-10-01

An imaging Fourier-transform spectrometer has been used to determine low spatial resolution temperature and chemical species concentration distributions of aircraft jet engine exhaust plumes. An overview of the imaging Fourier transform spectrometer and the methodology of the project is presented. Results to date are shared and future work is discussed. Exhaust plume data from a Turbine Technologies, LTD, SR-30 turbojet engine at three engine settings was collected using a Telops Field-portable Imaging Radiometric Spectrometer Technology Mid-Wave Extended (FIRST-MWE). Although the plume exhibited high temporal frequency fluctuations, temporal averaging of hyper-spectral data-cubes produced steady-state distributions, which, when co-added and Fourier transformed, produced workable spectra. These spectra were then reduced using a simplified gaseous effluent model to fit forward-modeled spectra obtained from the Line-By-Line Radiative Transfer Model (LBLRTM) and the high-resolution transmission (HITRAN) molecular absorption database to determine approximate temperature and concentration distributions. It is theorized that further development of the physical model will produce better agreement between measured and modeled data.

Detecting the spatial chirp signals by fractional Fourier lens with transformation materials

NASA Astrophysics Data System (ADS)

Chen, J.; Hu, J.

2018-02-01

Fractional Fourier transform (FrFT) is the general form of the Fourier transform and is an important tool in signal processing. As one typical application of FrFT, detecting the chirp rate (CR, or known as the rate of frequency change) of a chirp signal is important in many optical measurements. The optical FrFT that based on graded index lens fails to detect the high CR chirp because the short wave propagation distance of the impulse in the lens will weaken the paraxial approximation condition. With the help of transformation optics, the improved FrFT lens is proposed to adjust the high CR as well as the impulse location of the given input chirp signal. The designed transformation materials can implement the effect of space compression, making the input chirp signal is equivalent to have lower CR, therefore the system can satisfy the paraxial approximation better. As a result, this lens can improve the detection precision for the high CR. The numerical simulations verified the design. The proposed device may have both theoretical and practical values, and the design demonstrates the ability and flexibility of TO in spatial signal processing.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

USGS Publications Warehouse

Hsi-Ping, Liu

1990-01-01

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment. -Author

Method and apparatus for generating motor current spectra to enhance motor system fault detection

DOEpatents

Linehan, Daniel J.; Bunch, Stanley L.; Lyster, Carl T.

1995-01-01

A method and circuitry for sampling periodic amplitude modulations in a nonstationary periodic carrier wave to determine frequencies in the amplitude modulations. The method and circuit are described in terms of an improved motor current signature analysis. The method insures that the sampled data set contains an exact whole number of carrier wave cycles by defining the rate at which samples of motor current data are collected. The circuitry insures that a sampled data set containing stationary carrier waves is recreated from the analog motor current signal containing nonstationary carrier waves by conditioning the actual sampling rate to adjust with the frequency variations in the carrier wave. After the sampled data is transformed to the frequency domain via the Discrete Fourier Transform, the frequency distribution in the discrete spectra of those components due to the carrier wave and its harmonics will be minimized so that signals of interest are more easily analyzed.

Orbital stability of periodic traveling wave solutions for the Kawahara equation

NASA Astrophysics Data System (ADS)

de Andrade, Thiago Pinguello; Cristófani, Fabrício; Natali, Fábio

2017-05-01

In this paper, we investigate the orbital stability of periodic traveling waves for the Kawahara equation. We prove that the periodic traveling wave, under certain conditions, minimizes a convenient functional by using an adaptation of the method developed by Grillakis et al. [J. Funct. Anal. 74, 160-197 (1987)]. The required spectral properties to ensure the orbital stability are obtained by knowing the positiveness of the Fourier transform of the associated periodic wave established by Angulo and Natali [SIAM J. Math. Anal. 40, 1123-1151 (2008)].

Non-contact feature detection using ultrasonic Lamb waves

DOEpatents

Sinha, Dipen N [Los Alamos, NM

2011-06-28

Apparatus and method for non-contact ultrasonic detection of features on or within the walls of hollow pipes are described. An air-coupled, high-power ultrasonic transducer for generating guided waves in the pipe wall, and a high-sensitivity, air-coupled transducer for detecting these waves, are disposed at a distance apart and at chosen angle with respect to the surface of the pipe, either inside of or outside of the pipe. Measurements may be made in reflection or transmission modes depending on the relative position of the transducers and the pipe. Data are taken by sweeping the frequency of the incident ultrasonic waves, using a tracking narrow-band filter to reduce detected noise, and transforming the frequency domain data into the time domain using fast Fourier transformation, if required.

Chirped-Pulse Millimeter-Wave Spectroscopy of Rydberg-Rydberg Transitions

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

Prozument, Kirill; Colombo, Anthony P.; Zhou Yan

2011-09-30

Transitions between Rydberg states of Ca atoms, in a pulsed, supersonic atomic beam, are directly detected by chirped-pulse millimeter-wave spectroscopy. Broadband, high-resolution spectra with accurate relative intensities are recorded instantly. Free induction decay (FID) of atoms, polarized by the chirped pulse, at their Rydberg-Rydberg transition frequencies, is heterodyne detected, averaged in the time domain, and Fourier transformed into the frequency domain. Millimeter-wave transient nutations are observed, and the possibility of FID evolving to superradiance is discussed.

Millimeter-Wave Spectroscopy for Analytical Chemistry: Thermal Evolution of Low Volatility Impurities and Detection with a Fourier Transform Molecular Rotational Resonance Spectrometer (tev Ft-Mrr

NASA Astrophysics Data System (ADS)

Harris, Brent; Fields, Shelby S.; Neill, Justin L.; Pulliam, Robin; Muckle, Matt; Pate, Brooks

2016-06-01

Recent advances in Fourier transform millimeter-wave spectroscopy techniques have renewed the application reach of molecular rotational spectroscopy for analytical chemistry. We present a sampling method for sub ppm analysis of low volatility impurities by thermal evolution from solid powders using a millimeter-wave Fourier transform molecular rotational resonance (FT-MRR) spectrometer for detection. This application of FT-MRR is relevant to the manufacturing of safe oral pharmaceuticals. Low volatility impurities can be challenging to detect at 1 ppm levels with chromatographic techniques. One such example of a potentially mutagenic impurity is acetamide (v.p. 1 Torr at 40 C, m.p. 80 C). We measured the pure reference spectrum of acetamide by flowing the sublimated vapor pressure of acetamide crystals through the FT-MRR spectrometer. The spectrometer lower detection level (LDL) for a broadband (> 20 GHz, 10 min.) spectrum is 300 nTorr, 30 pmol, or 2 ng. For a 50 mg powder, perfect sample transfer efficiency can yield a w/w % detection limit of 35 ppb. We extended the sampling method for the acetamide reference measurement to an acetaminophen sample spiked with 5000 ppm acetamide in order to test the sample transfer efficiency when liberated from an pharmaceutical powder. A spectral reference matching algorithm detected the presence of several impurities including acetaldehyde, acetic acid, and acetonitrile that evolved at the melting point of acetaminophen, demonstrating the capability of FT-MRR for identification without a routine chemical standard. The method detection limit (MDL) without further development is less than 10 ppm w/w %. Resolved FT-MRR mixture spectra will be presented with a description of sampling methods.

Two Long-Wave Infrared Spectral Polarimeters for Use in Understanding Polarization Phenomenology

DTIC Science & Technology

2002-05-01

3550 Aberdeen SE Kirtland Air Force Base, New Mexico 87117 Abstract. Spectrally varying long-wave infrared ( LWIR ) polarization measurements can be used...to identify materials and to discriminate samples from a cluttered background. Two LWIR instruments have been built and fielded by the Air Force...Research Laboratory: a multispectral LWIR imaging polarimeter (LIP) and a full-Stokes Fourier transform in- frared (FTIR) spectral polarimeter (FSP

Isotropic Backward Waves Supported by a Spiral Array Metasurface.

PubMed

Tremain, Ben; Hooper, Ian R; Sambles, J Roy; Hibbins, Alastair P

2018-05-08

A planar metallic metasurface formed of spiral elements is shown to support an isotropic backward wave over a narrow band of microwave frequencies. The magnetic field of this left-handed mode is mapped experimentally using a near-field scanning technique, allowing the anti-parallel group and phase velocities to be directly visualised. The corresponding dispersion relation and isofrequency contours are obtained through Fourier transformation of the field images.

Visco-elastic controlled-source full waveform inversion without surface waves

NASA Astrophysics Data System (ADS)

Paschke, Marco; Krause, Martin; Bleibinhaus, Florian

2016-04-01

We developed a frequency-domain visco-elastic full waveform inversion for onshore seismic experiments with topography. The forward modeling is based on a finite-difference time-domain algorithm by Robertsson that uses the image-method to ensure a stress-free condition at the surface. The time-domain data is Fourier-transformed at every point in the model space during the forward modeling for a given set of frequencies. The motivation for this approach is the reduced amount of memory when computing kernels, and the straightforward implementation of the multiscale approach. For the inversion, we calculate the Frechet derivative matrix explicitly, and we implement a Levenberg-Marquardt scheme that allows for computing the resolution matrix. To reduce the size of the Frechet derivative matrix, and to stabilize the inversion, an adapted inverse mesh is used. The node spacing is controlled by the velocity distribution and the chosen frequencies. To focus the inversion on body waves (P, P-coda, and S) we mute the surface waves from the data. Consistent spatiotemporal weighting factors are applied to the wavefields during the Fourier transform to obtain the corresponding kernels. We test our code with a synthetic study using the Marmousi model with arbitrary topography. This study also demonstrates the importance of topography and muting surface waves in controlled-source full waveform inversion.

Accounting for the Spatial Observation Window in the 2-D Fourier Transform Analysis of Shear Wave Attenuation.

PubMed

Rouze, Ned C; Deng, Yufeng; Palmeri, Mark L; Nightingale, Kathryn R

2017-10-01

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the 2-D Fourier transform (2DFT) of the shear wave signal and measuring the phase velocity c(ω) and attenuation α(ω) from the peak location and full width at half-maximum (FWHM) of the 2DFT signal at discrete frequencies. However, when the shear wave is observed over a finite spatial range, the 2DFT signal is a convolution of the true signal and the observation window, and measurements using the FWHM can yield biased results. In this study, we describe a method to account for the size of the spatial observation window using a model of the 2DFT signal and a non-linear, least-squares fitting procedure to determine c(ω) and α(ω). Results from the analysis of finite-element simulation data agree with c(ω) and α(ω) calculated from the material parameters used in the simulation. Results obtained in a viscoelastic phantom indicate that the measured attenuation is independent of the observation window and agree with measurements of c(ω) and α(ω) obtained using the previously described progressive phase and exponential decay analysis. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Homogenization of Electromagnetic and Seismic Wavefields for Joint Inverse Modeling

NASA Astrophysics Data System (ADS)

Newman, G. A.; Commer, M.; Petrov, P.; Um, E. S.

2011-12-01

A significant obstacle in developing a robust joint imaging technology exploiting seismic and electromagnetic (EM) wave fields is the resolution at which these different geophysical measurements sense the subsurface. Imaging of seismic reflection data is an order of magnitude finer in resolution and scale compared to images produced with EM data. A consistent joint image of the subsurface geophysical attributes (velocity, electrical conductivity) requires/demands the different geophysical data types be similar in their resolution of the subsurface. The superior resolution of seismic data results from the fact that the energy propagates as a wave, while propagation of EM energy is diffusive and attenuates with distance. On the other hand, the complexity of the seismic wave field can be a significant problem due to high reflectivity of the subsurface and the generation of multiple scattering events. While seismic wave fields have been very useful in mapping the subsurface for energy resources, too much scattering and too many reflections can lead to difficulties in imaging and interpreting seismic data. To overcome these obstacles a formulation for joint imaging of seismic and EM wave fields is introduced, where each data type is matched in resolution. In order to accomplish this, seismic data are first transformed into the Laplace-Fourier Domain, which changes the modeling of the seismic wave field from wave propagation to diffusion. Though high frequency information (reflectivity) is lost with this transformation, several benefits follow: (1) seismic and EM data can be easily matched in resolution, governed by the same physics of diffusion, (2) standard least squares inversion works well with diffusive type problems including both transformed seismic and EM, (3) joint imaging of seismic and EM data may produce better starting velocity models critical for successful reverse time migration or full waveform imaging of seismic data (non transformed) and (4) possibilities to image across multiple scale lengths, incorporating different types of geophysical data and attributes in the process. Important numerical details of 3D seismic wave field simulation in the Laplace-Fourier domain for both acoustic and elastic cases will also be discussed.

Extraction of guided wave dispersion curve in isotropic and anisotropic materials by Matrix Pencil method.

PubMed

Chang, C Y; Yuan, F G

2018-05-16

Guided wave dispersion curves in isotropic and anisotropic materials are extracted automatically from measured data by Matrix Pencil (MP) method investigating through k-t or x-ω domain with a broadband signal. A piezoelectric wafer emits a broadband excitation, linear chirp signal to generate guided waves in the plate. The propagating waves are measured at discrete locations along the lines for one-dimensional laser Doppler vibrometer (1-D LDV). Measurements are first Fourier transformed into either wavenumber-time k-t domain or space-frequency x-ω domain. MP method is then employed to extract the dispersion curves explicitly associated with different wave modes. In addition, the phase and group velocity are deduced by the relations between wavenumbers and frequencies. In this research, the inspections for dispersion relations on an aluminum plate by MP method from k-t or x-ω domain are demonstrated and compared with two-dimensional Fourier transform (2-D FFT). Other experiments on a thicker aluminum plate for higher modes and a composite plate are analyzed by MP method. Extracted relations of composite plate are confirmed by three-dimensional (3-D) theoretical curves computed numerically. The results explain that the MP method not only shows more accuracy for distinguishing the dispersion curves on isotropic material, but also obtains good agreements with theoretical curves on anisotropic and laminated materials. Copyright © 2018 Elsevier B.V. All rights reserved.

Local Complex Potential Based Time Dependent Wave Packet Approach to Calculation of Vibrational Excitation Cross-sections in e-N2, e-H2 and e-CO Scattering

NASA Astrophysics Data System (ADS)

Sarma, Manabendra; Singh, Raman K.; Mishra, Manoj K.

2007-12-01

Vibrational excitation cross-sections σn←m(E) in resonant e-N2, e-CO and e-H2 scattering are calculated from transition matrix elements Tn←m(E) obtained using Fourier transform of the cross correlation function <φn(R)|ψm(R,t)> where ψm(R,t); e-iHA-(R)t/ℏφm(R). Time evolution under the influence of the resonance anionic Hamiltonian HA-(A- = N2-/CO/H2-) is effected using Lanczos and fast Fourier transforms and the target (A) vibrational eigenfunctions φm(R) and φn(R) are calculated using Fourier grid Hamiltonian method applied to PE curve of the neutral target. The resulting vibrational excitation cross-section profiles provide reasonable agreement with experimental results and the cross correlation functions offer an unequivocal differentiation between the boomerang and impulse models.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

PubMed

Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Image processing to optimize wave energy converters

NASA Astrophysics Data System (ADS)

Bailey, Kyle Marc-Anthony

The world is turning to renewable energies as a means of ensuring the planet's future and well-being. There have been a few attempts in the past to utilize wave power as a means of generating electricity through the use of Wave Energy Converters (WEC), but only recently are they becoming a focal point in the renewable energy field. Over the past few years there has been a global drive to advance the efficiency of WEC. Placing a mechanical device either onshore or offshore that captures the energy within ocean surface waves to drive a mechanical device is how wave power is produced. This paper seeks to provide a novel and innovative way to estimate ocean wave frequency through the use of image processing. This will be achieved by applying a complex modulated lapped orthogonal transform filter bank to satellite images of ocean waves. The complex modulated lapped orthogonal transform filterbank provides an equal subband decomposition of the Nyquist bounded discrete time Fourier Transform spectrum. The maximum energy of the 2D complex modulated lapped transform subband is used to determine the horizontal and vertical frequency, which subsequently can be used to determine the wave frequency in the direction of the WEC by a simple trigonometric scaling. The robustness of the proposed method is provided by the applications to simulated and real satellite images where the frequency is known.

[Identification of different Citrus sinensis (L.) Osbeck trees varieties using Fourier transform infrared spectroscopy and hierarchical cluster analysis].

PubMed

Yi, Shi-Lai; Deng, Lie; He, Shao-Lan; Shi, You-Ming; Zheng, Yong-Qiang; Lu, Qiang; Xie, Rang-Jin; Wei, Xian-Guoi; Li, Song-Wei; Jian, Shui-Xian

2012-11-01

Researched on diversity of the spring leaf samples of seven different Citrus sinensis (L.) Osbeck varieties by Fourier transform infrared (FTIR) spectroscopy technology, the results showed that the Fourier transform infrared spectra of seven varieties leaves was composited by the absorption band of cellulose and polysaccharide mainly, the wave number of characteristics absorption peaks were similar at their FTIR spectra. However, there were some differences in shape of peaks and relatively absorption intensity. The conspicuous difference was presented at the region between 1 500 and 700 cm(-1) by second derivative spectra. Through the hierarchical cluster analysis (HCA) of second derivative spectra between 1 500 and 700 cm(-1), the results showed that the clustering of the different varieties of Citrus sinensis (L.) Osbeck varieties was classification according to genetic relationship. The results showed that FTIR spectroscopy combined with hierarchical cluster analysis could be used to identify and classify of citrus varieties rapidly, it was an extension method to study on early leaves of varieties orange seedlings.

Adaptive spread spectrum receiver using acoustic surface wave technology

NASA Astrophysics Data System (ADS)

Das, P.; Milstein, L. B.

1984-05-01

This technical report summarizes the results of the research we have been engaged in regarding the use of surface acoustic wave devices in direct sequence spread spectrum receivers. The heart of this research has been the use of the device as a real-time Fourier transformer. A system of this type is sometimes referred to as a compressive receiver, and our use of the system has been primarily as a means to implement a narrowband interference rejection filter. In addition, we have studied many other topics such as rapid acquisition, Hilbert transform generation, etc. and these topics are all overviewed in this report.

Radar Measurements of Ocean Surface Waves using Proper Orthogonal Decomposition

DTIC Science & Technology

2017-03-30

rely on use of Fourier transforms (FFT) and filtering spectra on the linear dispersion relationship for ocean surface waves. This report discusses...the measured signal (e.g., Young et al., 1985). In addition, the methods often rely on filtering the FFT of radar backscatter or Doppler velocities...to those obtained with conventional FFT and dispersion curve filtering techniques (iv) Compare both results of(iii) to ground truth sensors (i .e

Droplet characteristic measurement in Fourier interferometry imaging and behavior at the rainbow angle.

PubMed

Briard, Paul; Saengkaew, Sawitree; Wu, Xuecheng; Meunier-Guttin-Cluzel, Siegfried; Chen, Linghong; Cen, Kefa; Gréhan, Gérard

2013-01-01

This paper presents the possibility of measuring the three-dimensional (3D) relative locations and diameters of a set of spherical particles and discusses the behavior of the light recorded around the rainbow angle, an essential step toward refractive index measurements. When a set of particles is illuminated by a pulsed incident wave, the particles act as spherical light wave sources. When the pulse duration is short enough to fix the particle location (typically about 10 ns), interference fringes between these different spherical waves can be recorded. The Fourier transform of the fringes divides the complex fringe systems into a series of spots, with each spot characterizing the interference between a pair of particles. The analyses of these spots (in position and shape) potentially allow the measurement of particle characteristics (3D relative position, particle diameter, and particle refractive index value).

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Mode analysis for energetics of a moving charge in Lorentz- and C P T -violating electrodynamics

NASA Astrophysics Data System (ADS)

DeCosta, Richard; Altschul, Brett

2018-03-01

In isotropic but Lorentz- and C P T -violating electrodynamics, it is known that a charge in uniform motion does not lose any energy to Cerenkov radiation. This presents a puzzle, since the radiation appears to be kinematically allowed for many modes. Studying the Fourier transforms of the most important terms in the modified magnetic field and Poynting vector, we confirm the vanishing of the radiation rate. Moreover, we show that the Fourier transform of the field changes sign between small and large wave numbers. This enables modes with very long wavelengths to carry negative energies, which cancel out the positive energies carried away by modes with shorter wavelengths. This cancelation had previously been inferred but never explicitly demonstrated.

Concerning the Spatial Heterodyne Spectrometer

DOE PAGES

Lenzner, Matthias; Diels, Jean -Claude

2016-01-22

A modified Spatial Heterodyne Spectrometer (SHS) is used for measuring atomic emission spectra with high resolution. This device is basically a Fourier Transform Spectrometer, but the Fourier transform is taken in the directions perpendicular to the optical propagation and heterodyned around one preset wavelength. In recent descriptions of this device, one specific phenomenon - the tilt of the energy front of wave packets when diffracted from a grating - was neglected. This led to an overestimate of the resolving power of this spectrograph, especially in situations when the coherence length of the radiation under test is in the order ofmore » the effective aperture of the device. In conclusion, the limits of usability are shown here together with some measurements of known spectral lines.« less

Ramanujan sums for signal processing of low-frequency noise.

PubMed

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums c(q)(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.

Ramanujan sums for signal processing of low-frequency noise

NASA Astrophysics Data System (ADS)

Planat, Michel; Rosu, Haret; Perrine, Serge

2002-11-01

An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums cq(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals.

Diagnostics of normal and cancer tissues by fiberoptic evanescent wave Fourier transform IR (FEW-FTIR) spectroscopy

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.

1998-06-01

Fourier Transform Infrared (FTIR) Spectroscopy using optical fibers operated in the attenuated total reflection (ATR) regime in the mid-IR region in the range 850 to 4000 cm-1 has recently found an application in the noninvasive diagnostics of tissues in vivo. The method is suitable for nondestructive, nontoxic, fast (seconds), direct measurements of the spectra of normal and pathological tissues in vitro, ex vivo, and in vivo in real time. The aim of our studies is the express testing of various tumor tissues at the early stages of their development. The method is expected to be further developed for endoscopic and biopsy applications as well as for the research of different materials.

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Detection of Rossby Waves in Multi-Parameters in Multi-Mission Satellite Observations and HYCOM Simulations in the Indian Ocean

NASA Technical Reports Server (NTRS)

Subrahmanyam, Bulusu; Heffner, David M.; Cromwell, David; Shriver, Jay F.

2009-01-01

Rossby waves are difficult to detect with in situ methods. However, as we show in this paper, they can be clearly identified in multi-parameters in multi-mission satellite observations of sea surface height (SSH), sea surface temperature (SST) and ocean color observations of chlorophyll-a (chl-a), as well as 1/12-deg global HYbrid Coordinate Ocean Model (HYCOM) simulations of SSH, SST and sea surface salinity (SSS) in the Indian Ocean. While the surface structure of Rossby waves can be elucidated from comparisons of the signal in different sea surface parameters, models are needed to gain direct information about how these waves affect the ocean at depth. The first three baroclinic modes of the Rossby waves are inferred from the Fast Fourier Transform (FFT), and two-dimensional Radon Transform (2D RT). At many latitudes the first and second baroclinic mode Rossby wave phase speeds from satellite observations and model parameters are identified.

Method and apparatus for generating motor current spectra to enhance motor system fault detection

DOEpatents

Linehan, D.J.; Bunch, S.L.; Lyster, C.T.

1995-10-24

A method and circuitry are disclosed for sampling periodic amplitude modulations in a nonstationary periodic carrier wave to determine frequencies in the amplitude modulations. The method and circuit are described in terms of an improved motor current signature analysis. The method insures that the sampled data set contains an exact whole number of carrier wave cycles by defining the rate at which samples of motor current data are collected. The circuitry insures that a sampled data set containing stationary carrier waves is recreated from the analog motor current signal containing nonstationary carrier waves by conditioning the actual sampling rate to adjust with the frequency variations in the carrier wave. After the sampled data is transformed to the frequency domain via the Discrete Fourier Transform, the frequency distribution in the discrete spectra of those components due to the carrier wave and its harmonics will be minimized so that signals of interest are more easily analyzed. 29 figs.

Parameter identification of JONSWAP spectrum acquired by airborne LIDAR

NASA Astrophysics Data System (ADS)

Yu, Yang; Pei, Hailong; Xu, Chengzhong

2017-12-01

In this study, we developed the first linear Joint North Sea Wave Project (JONSWAP) spectrum (JS), which involves a transformation from the JS solution to the natural logarithmic scale. This transformation is convenient for defining the least squares function in terms of the scale and shape parameters. We identified these two wind-dependent parameters to better understand the wind effect on surface waves. Due to its efficiency and high-resolution, we employed the airborne Light Detection and Ranging (LIDAR) system for our measurements. Due to the lack of actual data, we simulated ocean waves in the MATLAB environment, which can be easily translated into industrial programming language. We utilized the Longuet-Higgin (LH) random-phase method to generate the time series of wave records and used the fast Fourier transform (FFT) technique to compute the power spectra density. After validating these procedures, we identified the JS parameters by minimizing the mean-square error of the target spectrum to that of the estimated spectrum obtained by FFT. We determined that the estimation error is relative to the amount of available wave record data. Finally, we found the inverse computation of wind factors (wind speed and wind fetch length) to be robust and sufficiently precise for wave forecasting.

Planar metasurface retroreflector

NASA Astrophysics Data System (ADS)

Arbabi, Amir; Arbabi, Ehsan; Horie, Yu; Kamali, Seyedeh Mahsa; Faraon, Andrei

2017-07-01

Metasurfaces are two-dimensional arrangements of subwavelength scatterers that control the propagation of optical waves. Here, we show that cascaded metasurfaces, each performing a predefined mathematical transformation, provide a new optical design framework that enables new functionalities not yet demonstrated with single metasurfaces. Specifically, we demonstrate that retroreflection can be achieved with two vertically stacked planar metasurfaces, the first performing a spatial Fourier transform and its inverse, and the second imparting a spatially varying momentum to the Fourier transform of the incident light. Using this concept, we fabricate and test a planar monolithic near-infrared retroreflector composed of two layers of silicon nanoposts, which reflects light along its incident direction with a normal incidence efficiency of 78% and a large half-power field of view of 60°. The metasurface retroreflector demonstrates the potential of cascaded metasurfaces for implementing novel high-performance components, and enables low-power and low-weight passive optical transmitters.

Controlling matter waves in momentum space

NASA Astrophysics Data System (ADS)

Lin, De-Hone

2014-07-01

The transformation design method of momentum for matter waves in a harmonic trap is proposed. As applications, we design (1) a momentum invisibility cloak to control the distribution of a wave function in momentum space, (2) a quantum localization cloak that localizes a matter wave around zero momentum, and (3) the unusual quantum states of momentum space. Comprehension of these momentum cloaks in position space through the Fourier transformation is presented. In contrast to the construct of quantum cloaks in position space, the momentum cloaks presented here can only be reached by controlling the spring parameter of the trap and offering a potential there, without needing to control the effective mass of quantum particles themselves. The presented discussions also provide a possible inspiration to help localize and maintain a quantum state in momentum space by way of controlling the shape of a trap and a supplied potential.

An introduction to wavelet analysis in oceanography and meteorology - With application to the dispersion of Yanai waves

NASA Technical Reports Server (NTRS)

Meyers, Steven D.; Kelly, B. G.; O'Brien, J. J.

1993-01-01

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumbers, possibly due to interaction with the basin boundaries.

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

ERIC Educational Resources Information Center

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Delta function excitation of waves in the earth's ionosphere

NASA Technical Reports Server (NTRS)

Vidmar, R. J.; Crawford, F. W.; Harker, K. J.

1983-01-01

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

An Improvement to the Fourier Series Method for Inversion of Laplace Transforms Applied to Elastic and Viscoelastic Waves

DTIC Science & Technology

2007-01-01

Lawrence Livermore National Laboratory Report UCRL -MA-107254 Rev. 1. NO. OF COPIES ORGANIZATION 1 DEFENSE TECHNICAL (PDF INFORMATION CTR...AFB FL 32542 3 DARPA L CHRISTODOULOU W COBLENZ S WAX 3701 N FAIRFAX DR ARLINGTON VA 22203-1714 1 DIRECTOR US ARMY ARDEC

Remote Skin Tissue Diagnostics In Vivo By Fiber Optic Evanescent Wave Fourier Transform Infrared (FEW-FTIR) Spectroscopy

NASA Astrophysics Data System (ADS)

Kolyakov, Sergei; Afanasyeva, Natalia; Bruch, Reinhard; Afanasyeva, Natalia

1998-05-01

The new method of fiber optical evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy has been applied to the diagnostics of normal skin tissue, as well as precancerous and cancerous conditions. The FEW-FTIR technique is nondestructive and sensitive to changes of vibrational spectra in the IR region, without heating and damaging human and animal skin tissue. Therefore this method and technique is an ideal diagnostic tool for tumor and cancer characterization at an early stage of development on a molecular level. The application of fiber optic technology in the middle infrared (MIR) region is relatively inexpensive and can be adapted easily to any commercially available tabletop FTIR spectrometers. This method of diagnostics is fast (several seconds), and can be applied to many fields. Noninvasive medical diagnostics of skin cancer and other skin diseases in vivo, ex vivo, and in vitro allow for the development of convenient, remote clinical applications in dermatology and related fields. The spectral variations from normal to pathological skin tissue and environmental influence on skin have been measured.

Analysis of Gravitational Signals from Core-Collapse Supernovae (CCSNe) using MatLab

NASA Astrophysics Data System (ADS)

Frere, Noah; Mezzacappa, Anthony; Yakunin, Konstantin

2017-01-01

When a massive star runs out of fuel, it collapses under its own weight and rebounds in a powerful supernova explosion, sending, among other things, ripples through space-time, known as gravitational waves (GWs). GWs can be detected by earth-based observatories, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO). Observers must compare the data from GW detectors with theoretical waveforms in order to confirm that the detection of a GW signal from a particular source has occurred. GW predictions for core collapse supernovae (CCSNe) rely on computer simulations. The UTK/ORNL astrophysics group has performed such simulations. Here, I analyze the resulting waveforms, using Matlab, to generate their Fourier transforms, short-time Fourier transforms, energy spectra, evolution of frequencies, and frequency maxima. One product will be a Matlab interface for analyzing and comparing GW predictions based on data from future simulations. This interface will make it easier to analyze waveforms and to share the results with the GW astrophysics community. Funding provided by Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA.

Study of Fourier transform spectrometer based on Michelson interferometer wave-meter

NASA Astrophysics Data System (ADS)

Peng, Yuexiang; Wang, Liqiang; Lin, Li

2008-03-01

A wave-meter based on Michelson interferometer consists of a reference and a measurement channel. The voice-coiled motor using PID means can realize to move in stable motion. The wavelength of a measurement laser can be obtained by counting interference fringes of reference and measurement laser. Reference laser with frequency stabilization creates a cosine interferogram signal whose frequency is proportional to velocity of the moving motor. The interferogram of the reference laser is converted to pulse signal, and it is subdivided into 16 times. In order to get optical spectrum, the analog signal of measurement channel should be collected. The Analog-to-Digital Converter (ADC) for measurement channel is triggered by the 16-times pulse signal of reference laser. So the sampling rate is constant only depending on frequency of reference laser and irrelative to the motor velocity. This means the sampling rate of measurement channel signals is on a uniform time-scale. The optical spectrum of measurement channel can be processed with Fast Fourier Transform (FFT) method by DSP and displayed on LCD.

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

Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-productmore » carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.« less

Refraction of coastal ocean waves

NASA Technical Reports Server (NTRS)

Shuchman, R. A.; Kasischke, E. S.

1981-01-01

Refraction of gravity waves in the coastal area off Cape Hatteras, NC as documented by synthetic aperture radar (SAR) imagery from Seasat orbit 974 (collected on September 3, 1978) is discussed. An analysis of optical Fourier transforms (OFTs) from more than 70 geographical positions yields estimates of wavelength and wave direction for each position. In addition, independent estimates of the same two quantities are calculated using two simple theoretical wave-refraction models. The OFT results are then compared with the theoretical results. A statistical analysis shows a significant degree of linear correlation between the data sets. This is considered to indicate that the Seasat SAR produces imagery whose clarity is sufficient to show the refraction of gravity waves in shallow water.

Experimental Investigation of the Properties of an Acoustic Wave Induced by Laser Ablation of a Solid Target in Water-Confined Plasma Propulsion

NASA Astrophysics Data System (ADS)

Zheng, Zhiyuan; Gao, Hua; Gao, Lu; Xing, Jie

2014-11-01

Acoustic waves generated in nanosecond pulsed-laser ablation of a solid target in both air and water-confined environments were measured experimentally. It was found that the amplitude of the acoustic wave tended to decrease with an increase in water thickness. The waves were analyzed by means of fast Fourier transform. It was shown that there are several frequency components in the acoustic waves with the dominant frequency shifting from high frequency to low frequency as the thickness of the water layer increases. Furthermore, strong acoustic pressure led to enhancement of the coupling of the laser energy to the target in laser plasma propulsion.

Using 3D Simulation of Elastic Wave Propagation in Laplace Domain for Electromagnetic-Seismic Inverse Modeling

NASA Astrophysics Data System (ADS)

Petrov, P.; Newman, G. A.

2010-12-01

Quantitative imaging of the subsurface objects is essential part of modern geophysical technology important in oil and gas exploration and wide-range engineering applications. A significant advancement in developing a robust, high resolution imaging technology is concerned with using the different geophysical measurements (gravity, EM and seismic) sense the subsurface structure. A joint image of the subsurface geophysical attributes (velocity, electrical conductivity and density) requires the consistent treatment of the different geophysical data (electromagnetic and seismic) due to their differing physical nature - diffusive and attenuated propagation of electromagnetic energy and nonlinear, multiple scattering wave propagation of seismic energy. Recent progress has been reported in the solution of this problem by reducing the complexity of seismic wave field. Works formed by Shin and Cha (2009 and 2008) suggests that low-pass filtering the seismic trace via Laplace-Fourier transformation can be an effective approach for obtaining seismic data that has similar spatial resolution to EM data. The effect of Laplace- Fourier transformation on the low-pass filtered trace changes the modeling of the seismic wave field from multi-wave propagation to diffusion. The key benefit of transformation is that diffusive wave-field inversion works well for both data sets seismic (Shin and Cha, 2008) and electromagnetic (Commer and Newman 2008, Newman et al., 2010). Moreover the different data sets can also be matched for similar and consistent resolution. Finally, the low pass seismic image is also an excellent choice for a starting model when analyzing the entire seismic waveform to recover the high spatial frequency components of the seismic image; its reflectivity (Shin and Cha, 2009). Without a good starting model full waveform seismic imaging and migration can encounter serious difficulties. To produce seismic wave fields consistent for joint imaging in the Laplace-Fourier domain we had developed 3D code for full-wave field simulation in the elastic media which take into account nonlinearity introduced by free-surface effects. Our approach is based on the velocity-stress formulation. In the contrast to conventional formulation we defined the material properties such as density and Lame constants not at nodal points but within cells. This second order finite differences method formulated in the cell-based grid, generate numerical solutions compatible with analytical ones within the range errors determinate by dispersion analysis. Our simulator will be embedded in an inversion scheme for joint seismic- electromagnetic imaging. It also offers possibilities for preconditioning the seismic wave propagation problems in the frequency domain. References. Shin, C. & Cha, Y. (2009), Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int. 177(3), 1067- 1079. Shin, C. & Cha, Y. H. (2008), Waveform inversion in the Laplace domain, Geophys. J. Int. 173(3), 922-931. Commer, M. & Newman, G. (2008), New advances in three-dimensional controlled-source electromagnetic inversion, Geophys. J. Int. 172(2), 513-535. Newman, G. A., Commer, M. & Carazzone, J. J. (2010), Imaging CSEM data in the presence of electrical anisotropy, Geophysics, in press.

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

DOE PAGES

Paul, J.; Dey, P.; Tokumoto, T.; ...

2014-10-07

The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. Furthermore, the lineshapes of themore » 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.« less

Coherent field propagation between tilted planes.

PubMed

Stock, Johannes; Worku, Norman Girma; Gross, Herbert

2017-10-01

Propagating electromagnetic light fields between nonparallel planes is of special importance, e.g., within the design of novel computer-generated holograms or the simulation of optical systems. In contrast to the extensively discussed evaluation between parallel planes, the diffraction-based propagation of light onto a tilted plane is more burdensome, since discrete fast Fourier transforms cannot be applied directly. In this work, we propose a quasi-fast algorithm (O(N 3  log N)) that deals with this problem. Based on a proper decomposition into three rotations, the vectorial field distribution is calculated on a tilted plane using the spectrum of plane waves. The algorithm works on equidistant grids, so neither nonuniform Fourier transforms nor an explicit complex interpolation is necessary. The proposed algorithm is discussed in detail and applied to several examples of practical interest.

Broadband millimeter-wave GaAs transmitters and receivers using planar bow-tie antennas

NASA Technical Reports Server (NTRS)

Konishi, Y.; Kamegawa, M.; Case, M.; Yu, R.; Rodwell, M. J. W.; York, R. A.; Rutledge, D. B.

1992-01-01

We report broadband monolithic transmitters and receivers IC's for mm-wave electromagnetic measurements. The IC's use nonlinear transmission lines (NLTL) and sampling circuits as picosecond pulse generators and detectors. The pulses are radiated and received by planar monolithic bow-tie antennas, collimated with silicon substrate lenses and off-axis parabolic reflectors. Through Fourier transformation of the received pulse, 30-250 GHz free space gain-frequency measurements are demonstrated with an accuracy approximately = 0.17 dB, RMS.

Extended sources near-field processing of experimental aperture synthesis data and application of the Gerchberg method for enhancing radiometric three-dimensional millimetre-wave images in security screening portals

NASA Astrophysics Data System (ADS)

Salmon, Neil A.

2017-10-01

Aperture synthesis for passive millimetre wave imaging provides a means to screen people for concealed threats in the extreme near-field configuration of a portal, a regime where the imager to subject distance is of the order of both the required depth-of-field and the field-of-view. Due to optical aberrations, focal plane array imagers cannot deliver the large depth-of-fields and field-of-views required in this regime. Active sensors on the other hand can deliver these but face challenges of illumination, speckle and multi-path issues when imaging canyon regions of the body. Fortunately an aperture synthesis passive millimetre wave imaging system can deliver large depth-of-fields and field-of-views, whilst having no speckle effects, as the radiometric emission from the human body is spatially incoherent. Furthermore, as in portal security screening scenarios the aperture synthesis imaging technique delivers a half-wavelength spatial resolution, it can effectively screen the whole of the human body. Some recent measurements are presented that demonstrate the three-dimensional imaging capability of extended sources using a 22 GHz aperture synthesis system. A comparison is made between imagery generated via the analytic Fourier transform and a gridding fast Fourier transform method. The analytic Fourier transform enables aliasing in the imagery to be more clearly identified. Some initial results are also presented of how the Gerchberg technique, an image enhancement algorithm used in radio astronomy, is adapted for three-dimensional imaging in security screening. This technique is shown to be able to improve the quality of imagery, without adding extra receivers to the imager. The requirements of a walk through security screening system for use at entrances to airport departure lounges are discussed, concluding that these can be met by an aperture synthesis imager.

Real-time wideband cylindrical holographic surveillance system

DOEpatents

Sheen, David M.; McMakin, Douglas L.; Hall, Thomas E.; Severtsen, Ronald H.

1999-01-01

A wideband holographic cylindrical surveillance system including a transceiver for generating a plurality of electromagnetic waves; antenna for transmitting the electromagnetic waves toward a target at a plurality of predetermined positions in space; the transceiver also receiving and converting electromagnetic waves reflected from the target to electrical signals at a plurality of predetermined positions in space; a computer for processing the electrical signals to obtain signals corresponding to a holographic reconstruction of the target; and a display for displaying the processed information to determine nature of the target. The computer has instructions to apply Fast Fourier Transforms and obtain a three dimensional cylindrical image.

The ISPM unified radio and plasma wave experiment

NASA Technical Reports Server (NTRS)

Stone, R. G.; Caldwell, J.; Deconchy, Y.; Deschanciaux, C.; Ebbett, R.; Epstein, G.; Groetz, K.; Harvey, C. C.; Hoang, S.; Howard, R.

1983-01-01

Hardware for the International Solar Polar Mission (ISPM) Unified Radio and Plasma (URAP) wave experiment is presented. The URAP determines direction and polarization of distant radio sources for remote sensing of the heliosphere, and studies local wave phenomena which determine the transport coefficients of the ambient plasma. Electric and magnetic field antennas and preamplifiers; the electromagnetic compatibility plan and grounding; radio astronomy and plasma frequency receivers; a fast Fourier transformation data processing unit waveform analyzer; dc voltage measurements; a fast envelope sampler for the solar wind, and plasmas near Jupiter; a sounder; and a power converter are described.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

PubMed

Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

2015-09-01

A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

Optical calculation of correlation filters for a robotic vision system

NASA Technical Reports Server (NTRS)

Knopp, Jerome

1989-01-01

A method is presented for designing optical correlation filters based on measuring three intensity patterns: the Fourier transform of a filter object, a reference wave and the interference pattern produced by the sum of the object transform and the reference. The method can produce a filter that is well matched to both the object, its transforming optical system and the spatial light modulator used in the correlator input plane. A computer simulation was presented to demonstrate the approach for the special case of a conventional binary phase-only filter. The simulation produced a workable filter with a sharp correlation peak.

First low frequency all-sky search for continuous gravitational wave signals

NASA Astrophysics Data System (ADS)

Aasi, J.; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Amariutei, D. V.; Andersen, M.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Ashton, G.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Bartlett, J.; Barton, M. A.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Behnke, B.; Bejger, M.; Belczynski, C.; Bell, A. S.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Bork, R.; Born, M.; Boschi, V.; Bose, Sukanta; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Branco, V.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Calderón Bustillo, J.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Celerier, C.; Cella, G.; Cepeda, C.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, X.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Colombini, M.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Damjanic, M. D.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Dominguez, E.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Edwards, M.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J. M.; Eikenberry, S. S.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fairhurst, S.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Feldbaum, D.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frede, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; Gergely, L. Á.; Germain, V.; Ghosh, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gleason, J. R.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez, J.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Goßler, S.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Groot, P.; Grote, H.; Grover, K.; Grunewald, S.; Guidi, G. M.; Guido, C. J.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammer, D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hoelscher-Obermaier, J.; Hofman, D.; Hollitt, S. E.; Holt, K.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh, M.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Islas, G.; Isler, J. C.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacobson, M. B.; Jang, H.; Jaranowski, P.; Jawahar, S.; Ji, Y.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Haris, K.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Karlen, J. L.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kerrigan, J.; Key, J. S.; Khalili, F. Y.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, K.; Kim, N. G.; Kim, N.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kline, J. T.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, A.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, J.; Lee, J. P.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Lewis, J. B.; Li, T. G. F.; Libson, A.; Lin, A. C.; Littenberg, T. B.; Lockerbie, N. A.; Lockett, V.; Lodhia, D.; Logue, J.; Lombardi, A. L.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lubinski, M. J.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; Macarthur, J.; Macdonald, E. P.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Madden-Fong, D. X.; Magaña-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mangini, N. M.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Mastrogiovanni, S.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Mehmet, M.; Meidam, J.; Meinders, M.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moe, B.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Mukherjee, A.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nagy, M. F.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Okounkova, M.; Oppermann, P.; Oram, R.; O'Reilly, B.; Ortega, W. E.; O'Shaughnessy, R.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Padilla, C. T.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pan, Y.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Papa, M. A.; Paris, H. R.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patrick, Z.; Pedraza, M.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Pickenpack, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poeld, J. H.; Poggiani, R.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Rácz, I.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rodger, A. S.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Saleem, M.; Salemi, F.; Sammut, L.; Sanchez, E.; Sandberg, V.; Sanders, J. R.; Santiago-Prieto, I.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Savage, R.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Sevigny, A.; Shaddock, D. A.; Shaffery, P.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Shoemaker, D. H.; Sidery, T. L.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Steplewski, S.; Stevenson, S. P.; Stone, R.; Strain, K. A.; Straniero, N.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepanczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Tse, M.; Turconi, M.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; van den Broeck, C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, M.; Wade, L. E.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whitcomb, S. E.; White, D. J.; Whiting, B. F.; Williams, K. J.; Williams, L.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Yablon, J.; Yakushin, I.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zhang, Fan; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2016-02-01

In this paper we present the results of the first low frequency all-sky search of continuous gravitational wave signals conducted on Virgo VSR2 and VSR4 data. The search covered the full sky, a frequency range between 20 and 128 Hz with a range of spin-down between -1.0 ×10-10 and +1.5 ×10-11 Hz /s , and was based on a hierarchical approach. The starting point was a set of short fast Fourier transforms, of length 8192 s, built from the calibrated strain data. Aggressive data cleaning, in both the time and frequency domains, has been done in order to remove, as much as possible, the effect of disturbances of instrumental origin. On each data set a number of candidates has been selected, using the FrequencyHough transform in an incoherent step. Only coincident candidates among VSR2 and VSR4 have been examined in order to strongly reduce the false alarm probability, and the most significant candidates have been selected. The criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect of large instrumental artifacts. Selected candidates have been subject to a follow-up by constructing a new set of longer fast Fourier transforms followed by a further incoherent analysis, still based on the FrequencyHough transform. No evidence for continuous gravitational wave signals was found, and therefore we have set a population-based joint VSR2-VSR4 90% confidence level upper limit on the dimensionless gravitational wave strain in the frequency range between 20 and 128 Hz. This is the first all-sky search for continuous gravitational waves conducted, on data of ground-based interferometric detectors, at frequencies below 50 Hz. We set upper limits in the range between about 1 0-24 and 2 ×10-23 at most frequencies. Our upper limits on signal strain show an improvement of up to a factor of ˜2 with respect to the results of previous all-sky searches at frequencies below 80 Hz.

Electromagnetic plasma wave propagation along a magnetic field. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Olson, C. L.

1970-01-01

The linearized response of a Vlasov plasma to the steady-state excitation of transverse plasma waves along an external magnetic field is examined. Assuming a delta-function excitation mechanism, and performing a detailed Vlasov-Maxwell equation analysis using Fourier-Laplace transforms, the plasma response is found to consist of three terms: a branch-cut term, a free-streaming term, and a dielectric-pole term. Also considered is the phenomenon of plasma wave echoes. The case of longitudinal electrostatic waves is extended to the case of transverse plasma waves that propagate along an external magnetic field. It is shown that a transverse echo results in lowest order only when one excitation is transverse and the other is longitudinal.

Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Xu, Wen-Cheng; Luo, Zhi-Chao

2016-09-01

We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Nondestructive quantification of the soluble-solids content and the available acidity of apples by Fourier-transform near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Ying, Yibin; Liu, Yande; Tao, Yang

2005-09-01

This research evaluated the feasibility of using Fourier-transform near-infrared (FT-NIR) spectroscopy to quantify the soluble-solids content (SSC) and the available acidity (VA) in intact apples. Partial least-squares calibration models, obtained from several preprocessing techniques (smoothing, derivative, etc.) in several wave-number ranges were compared. The best models were obtained with the high coefficient determination (r) 0.940 for the SSC and a moderate r of 0.801 for the VA, root-mean-square errors of prediction of 0.272% and 0.053%, and root-mean-square errors of calibration of 0.261% and 0.046%, respectively. The results indicate that the FT-NIR spectroscopy yields good predictions of the SSC and also showed the feasibility of using it to predict the VA of apples.

Documentation for subroutine REDUC3, an algorithm for the linear filtering of gridded magnetic data

USGS Publications Warehouse

Blakely, Richard J.

1977-01-01

Subroutine REDUC3 transforms a total field anomaly h1(x,y) , measured on a horizontal and rectangular grid, into a new anomaly h2(x,y). This new anomaly is produced by the same source as h1(x,y) , but (1) is observed at a different elevation, (2) has a source with a different direction of magnetization, and/or (3) has a different direction of residual field. Case 1 is tantamount to upward or downward continuation. Cases 2 and 3 are 'reduction to the pole', if the new inclinations of both the magnetization and regional field are 90 degrees. REDUC3 is a filtering operation applied in the wave-number domain. It first Fourier transforms h1(x,y) , multiplies by the appropriate filter, and inverse Fourier transforms the result to obtain h2(x,y). No assumptions are required about the shape of the source or how the intensity of magnetization varies within it.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

ERIC Educational Resources Information Center

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Quantitative subsurface analysis using frequency modulated thermal wave imaging

NASA Astrophysics Data System (ADS)

Subhani, S. K.; Suresh, B.; Ghali, V. S.

2018-01-01

Quantitative depth analysis of the anomaly with an enhanced depth resolution is a challenging task towards the estimation of depth of the subsurface anomaly using thermography. Frequency modulated thermal wave imaging introduced earlier provides a complete depth scanning of the object by stimulating it with a suitable band of frequencies and further analyzing the subsequent thermal response using a suitable post processing approach to resolve subsurface details. But conventional Fourier transform based methods used for post processing unscramble the frequencies with a limited frequency resolution and contribute for a finite depth resolution. Spectral zooming provided by chirp z transform facilitates enhanced frequency resolution which can further improves the depth resolution to axially explore finest subsurface features. Quantitative depth analysis with this augmented depth resolution is proposed to provide a closest estimate to the actual depth of subsurface anomaly. This manuscript experimentally validates this enhanced depth resolution using non stationary thermal wave imaging and offers an ever first and unique solution for quantitative depth estimation in frequency modulated thermal wave imaging.

Numerical modeling of guided ultrasonic waves generated and received by piezoelectric wafer in a Delaminated composite beam

NASA Astrophysics Data System (ADS)

Xu, G. D.; Xu, B. Q.; Xu, C. G.; Luo, Y.

2017-05-01

A spectral finite element method (SFEM) is developed to analyze guided ultrasonic waves in a delaminated composite beam excited and received by a pair of surface-bonded piezoelectric wafers. The displacements of the composite beam and the piezoelectric wafer are represented by Timoshenko beam and Euler Bernoulli theory respectively. The linear piezoelectricity is used to model the electrical-mechanical coupling between the piezoelectric wafer and the beam. The coupled governing equations and the boundary conditions in time domain are obtained by using the Hamilton's principle, and then the SFEM are formulated by transforming the coupled governing equations into frequency domain via the discrete Fourier transform. The guided waves are analyzed while the interaction of waves with delamination is also discussed. The elements needed in SFEM is far fewer than those for finite element method (FEM), which result in a much faster solution speed in this study. The high accuracy of the present SFEM is verified by comparing with the finite element results.

Fourier-Domain Shift Matching: A Robust Time-of-Flight Approach for Shear Wave Speed Estimation.

PubMed

Rosen, David; Jiang, Jingfeng

2018-05-01

Our primary objective of this work was to design and test a new time-of-flight (TOF) method that allows measurements of shear wave speed (SWS) following impulsive excitation in soft tissues. Particularly, under the assumption of the local plane shear wave, this work named the Fourier-domain shift matching (FDSM) method, estimates SWS by aligning a series of shear waveforms either temporally or spatially using a solution space deduced by characteristic curves of the well-known 1-D wave equation. The proposed SWS estimation method was tested using computer-simulated data, and tissue-mimicking phantom and ex vivo tissue experiments. Its performance was then compared with three other known TOF methods: lateral time-to-peak (TTP) method with robust random sampling consensus (RANSAC) fitting method, Radon sum transformation method, and a modified cross correlation method. Hereafter, these three TOF methods are referred to as the TTP-RANSAC, Radon sum, and X-corr methods, respectively. In addition to an adapted form of the 2-D Fourier transform (2-D FT)-based method in which the (group) SWS was approximated by averaging phase SWS values was considered for comparison. Based on data evaluated, we found that the overall performance of the above-mentioned temporal implementation of the proposed FDSM method was most similar to the established Radon sum method (correlation = 0.99, scale factor = 1.03, and mean difference = 0.07 m/s), and the 2-D FT (correlation = 0.98, scale factor = 1.00, and mean difference = 0.10 m/s) at high signal quality. However, results obtained from the 2-D FT method diverged (correlation = 0.201) from these of the proposed temporal implementation in the presence of diminished signal quality, whereas the agreement between the Radon sum approach and the proposed temporal implementation largely remained the same (correlation = 0.98).

Fourier-transform-based model for carrier transport in semiconductor heterostructures: Longitudinal optical phonon scattering

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

Lü, X.; Schrottke, L.; Grahn, H. T.

We present scattering rates for electrons at longitudinal optical phonons within a model completely formulated in the Fourier domain. The total intersubband scattering rates are obtained by averaging over the intrasubband electron distributions. The rates consist of the Fourier components of the electron wave functions and a contribution depending only on the intersubband energies and the intrasubband carrier distributions. The energy-dependent part can be reproduced by a rational function, which allows for the separation of the scattering rates into a dipole-like contribution, an overlap-like contribution, and a contribution which can be neglected for low and intermediate carrier densities of themore » initial subband. For a balance between accuracy and computation time, the number of Fourier components can be adjusted. This approach facilitates an efficient design of complex heterostructures with realistic, temperature- and carrier density-dependent rates.« less

Experimental investigation of shock wave diffraction over a single- or double-sphere model

NASA Astrophysics Data System (ADS)

Zhang, L. T.; Wang, T. H.; Hao, L. N.; Huang, B. Q.; Chen, W. J.; Shi, H. H.

2017-01-01

In this study, the unsteady drag produced by the interaction of a shock wave with a single- and a double-sphere model is measured using imbedded accelerometers. The shock wave is generated in a horizontal circular shock tube with an inner diameter of 200 mm. The effect of the shock Mach number and the dimensionless distance between spheres is investigated. The time-history of the drag coefficient is obtained based on Fast Fourier Transformation (FFT) band-block filtering and polynomial fitting of the measured acceleration. The measured peak values of the drag coefficient, with the associated uncertainty, are reported.

Real-time wideband cylindrical holographic surveillance system

DOEpatents

Sheen, D.M.; McMakin, D.L.; Hall, T.E.; Severtsen, R.H.

1999-01-12

A wideband holographic cylindrical surveillance system is disclosed including a transceiver for generating a plurality of electromagnetic waves; antenna for transmitting the electromagnetic waves toward a target at a plurality of predetermined positions in space; the transceiver also receiving and converting electromagnetic waves reflected from the target to electrical signals at a plurality of predetermined positions in space; a computer for processing the electrical signals to obtain signals corresponding to a holographic reconstruction of the target; and a display for displaying the processed information to determine nature of the target. The computer has instructions to apply Fast Fourier Transforms and obtain a three dimensional cylindrical image. 13 figs.

Subsonic and Supersonic Jet Noise Calculations Using PSE and DNS

NASA Technical Reports Server (NTRS)

Balakumar, P.; Owis, Farouk

1999-01-01

Noise radiated from a supersonic jet is computed using the Parabolized Stability Equations (PSE) method. The evolution of the instability waves inside the jet is computed using the PSE method and the noise radiated to the far field from these waves is calculated by solving the wave equation using the Fourier transform method. We performed the computations for a cold supersonic jet of Mach number 2.1 which is excited by disturbances with Strouhal numbers St=.2 and .4 and the azimuthal wavenumber m=l. Good agreement in the sound pressure level are observed between the computed and the measured (Troutt and McLaughlin 1980) results.

High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited].

PubMed

Hayashi, Shin'ichiro; Nawata, Koji; Sakai, Hiroshi; Taira, Takunori; Minamide, Hiroaki; Kawase, Kodo

2012-01-30

We report on the development of a high-peak-power, single-longitudinal-mode and tunable injection-seeded terahertz-wave parametric generator using MgO:LiNbO3, which operates at room temperature. The high peak power (> 120 W) is enough to allow easy detection by commercial and calibrated pyroelectric detectors, and the spectral resolution (< 10 GHz) is the Fourier transform limit of the sub-nanosecond terahertz-wave pulse. The tunability (1.2-2.8 THz) and the small footprint size (A3 paper, 29.7 × 42 cm) are suitable for a variety of applications.

An efficient 3-dim FFT for plane wave electronic structure calculations on massively parallel machines composed of multiprocessor nodes

NASA Astrophysics Data System (ADS)

Goedecker, Stefan; Boulet, Mireille; Deutsch, Thierry

2003-08-01

Three-dimensional Fast Fourier Transforms (FFTs) are the main computational task in plane wave electronic structure calculations. Obtaining a high performance on a large numbers of processors is non-trivial on the latest generation of parallel computers that consist of nodes made up of a shared memory multiprocessors. A non-dogmatic method for obtaining high performance for such 3-dim FFTs in a combined MPI/OpenMP programming paradigm will be presented. Exploiting the peculiarities of plane wave electronic structure calculations, speedups of up to 160 and speeds of up to 130 Gflops were obtained on 256 processors.

Laboratory rotational spectroscopy of cyano substituted polycyclic aromatic hydrocarbons

NASA Astrophysics Data System (ADS)

McNaughton, Don; Jahn, Michaela K.; Travers, Michael J.; Wachsmuth, Dennis; Godfrey, Peter D.; Grabow, Jens-Uwe

2018-06-01

The rotational spectra of the four cyano substituted polycyclic aromatic hydrocarbon (PAH) molecules 1-cyanonaphthalene, 2-cyanonaphthalene, 9-cyanoanthracene, and 9-cyanophenanthrene have been recorded in molecular expansions using a Stark-modulated millimetre-wave spectrometer and a Fourier transform microwave spectrometer in the centimetre-wave region. The spectra have been assigned and fitted to provide molecular constants and quadrupole hyperfine constants of sufficient accuracy to enable complete hyperfine structure line predictions for interstellar searches. The data may provide a route into detection of small PAHs in the interstellar medium.

Pair-density waves, charge-density waves, and vortices in high-Tc cuprates

NASA Astrophysics Data System (ADS)

Dai, Zhehao; Zhang, Ya-Hui; Senthil, T.; Lee, Patrick A.

2018-05-01

A recent scanning tunneling microscopy (STM) experiment reports the observation of a charge-density wave (CDW) with a period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately 4a period CDWs that are commonly observed in the cuprates. Inspired by this work, we study a model where a bidirectional pair-density wave (PDW) with period 8 is at play. This further divides into two classes: (1) where the PDW is a competing state of the d -wave superconductor and can exist only near the vortex core where the d -wave order is suppressed and (2) where the PDW is the primary order, the so-called "mother state" that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge-density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the d -wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period-8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions. There is also a line of zeros in the inverse Fourier transform of filtered data. We propose that these are key experimental signatures that can distinguish between the PDW-driven scenario from the more mundane option that the period-8 CDW is primary. We discuss the pro's and con's of the options considered above. Finally, we attempt to place the STM experiment in the broader context of pseudogap physics of underdoped cuprates and relate this observation to the unusual properties of x-ray scattering data on CDW carried out to very high magnetic field.

New developments in photoacoustics

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

Rosencwaig, A.

1981-07-01

There have been several important new developments in the fields of photoacoustics and photoacoustic spectroscopy. Photoactoustic techniques are now being used in ferromagnetic and electron spin resonance experiments, and there have been rapid advances in Fourier-transform infrared photoacoustic spectroscopy. In addition, the calorimetric aspects of photoacoustics are now being extensively exploited for phase transition studies, and to perform thermal-wave imaging and microscopy.

Tracking Polymer Cure Via Embedded Optical Fibers

NASA Technical Reports Server (NTRS)

Dean, David L.; Davidson, T. Fred

1993-01-01

Fourier-transform infrared spectroscopy applied in interior of specimen of material by bringing infrared light through specimen in optical fiber. Light interacts with material via evanescent-wave effect. Spectra obtained in this way at various times during curing process also combined with data from ultrasonic, thermographic, and dielectric-impedance monitoring, and other measurement techniques to obtain more complete characterization of progress of curing process.

Diagnostics of cancer tissues by fiber optic evanescent wave Fourier transform IR (FEW-FTIR) spectroscopy

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Letokhov, Vladilen S.; Golovkina, Viktoriya N.

1997-08-01

Fiber optic evanescent wave Fourier transform infrared (FEW- FTIR) spectroscopy using fiberoptic sensors operated in the attenuated total reflection (ATR) regime in the middle infrared (IR) region of the spectrum (850 - 1850 cm-1) has recently found application in the diagnostics of tissues. The method is suitable for noninvasive and rapid (seconds) direct measurements of the spectra of normal and pathological tissues in vitro, ex vivo and in vivo. The aim of our studies is the express testing of various tumor tissues at the early stages of their development. The method is expected to be further developed for endoscopic and biopsy applications. We measured in vivo the skin normal and malignant tissues on surface (directly on patients) in various cases of basaloma, melanoma and nevus. The experiments were performed in operating room for measurements of skin in the depth (under/in the layers of epidermis), human breast, stomach, lung, kidney tissues. The breast and skin tissues at different stages of tumor or cancer were distinguished very clearly in spectra of amide, side cyclic and noncyclic hydrogen bonded fragments of aminoacid residuals, phosphate groups and sugars. Computer monitoring is being developed for diagnostics.

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

USGS Publications Warehouse

Zhang, R.R.; Ma, S.; Safak, E.; Hartzell, S.

2003-01-01

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.

Thermal stabilization of static single-mirror Fourier transform spectrometers

NASA Astrophysics Data System (ADS)

Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.

2017-05-01

Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

Time-frequency analysis of acoustic signals in the audio-frequency range generated during Hadfield's steel friction

NASA Astrophysics Data System (ADS)

Dobrynin, S. A.; Kolubaev, E. A.; Smolin, A. Yu.; Dmitriev, A. I.; Psakhie, S. G.

2010-07-01

Time-frequency analysis of sound waves detected by a microphone during the friction of Hadfield’s steel has been performed using wavelet transform and window Fourier transform methods. This approach reveals a relationship between the appearance of quasi-periodic intensity outbursts in the acoustic response signals and the processes responsible for the formation of wear products. It is shown that the time-frequency analysis of acoustic emission in a tribosystem can be applied, along with traditional approaches, to studying features in the wear and friction process.

Measuring ocean waves from space; Proceedings of the Symposium, Johns Hopkins University, Laurel, MD, Apr. 15-17, 1986

NASA Technical Reports Server (NTRS)

Beal, Robert C. (Editor)

1987-01-01

Papers are presented on ocean-wave prediction; the quasi-universal form of the spectra of wind-generated gravity waves at different stages of their development; the limitations of the spectral measurements and observations of the group structure of surface waves; the effect of swell on the growth of wind wave; operational wave forecasting; ocean-wave models, and seakeeping using directional wave spectra. Consideration is given to microwave measurements of the ocean-wave directional spectra; SIR research; estimating wave energy spectra from SAR imagery, with the radar ocean-wave spectrometer, and SIR-B; the wave-measurement capabilities of the surface contour radar and the airborne oceanographic lidar; and SIR-B ocean-wave enhancement with fast-Fourier transform techniques. Topics discussed include wave-current interaction; the design and applicability of Spectrasat; the need for a global wave monitoring system; the age and source of ocean swell observed in Hurricane Josephine; and the use of satellite technology for insulin treatment.

The Fourier analysis of biological transients.

PubMed

Harris, C M

1998-08-31

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Fourier transform magnitudes are unique pattern recognition templates.

PubMed

Gardenier, P H; McCallum, B C; Bates, R H

1986-01-01

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Spin wave propagation in perpendicular magnetized 20 nm Yttrium Iron Garnet with different antenna design

NASA Astrophysics Data System (ADS)

Chen, Jilei; Stueckler, Tobias; Zhang, Youguang; Zhao, Weisheng; Yu, Haiming; Chang, Houchen; Liu, Tao; Wu, Mingzhong; Liu, Chuanpu; Liao, Zhimin; Yu, Dapeng; Fert Beijing research institute Team; Colorado State University Team; Peking University Collaboration

Magnonics offers a new way to transport information using spin waves free of charge current and could lead to a new paradigm in the area of computing. Forward volume (FV) mode spin wave with perpendicular magnetized configuration is suitable for spin wave logic device because it is free of non-reciprocity effect. Here, we study FV mode spin wave propagation in YIG thin film with an ultra-low damping. We integrated differently designed antenna i.e., coplanar waveguide and micro stripline with different dimensions. The k vectors of the spin waves defined by the design of the antenna are calculated using Fourier transform. We show FV mode spin wave propagation results by measuring S12 parameter from vector network analyzer and we extract the group velocity of the FV mode spin wave as well as its dispersion relations.

If EM waves don't interfere, what causes interferograms?

NASA Astrophysics Data System (ADS)

Wellard, Stanley J.

2012-10-01

Photonics engineers involved in designing and operating Fourier transform spectrometers (FTS) often rely on Maxwell's wave equations and time-frequency (distance-wavenumber) Fourier theory as models to understand and predict the conversion of optical energy to electrical signals in their instruments. Dr. Chandrasekhar Roychoudhuri and his colleagues, at last year's conference, presented three significant concepts that might completely change the way we comprehend the interaction of light and matter and the way interference information is generated. The first concept is his non-interaction of waves (NIW) formulation, which puts in place an optical wave description that more accurately describe the properties of the finite time and spatial signals of an optical system. The second is a new description for the cosmic EM environment that recognizes that space is really filled with the ether of classical electromagnetics. The third concept is a new metaphysics or metaphotonics that compares the photon as a particle in a void against the photon as a wave in a medium to see which best explain the twelve different aspects of light. Dr. Henry Lindner presents a compelling case that photons are waves in a medium and particles (electrons, protons, atoms) are wave-structures embedded in the new ether. Discussion of the three new principles is intended to increase the curiosity of photonics engineers to investigate these changes in the nature of light and matter.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

PubMed

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Hasanyan, Davresh; Librescu, iviu; Qin, Zhanming

2005-01-01

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Polyphase-discrete Fourier transform spectrum analysis for the Search for Extraterrestrial Intelligence sky survey

NASA Technical Reports Server (NTRS)

Zimmerman, G. A.; Gulkis, S.

1991-01-01

The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).

Photoacoustic detection of blood in dental pulp by using short-time Fourier transform

NASA Astrophysics Data System (ADS)

Yamada, Azusa; Kakino, Satoko; Matsuura, Yuji

2016-03-01

A method based on photoacoustic analysis is proposed to diagnose dental pulp vitality. Photoacoustic analysis enables to get signal from deeper tissues than other optical analyses and therefore, signal detection from root canal of thick dental tissues such as molar teeth is expected. As a light source for excitation of photoacoustic waves, a microchip Q-switched YAG laser with a wavelength of 1064 nm was used and owing to large penetration depth of the near infrared laser, photoacoustic signals from dental root were successfully obtained. It was found that the photoacoustic signals from the teeth containing hemoglobin solution in the pulp cavity provide vibration in high frequency region. It was also shown that the intensities of the high frequency component have correlation with the hemoglobin concentration of solution. We applied short-time Fourier transform for evaluation of photoacoustic signals and this analysis clearly showed photoacoustic signals from dental root.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

Nondestructive quantification of the soluble-solids content and the available acidity of apples by Fourier-transform near-infrared spectroscopy

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

Ying Yibin; Liu Yande; Tao Yang

2005-09-01

This research evaluated the feasibility of using Fourier-transform near-infrared (FT-NIR) spectroscopy to quantify the soluble-solids content (SSC) and the available acidity (VA) in intact apples. Partial least-squares calibration models, obtained from several preprocessing techniques (smoothing, derivative, etc.) in several wave-number ranges were compared. The best models were obtained with the high coefficient determination (r{sup 2}) 0.940 for the SSC and a moderate r{sup 2} of 0.801 for the VA, root-mean-square errors of prediction of 0.272% and 0.053%, and root-mean-square errors of calibration of 0.261% and 0.046%, respectively. The results indicate that the FT-NIR spectroscopy yields good predictions of the SSCmore » and also showed the feasibility of using it to predict the VA of apples.« less

Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

PubMed

Grau, L; Laulagnet, B

2015-05-01

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

Further SEASAT SAR coastal ocean wave analysis

NASA Technical Reports Server (NTRS)

Kasischke, E. S.; Shuchman, R. A.; Meadows, G. A.; Jackson, P. L.; Tseng, Y.

1981-01-01

Analysis techniques used to exploit SEASAT synthetic aperture radar (SAR) data of gravity waves are discussed and the SEASAT SAR's ability to monitor large scale variations in gravity wave fields in both deep and shallow water is evaluated. The SAR analysis techniques investigated included motion compensation adjustments and the semicausal model for spectral analysis of SAR wave data. It was determined that spectra generated from fast Fourier transform analysis (FFT) of SAR wave data were not significantly altered when either range telerotation adjustments or azimuth focus shifts were used during processing of the SAR signal histories, indicating that SEASAT imagery of gravity waves is not significantly improved or degraded by motion compensation adjustments. Evaluation of the semicausal (SC) model using SEASAT SAR data from Rev. 974 indicates that the SC spectral estimates were not significantly better than the FFT results.

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

NASA Astrophysics Data System (ADS)

Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

2017-10-01

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate difficulties that arise in the analysis of the Purcell effect because of the divergence of the integral describing the effective volume of the mode in open systems.

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Applications of the diffraction and interference of light and electronic waves

NASA Astrophysics Data System (ADS)

Bahrim, Cristian; Lanning, Robert

2010-10-01

As part of a NSF sponsored program, called STAIRSTEP, at Lamar University we work on improving the basic knowledge of our physics majors in topics with broader impact in various areas of science and engineering [1]. The purpose is to facilitate a deeper understanding of some fundamental concepts in the field of optics through hands-on experience [2]. We choose to study the interference/diffraction of light and matter waves, because of its fundamental importance in physics with many applications. We target multiple goals in our field of study such as to understand the formation of electronic waves (wave packets) and their interaction with atoms in crystals (electron diffraction); the Fourier analysis of light with applications in spectroscopy, etc. We can show that a crystal lattice Fourier transforms the sinusoidal waves associated to free electrons fired toward the crystal. Our studies led to a simple and instructive recipe for discovering the arrangement of atoms in crystals from the analysis of the diffraction patterns produced by radiation or by electrons transmitted through crystals. [1] Doerschuk P. et al., 39th ASEE/IEEE Frontiers in Education Conference, San Antonio 2009, M3F-1. [2] Bahrim C, Innovation 2006 -- World Innovations in Engineering Education and Research, Chapter 17, iNEER Innovation Series, ISBN 0-9741252-5-3.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates.

PubMed

Hosten, Bernard; Moreau, Ludovic; Castaings, Michel

2007-06-01

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.

3D transient electromagnetic simulation using a modified correspondence principle for wave and diffusion fields

NASA Astrophysics Data System (ADS)

Hu, Y.; Ji, Y.; Egbert, G. D.

2015-12-01

The fictitious time domain method (FTD), based on the correspondence principle for wave and diffusion fields, has been developed and used over the past few years primarily for marine electromagnetic (EM) modeling. Here we present results of our efforts to apply the FTD approach to land and airborne TEM problems which can reduce the computer time several orders of magnitude and preserve high accuracy. In contrast to the marine case, where sources are in the conductive sea water, we must model the EM fields in the air; to allow for topography air layers must be explicitly included in the computational domain. Furthermore, because sources for most TEM applications generally must be modeled as finite loops, it is useful to solve directly for the impulse response appropriate to the problem geometry, instead of the point-source Green functions typically used for marine problems. Our approach can be summarized as follows: (1) The EM diffusion equation is transformed to a fictitious wave equation. (2) The FTD wave equation is solved with an explicit finite difference time-stepping scheme, with CPML (Convolutional PML) boundary conditions for the whole computational domain including the air and earth , with FTD domain source corresponding to the actual transmitter geometry. Resistivity of the air layers is kept as low as possible, to compromise between efficiency (longer fictitious time step) and accuracy. We have generally found a host/air resistivity contrast of 10-3 is sufficient. (3)A "Modified" Fourier Transform (MFT) allow us recover system's impulse response from the fictitious time domain to the diffusion (frequency) domain. (4) The result is multiplied by the Fourier transformation （FT） of the real source current avoiding time consuming convolutions in the time domain. (5) The inverse FT is employed to get the final full waveform and full time response of the system in the time domain. In general, this method can be used to efficiently solve most time-domain EM simulation problems for non-point sources.

Transform- and multi-domain deep learning for single-frame rapid autofocusing in whole slide imaging.

PubMed

Jiang, Shaowei; Liao, Jun; Bian, Zichao; Guo, Kaikai; Zhang, Yongbing; Zheng, Guoan

2018-04-01

A whole slide imaging (WSI) system has recently been approved for primary diagnostic use in the US. The image quality and system throughput of WSI is largely determined by the autofocusing process. Traditional approaches acquire multiple images along the optical axis and maximize a figure of merit for autofocusing. Here we explore the use of deep convolution neural networks (CNNs) to predict the focal position of the acquired image without axial scanning. We investigate the autofocusing performance with three illumination settings: incoherent Kohler illumination, partially coherent illumination with two plane waves, and one-plane-wave illumination. We acquire ~130,000 images with different defocus distances as the training data set. Different defocus distances lead to different spatial features of the captured images. However, solely relying on the spatial information leads to a relatively bad performance of the autofocusing process. It is better to extract defocus features from transform domains of the acquired image. For incoherent illumination, the Fourier cutoff frequency is directly related to the defocus distance. Similarly, autocorrelation peaks are directly related to the defocus distance for two-plane-wave illumination. In our implementation, we use the spatial image, the Fourier spectrum, the autocorrelation of the spatial image, and combinations thereof as the inputs for the CNNs. We show that the information from the transform domains can improve the performance and robustness of the autofocusing process. The resulting focusing error is ~0.5 µm, which is within the 0.8-µm depth-of-field range. The reported approach requires little hardware modification for conventional WSI systems and the images can be captured on the fly without focus map surveying. It may find applications in WSI and time-lapse microscopy. The transform- and multi-domain approaches may also provide new insights for developing microscopy-related deep-learning networks. We have made our training and testing data set (~12 GB) open-source for the broad research community.

Identification and classification of very low frequency waves on a coral reef flat

USGS Publications Warehouse

Gawehn, Matthijs; van Dongeran, Ap; van Rooijen, Arnold; Storlazzi, Curt; Cheriton, Olivia; Reniers, Ad

2016-01-01

Very low frequency (VLF, 0.001–0.005 Hz) waves are important drivers of flooding of low-lying coral reef-islands. In particular, VLF wave resonance is known to drive large wave runup and subsequent overwash. Using a 5 month data set of water levels and waves collected along a cross-reef transect on Roi-Namur Island in the Republic of the Marshall Islands, the observed VLF motions were categorized into four different classes: (1) resonant, (2) (nonresonant) standing, (3) progressive-growing, and (4) progressive-dissipative waves. Each VLF class is set by the reef flat water depth and, in the case of resonance, the incident-band offshore wave period. Using an improved method to identify VLF wave resonance, we find that VLF wave resonance caused prolonged (∼0.5–6.0 h), large-amplitude water surface oscillations at the inner reef flat ranging in wave height from 0.14 to 0.83 m. It was induced by relatively long-period, grouped, incident-band waves, and occurred under both storm and nonstorm conditions. Moreover, observed resonant VLF waves had nonlinear, bore-like wave shapes, which likely have a larger impact on the shoreline than regular, sinusoidal waveforms. As an alternative technique to the commonly used Fast Fourier Transformation, we propose the Hilbert-Huang Transformation that is more computationally expensive but can capture the wave shape more accurately. This research demonstrates that understanding VLF waves on reef flats is important for evaluating coastal flooding hazards.

Identification and classification of very low frequency waves on a coral reef flat

NASA Astrophysics Data System (ADS)

Gawehn, Matthijs; van Dongeren, Ap; van Rooijen, Arnold; Storlazzi, Curt D.; Cheriton, Olivia M.; Reniers, Ad

2016-10-01

Very low frequency (VLF, 0.001-0.005 Hz) waves are important drivers of flooding of low-lying coral reef-islands. In particular, VLF wave resonance is known to drive large wave runup and subsequent overwash. Using a 5 month data set of water levels and waves collected along a cross-reef transect on Roi-Namur Island in the Republic of the Marshall Islands, the observed VLF motions were categorized into four different classes: (1) resonant, (2) (nonresonant) standing, (3) progressive-growing, and (4) progressive-dissipative waves. Each VLF class is set by the reef flat water depth and, in the case of resonance, the incident-band offshore wave period. Using an improved method to identify VLF wave resonance, we find that VLF wave resonance caused prolonged (˜0.5-6.0 h), large-amplitude water surface oscillations at the inner reef flat ranging in wave height from 0.14 to 0.83 m. It was induced by relatively long-period, grouped, incident-band waves, and occurred under both storm and nonstorm conditions. Moreover, observed resonant VLF waves had nonlinear, bore-like wave shapes, which likely have a larger impact on the shoreline than regular, sinusoidal waveforms. As an alternative technique to the commonly used Fast Fourier Transformation, we propose the Hilbert-Huang Transformation that is more computationally expensive but can capture the wave shape more accurately. This research demonstrates that understanding VLF waves on reef flats is important for evaluating coastal flooding hazards.

The fractional Fourier transform and applications

NASA Technical Reports Server (NTRS)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

The τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the τq-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the τq-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

Antenna design for propagating spin wave spectroscopy in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Zhang, Yan; Yu, Ting; Chen, Ji-lei; Zhang, You-guang; Feng, Jian; Tu, Sa; Yu, Haiming

2018-03-01

In this paper, we investigate the characteristics of antenna for propagating-spin-wave-spectroscopy (PSWS) experiment in ferromagnetic thin films. Firstly, we simulate the amplitude and phase distribution of the high-frequency magnetic field around antenna by high frequency structure simulator (HFSS). And then k distribution of the antenna is obtained by fast Fourier transformation (FFT). Furthermore, three kinds of antenna designs, i.e. micro-strip line, coplanar waveguide (CPW), loop, are studied and compared. How the dimension parameter of antenna influence the corresponding high-frequency magnetic field amplitude and k distribution are investigated in details.

On increasing stability in the two dimensional inverse source scattering problem with many frequencies

NASA Astrophysics Data System (ADS)

Entekhabi, Mozhgan Nora; Isakov, Victor

2018-05-01

In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

Wavespace-Based Coherent Deconvolution

NASA Technical Reports Server (NTRS)

Bahr, Christopher J.; Cattafesta, Louis N., III

2012-01-01

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Separation of Migration and Tomography Modes of Full-Waveform Inversion in the Plane Wave Domain

NASA Astrophysics Data System (ADS)

Yao, Gang; da Silva, Nuno V.; Warner, Michael; Kalinicheva, Tatiana

2018-02-01

Full-waveform inversion (FWI) includes both migration and tomography modes. The migration mode acts like a nonlinear least squares migration to map model interfaces with reflections, while the tomography mode behaves as tomography to build a background velocity model. The migration mode is the main response of inverting reflections, while the tomography mode exists in response to inverting both the reflections and refractions. To emphasize one of the two modes in FWI, especially for inverting reflections, the separation of the two modes in the gradient of FWI is required. Here we present a new method to achieve this separation with an angle-dependent filtering technique in the plane wave domain. We first transform the source and residual wavefields into the plane wave domain with the Fourier transform and then decompose them into the migration and tomography components using the opening angles between the transformed source and residual plane waves. The opening angles close to 180° contribute to the tomography component, while the others correspond to the migration component. We find that this approach is very effective and robust even when the medium is relatively complicated with strong lateral heterogeneities, highly dipping reflectors, and strong anisotropy. This is well demonstrated by theoretical analysis and numerical tests with a synthetic data set and a field data set.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

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

Guided Wave Propagation Study on Laminated Composites by Frequency-Wavenumber Technique

NASA Technical Reports Server (NTRS)

Tian, Zhenhua; Yu, Lingyu; Leckey, Cara A. C.

2014-01-01

Toward the goal of delamination detection and quantification in laminated composites, this paper examines guided wave propagation and wave interaction with delamination damage in laminated carbon fiber reinforced polymer (CFRP) composites using frequency-wavenumber (f-kappa) analysis. Three-dimensional elastodynamic finite integration technique (EFIT) is used to acquire simulated time-space wavefields for a CFRP composite. The time-space wavefields show trapped waves in the delamination region. To unveil the wave propagation physics, the time-space wavefields are further analyzed by using two-dimensional (2D) Fourier transforms (FT). In the analysis results, new f-k components are observed when the incident guided waves interact with the delamination damage. These new f-kappa components in the simulations are experimentally verified through data obtained from scanning laser Doppler vibrometer (SLDV) tests. By filtering the new f-kappa components, delamination damage is detected and quantified.

Polarized reflectance and transmittance properties of windblown sea surfaces.

PubMed

Mobley, Curtis D

2015-05-20

Generation of random sea surfaces using wave variance spectra and Fourier transforms is formulated in a way that guarantees conservation of wave energy and fully resolves wave height and slope variances. Monte Carlo polarized ray tracing, which accounts for multiple scattering between light rays and wave facets, is used to compute effective Mueller matrices for reflection and transmission of air- or water-incident polarized radiance. Irradiance reflectances computed using a Rayleigh sky radiance distribution, sea surfaces generated with Cox-Munk statistics, and unpolarized ray tracing differ by 10%-18% compared with values computed using elevation- and slope-resolving surfaces and polarized ray tracing. Radiance reflectance factors, as used to estimate water-leaving radiance from measured upwelling and sky radiances, are shown to depend on sky polarization, and improved values are given.

The propagation of Lamb waves in multilayered plates: phase-velocity measurement

NASA Astrophysics Data System (ADS)

Grondel, Sébastien; Assaad, Jamal; Delebarre, Christophe; Blanquet, Pierrick; Moulin, Emmanuel

1999-05-01

Owing to the dispersive nature and complexity of the Lamb waves generated in a composite plate, the measurement of the phase velocities by using classical methods is complicated. This paper describes a measurement method based upon the spectrum-analysis technique, which allows one to overcome these problems. The technique consists of using the fast Fourier transform to compute the spatial power-density spectrum. Additionally, weighted functions are used to increase the probability of detecting the various propagation modes. Experimental Lamb-wave dispersion curves of multilayered plates are successfully compared with the analytical ones. This technique is expected to be a useful way to design composite parts integrating ultrasonic transducers in the field of health monitoring. Indeed, Lamb waves and particularly their velocities are very sensitive to defects.

Imaging ultrasonic dispersive guided wave energy in long bones using linear radon transform.

PubMed

Tran, Tho N H T; Nguyen, Kim-Cuong T; Sacchi, Mauricio D; Le, Lawrence H

2014-11-01

Multichannel analysis of dispersive ultrasonic energy requires a reliable mapping of the data from the time-distance (t-x) domain to the frequency-wavenumber (f-k) or frequency-phase velocity (f-c) domain. The mapping is usually performed with the classic 2-D Fourier transform (FT) with a subsequent substitution and interpolation via c = 2πf/k. The extracted dispersion trajectories of the guided modes lack the resolution in the transformed plane to discriminate wave modes. The resolving power associated with the FT is closely linked to the aperture of the recorded data. Here, we present a linear Radon transform (RT) to image the dispersive energies of the recorded ultrasound wave fields. The RT is posed as an inverse problem, which allows implementation of the regularization strategy to enhance the focusing power. We choose a Cauchy regularization for the high-resolution RT. Three forms of Radon transform: adjoint, damped least-squares, and high-resolution are described, and are compared with respect to robustness using simulated and cervine bone data. The RT also depends on the data aperture, but not as severely as does the FT. With the RT, the resolution of the dispersion panel could be improved up to around 300% over that of the FT. Among the Radon solutions, the high-resolution RT delineated the guided wave energy with much better imaging resolution (at least 110%) than the other two forms. The Radon operator can also accommodate unevenly spaced records. The results of the study suggest that the high-resolution RT is a valuable imaging tool to extract dispersive guided wave energies under limited aperture. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Fourier transform methods in local gravity modeling

NASA Technical Reports Server (NTRS)

Harrison, J. C.; Dickinson, M.

1989-01-01

New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.

User’s Guide for the VTRPE (Variable Terrain Radio Parabolic Equation) Computer Model

DTIC Science & Technology

1991-10-01

propagation effects and antenna characteristics in radar system performance calculations. the radar transmission equation is oiten employed. Fol- lowing Kerr.2...electromagnetic wave equations for the complex electric and magnetic radiation fields. The model accounts for the effects of nonuniform atmospheric refractivity...mission equation, that is used in the performance prediction and analysis of radar and communication systems. Optimized fast Fourier transform (FFT

Surface acoustic waves/silicon monolithic sensor processor

NASA Technical Reports Server (NTRS)

Kowel, S. T.; Kornreich, P. G.; Fathimulla, M. A.; Mehter, E. A.

1981-01-01

Progress is reported in the creation of a two dimensional Fourier transformer for optical images based on the zinc oxide on silicon technology. The sputtering of zinc oxide films using a micro etch system and the possibility of a spray-on technique based on zinc chloride dissolved in alcohol solution are discussed. Refinements to techniques for making platinum silicide Schottky barrier junctions essential for constructing the ultimate convolver structure are described.

Comparison of Image Processing Techniques using Random Noise Radar

DTIC Science & Technology

2014-03-27

detection UWB ultra-wideband EM electromagnetic CW continuous wave RCS radar cross section RFI radio frequency interference FFT fast Fourier transform...several factors including radar cross section (RCS), orientation, and material makeup. A single monostatic radar at some position collects only range and...Chapter 2 is to provide the theory behind noise radar and SAR imaging. Section 2.1 presents the basic concepts in transmitting and receiving random

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

Remote skin tissue diagnostics in vivo by fiber optic evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Butvina, Leonid N.

1998-04-01

The new method of fiber-optical evanescent wave Fourier transform IR (FEW-FTIR) spectroscopy has been applied to the diagnostics of normal tissue, as well as precancerous and cancerous conditions. The FEW-FTIR technique is nondestructive and sensitive to changes of vibrational spectra in the IR region, without heating and damaging human and animal skin tissue. Therefore this method and technique is an ideal diagnostic tool for tumor and cancer characterization at an early stage of development on a molecular level. The application of fiber optic technology in the middle IR region is relatively inexpensive and can be adapted easily to any commercially available tabletop FTIR spectrometers. This method of diagnostics is fast, remote, and can be applied to many fields Noninvasive medical diagnostics of skin cancer and other skin diseases in vivo, ex vivo, and in vitro allow for the development convenient, remote clinical applications in dermatology and related fields. The spectral variations from normal to pathological skin tissue and environmental influence on skin have been measured and assigned in the regions of 850-4000 cm-1. The lipid structure changes are discussed. We are able to develop the spectral histopathology as a fast and informative tool of analysis.

A plane wave generation method by wave number domain point focusing.

PubMed

Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann

2010-11-01

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

Analytical Time-Domain Solution of Plane Wave Propagation Across a Viscoelastic Rock Joint

NASA Astrophysics Data System (ADS)

Zou, Yang; Li, Jianchun; Laloui, Lyesse; Zhao, Jian

2017-10-01

The effects of viscoelastic filled rock joints on wave propagation are of great significance in rock engineering. The solutions in time domain for plane longitudinal ( P-) and transverse ( S-) waves propagation across a viscoelastic rock joint are derived based on Maxwell and Kelvin models which are, respectively, applied to describe the viscoelastic deformational behaviour of the rock joint and incorporated into the displacement discontinuity model (DDM). The proposed solutions are verified by comparing with the previous studies on harmonic waves, which are simulated by sinusoidal incident P- and S-waves. Comparison between the predicted transmitted waves and the experimental data for P-wave propagation across a joint filled with clay is conducted. The Maxwell is found to be more appropriate to describe the filled joint. The parametric studies show that wave propagation is affected by many factors, such as the stiffness and the viscosity of joints, the incident angle and the duration of incident waves. Furthermore, the dependences of the transmission and reflection coefficients on the specific joint stiffness and viscosity are different for the joints with Maxwell and Kelvin behaviours. The alternation of the reflected and transmitted waveforms is discussed, and the application scope of this study is demonstrated by an illustration of the effects of the joint thickness. The solutions are also extended for multiple parallel joints with the virtual wave source method and the time-domain recursive method. For an incident wave with arbitrary waveform, it is convenient to adopt the present approach to directly calculate wave propagation across a viscoelastic rock joint without additional mathematical methods such as the Fourier and inverse Fourier transforms.

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets

NASA Astrophysics Data System (ADS)

Singh, Iqbal; Kaur, Bikramjeet

2018-05-01

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

A Wave Diagnostics in Geophysics: Algorithmic Extraction of Atmosphere Disturbance Modes

NASA Astrophysics Data System (ADS)

Leble, S.; Vereshchagin, S.

2018-04-01

The problem of diagnostics in geophysics is discussed and a proposal based on dynamic projecting operators technique is formulated. The general exposition is demonstrated by an example of symbolic algorithm for the wave and entropy modes in the exponentially stratified atmosphere. The novel technique is developed as a discrete version for the evolution operator and the corresponding projectors via discrete Fourier transformation. Its explicit realization for directed modes in exponential one-dimensional atmosphere is presented via the correspondent projection operators in its discrete version in terms of matrices with a prescribed action on arrays formed from observation tables. A simulation based on opposite directed (upward and downward) wave train solution is performed and the modes' extraction from a mixture is illustrated.

Surface acoustic wave regulated single photon emission from a coupled quantum dot–nanocavity system

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

Weiß, M.; Kapfinger, S.; Wixforth, A.

2016-07-18

A coupled quantum dot–nanocavity system in the weak coupling regime of cavity-quantumelectrodynamics is dynamically tuned in and out of resonance by the coherent elastic field of a f{sub SAW} ≃ 800 MHz surface acoustic wave. When the system is brought to resonance by the sound wave, light-matter interaction is strongly increased by the Purcell effect. This leads to a precisely timed single photon emission as confirmed by the second order photon correlation function, g{sup (2)}. All relevant frequencies of our experiment are faithfully identified in the Fourier transform of g{sup (2)}, demonstrating high fidelity regulation of the stream of single photonsmore » emitted by the system.« less

Bilinear Time-frequency Analysis for Lamb Wave Signal Detected by Electromagnetic Acoustic Transducer

NASA Astrophysics Data System (ADS)

Sun, Wenxiu; Liu, Guoqiang; Xia, Hui; Xia, Zhengwu

2018-03-01

Accurate acquisition of the detection signal travel time plays a very important role in cross-hole tomography. The experimental platform of aluminum plate under the perpendicular magnetic field is established and the bilinear time-frequency analysis methods, Wigner-Ville Distribution (WVD) and the pseudo-Wigner-Ville distribution (PWVD), are applied to analyse the Lamb wave signals detected by electromagnetic acoustic transducer (EMAT). By extracting the same frequency component of the time-frequency spectrum as the excitation frequency, the travel time information can be obtained. In comparison with traditional linear time-frequency analysis method such as short-time Fourier transform (STFT), the bilinear time-frequency analysis method PWVD is more appropriate in extracting travel time and recognizing patterns of Lamb wave.

Open source acceleration of wave optics simulations on energy efficient high-performance computing platforms

NASA Astrophysics Data System (ADS)

Beck, Jeffrey; Bos, Jeremy P.

2017-05-01

We compare several modifications to the open-source wave optics package, WavePy, intended to improve execution time. Specifically, we compare the relative performance of the Intel MKL, a CPU based OpenCV distribution, and GPU-based version. Performance is compared between distributions both on the same compute platform and between a fully-featured computing workstation and the NVIDIA Jetson TX1 platform. Comparisons are drawn in terms of both execution time and power consumption. We have found that substituting the Fast Fourier Transform operation from OpenCV provides a marked improvement on all platforms. In addition, we show that embedded platforms offer some possibility for extensive improvement in terms of efficiency compared to a fully featured workstation.

Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform

NASA Astrophysics Data System (ADS)

Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.

2001-12-01

Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an n-th order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer polynomial transforms.

3D-FFT for Signature Detection in LWIR Images

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

Medvick, Patricia A.; Lind, Michael A.; Mackey, Patrick S.

Improvements in analysis detection exploitation are possible by applying whitened matched filtering within the Fourier domain to hyperspectral data cubes. We describe an implementation of a Three Dimensional Fast Fourier Transform Whitened Matched Filter (3DFFTMF) approach and, using several example sets of Long Wave Infra Red (LWIR) data cubes, compare the results with those from standard Whitened Matched Filter (WMF) techniques. Since the variability in shape of gaseous plumes precludes the use of spatial conformation in the matched filtering, the 3DFFTMF results were similar to those of two other WMF methods. Including a spatial low-pass filter within the Fourier spacemore » can improve signal to noise ratios and therefore improve detection limit by facilitating the mitigation of high frequency clutter. The improvement only occurs if the low-pass filter diameter is smaller than the plume diameter.« less

Holographic maps of quasiparticle interference

NASA Astrophysics Data System (ADS)

Dalla Torre, Emanuele G.; He, Yang; Demler, Eugene

2016-11-01

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Stable cavitation induces increased cytoplasmic calcium in L929 fibroblasts exposed to 1-MHz pulsed ultrasound.

PubMed

Tsukamoto, Akira; Higashiyama, Satoru; Yoshida, Kenji; Watanabe, Yoshiaki; Furukawa, Katsuko S; Ushida, Takashi

2011-12-01

An increase in cytoplasmic calcium (Ca(2+) increase) is a second messenger that is often observed under ultrasound irradiation. We hypothesize that cavitation is a physical mechanism that underlies the increase in Ca(2+) in these experiments. To control the presence of cavitation, the wave type was controlled in a sonication chamber. One wave type largely contained a traveling wave (wave type A) while the other wave type largely contained a standing wave (wave type B). Fast Fourier transform (FFT) analysis of a sound field produced by the wave types ascertained that stable cavitation was present only under wave type A ultrasound irradiation. Under the two controlled wave types, the increase in Ca(2+) in L929 fibroblasts was observed with fluorescence imaging. Under wave type A ultrasound irradiation, an increase in Ca(2+) was observed; however, no increase in Ca(2+) was observed under wave type B ultrasound irradiation. We conclude that stable cavitation is involved in the increase of Ca(2+) in cells subjected to pulsed ultrasound. Copyright © 2011 Elsevier B.V. All rights reserved.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Stepwise Iterative Fourier Transform: The SIFT

NASA Technical Reports Server (NTRS)

Benignus, V. A.; Benignus, G.

1975-01-01

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres.

PubMed

Li, Zheng-Jun; Wu, Zhen-Sen; Li, Hai-Ying

2011-02-01

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.

Efficient detection of a CW signal with a linear frequency drift

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.; Bailey, David H.

1989-01-01

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series.

Relationship between cutoff frequency and accuracy in time-interval photon statistics applied to oscillating signals

NASA Astrophysics Data System (ADS)

Rebolledo, M. A.; Martinez-Betorz, J. A.

1989-04-01

In this paper the accuracy in the determination of the period of an oscillating signal, when obtained from the photon statistics time-interval probability, is studied as a function of the precision (the inverse of the cutoff frequency of the photon counting system) with which time intervals are measured. The results are obtained by means of an experiment with a square-wave signal, where the Fourier or square-wave transforms of the time-interval probability are measured. It is found that for values of the frequency of the signal near the cutoff frequency the errors in the period are small.

An FMM-FFT Accelerated SIE Simulator for Analyzing EM Wave Propagation in Mine Environments Loaded With Conductors

PubMed Central

Sheng, Weitian; Zhou, Chenming; Liu, Yang; Bagci, Hakan; Michielssen, Eric

2018-01-01

A fast and memory efficient three-dimensional full-wave simulator for analyzing electromagnetic (EM) wave propagation in electrically large and realistic mine tunnels/galleries loaded with conductors is proposed. The simulator relies on Muller and combined field surface integral equations (SIEs) to account for scattering from mine walls and conductors, respectively. During the iterative solution of the system of SIEs, the simulator uses a fast multipole method-fast Fourier transform (FMM-FFT) scheme to reduce CPU and memory requirements. The memory requirement is further reduced by compressing large data structures via singular value and Tucker decompositions. The efficiency, accuracy, and real-world applicability of the simulator are demonstrated through characterization of EM wave propagation in electrically large mine tunnels/galleries loaded with conducting cables and mine carts. PMID:29726545

Statistical optics

NASA Astrophysics Data System (ADS)

Goodman, J. W.

This book is based on the thesis that some training in the area of statistical optics should be included as a standard part of any advanced optics curriculum. Random variables are discussed, taking into account definitions of probability and random variables, distribution functions and density functions, an extension to two or more random variables, statistical averages, transformations of random variables, sums of real random variables, Gaussian random variables, complex-valued random variables, and random phasor sums. Other subjects examined are related to random processes, some first-order properties of light waves, the coherence of optical waves, some problems involving high-order coherence, effects of partial coherence on imaging systems, imaging in the presence of randomly inhomogeneous media, and fundamental limits in photoelectric detection of light. Attention is given to deterministic versus statistical phenomena and models, the Fourier transform, and the fourth-order moment of the spectrum of a detected speckle image.

Ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids: a spectral finite element study.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2013-01-01

This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.

Equatorial waves in temperature in the altitude range 4 to 70 km

NASA Astrophysics Data System (ADS)

Krishna Murthy, B. V.; Satheesan, K.; Parameswaran, K.; Sasi, M. N.; Ramkumar, Geetha; Bhavanikumar, Y.; Raghunath, K.; Krishniah, M.

2002-04-01

Using altitude profiles of temperature in the range 4 to 70 km derived from Mesosphere-Stratosphere- Troposphere radar and lidar observations at Gadanki (13.5°N, 79.2°E) from 18 January 1999 to 5 March 1999, characteristics of equatorial waves are studied. Two-dimensional Fourier-transform analysis of the temperature profiles is carried out to identify the periodicities and their vertical wave numbers. From the characteristics obtained, equatorial slow Kelvin waves with periodicities 15.7 d, 9.4 d, 7.8 d and 6.7 d are identified in the troposphere and stratosphere regions and among these 7.8 d and 6.7 d periodicities are found to penetrate into the mesosphere. Equatorial waves with smaller periodicities in the range 5.2 d to 3.6 d are also observed. The vertical flux of horizontal momentum (zonal) of the identified slow Kelvin-wave periodicities in the altitude region 4-25 km is estimated. It is found that equatorial waves modulate tropical tropopause temperature and altitude.

[Study on Differential Optical Absorption Spectroscopy Data Processing Based on Chirp-Z Transformation].

PubMed

Zheng, Hai-ming; Li, Guang-jie; Wu, Hao

2015-06-01

Differential optical absorption spectroscopy (DOAS) is a commonly used atmospheric pollution monitoring method. Denoising of monitoring spectral data will improve the inversion accuracy. Fourier transform filtering method is effectively capable of filtering out the noise in the spectral data. But the algorithm itself can introduce errors. In this paper, a chirp-z transform method is put forward. By means of the local thinning of Fourier transform spectrum, it can retain the denoising effect of Fourier transform and compensate the error of the algorithm, which will further improve the inversion accuracy. The paper study on the concentration retrieving of SO2 and NO2. The results show that simple division causes bigger error and is not very stable. Chirp-z transform is proved to be more accurate than Fourier transform. Results of the frequency spectrum analysis show that Fourier transform cannot solve the distortion and weakening problems of characteristic absorption spectrum. Chirp-z transform shows ability in fine refactoring of specific frequency spectrum.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

Headspace Analysis of Volatile Compounds Using Segemented Chirped-Pulse Fourier Transform Mm-Wave Spectroscopy

NASA Astrophysics Data System (ADS)

Harris, Brent; Steber, Amanda; Pate, Brooks

2014-06-01

A chirped-pulse Fourier transform mm-wave spectrometer has been tested in analytical chemistry applications of headspace analysis of volatile species. A solid-state mm-wave light source (260-290 GHz) provides 30-50 mW of power. This power is sufficient to achieve optimal excitation of individual transitions of molecules with dipole moments larger than about 0.1 D. The chirped-pulse spectrometer has near 100% measurement duty cycle using a high-speed digitizer (4 GS/s) with signal accumulation in an FPGA. The combination of the ability to perform optimal pulse excitation and near 100% measurement duty cycle gives a spectrometer that is fully optimized for trace detection. The performance of the instrument is tested using an EPA sample (EPA VOC Mix 6 - Supelco) that contains a set of molecules that are fast eluting on gas chromatographs and, as a result, present analysis challenges to mass spectrometry. The ability to directly analyze the VOC mixture is tested by acquiring the full bandwidth (260-290 GHz) spectrum in a "high dynamic range" measurement mode that minimizes spurious spectrometer responses. The high-resolution of molecular rotational spectroscopy makes it easy to analyze this mixture without the need for chemical separation. The sensitivity of the instrument for individual molecule detection, where a single transition is polarized by the excitation pulse, is also tested. Detection limits in water will be reported. In the case of chloromethane, the detection limit (0.1 microgram/L), matches the sensitivity reported in the EPA measurement protocol (EPA Method 524) for GC/MS.

Solid perception mechanism by a shading pattern: spatial frequency components in a corrugated wave pattern.

PubMed

Nameda, N

1988-01-01

Illumination allows solid object perception to be obtained and depicted by a shading pattern produced by lighting. The shading cue, as one of solid perception cues (Gibson 1979), was investigated in regard to a white corrugated wave shape, using computer graphic device: Tospix-2. The reason the corrugated wave was chosen, is that an alternately bright and dark pattern, produced by shading, can be conveniently analyzed into contained spatial frequencies. This paper reports spatial frequency properties contained in the shading pattern. The shading patterns, input into the computer graphic device, are analyzed by Fourier Transformation by the same device. After the filtration by various spatial frequency low and high pass filters, Inverse Fourier Transformation is carried out for the residual components. The result of the analysis indicates that the third through higher harmonics components are important in regard to presenting a solid reality feeling in solid perception. Sakata (1983) also reported that an edged pattern, superimposed onto a lower sinusoidal pattern, was important in solid perception. The third through higher harmonics components express the changing position of luminance on the pattern, and a slanted plane relating to the light direction. Detection of a solid shape, constructed with flat planes, is assumed to be on the bottom of the perfect curved solid perception mechanism. Apparent evidence for this assumption, in difficult visual conditions, is that a flat paneled solid is seen before the curved solid. This mechanism is explained by two spatial frequency neural network systems, assumed as having correspondence with higher spatial frequency detection and lower spatial frequency detection.

Full-field ultrasonic inspection for a composite sandwich plate skin-core debonding detection using laser-based ultrasonics

NASA Astrophysics Data System (ADS)

Chong, See Yenn; Victor, Jared J.; Todd, Michael D.

2017-04-01

In this paper, a full-field ultrasonic guided wave method is proposed to inspect a composite sandwich specimen made for an aircraft engine nacelle. The back skin/core interface of the specimen is built with two fabricated disbond defects (diameters of 12.7 mm and 25.4 mm) by removing areas of the adhesive used to bond the back skin to the core. A laser ultrasonic interrogation system (LUIS) incorporated with a disbond detection algorithm is developed. The system consists of a 1-kHz laser ultrasonic scanning system and a single fixed ultrasonic sensor to interrogate ultrasonic guided waves in the sandwich specimen. The interest area of 400 mm × 400 mm is scanned at a 0.5 mm scan interval. The corresponding full-field ultrasonic data is obtained and generated in the three-dimensional (3-D) space-time domain. Then, the 3-D full-field ultrasonic data is Fourier transformed and the ultrasonic frequency spectra are analyzed to determine the dominant frequency that is sensitive to the disbond defects. Continuous wavelet transform (CWT) based on fast Fourier transform (FFT) is implemented as a single-frequency bandpass filter to filter the full-field ultrasonic data in the 3-D space-time domain at the selected dominant frequency. The LUIS has shown the ability to detect the disbond with diameters of 11 mm and 23 mm which match to the pre-determined disbond sizes well. For future research, a robust signal processing algorithm and a model-based matched filter will be investigated to make the detection process autonomous and improve detectability

Extreme ultraviolet interferometry

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

Goldberg, Kenneth A.

EUV lithography is a promising and viable candidate for circuit fabrication with 0.1-micron critical dimension and smaller. In order to achieve diffraction-limited performance, all-reflective multilayer-coated lithographic imaging systems operating near 13-nm wavelength and 0.1 NA have system wavefront tolerances of 0.27 nm, or 0.02 waves RMS. Owing to the highly-sensitive resonant reflective properties of multilayer mirrors and extraordinarily tight tolerances set forth for their fabrication, EUV optical systems require at-wavelength EUV interferometry for final alignment and qualification. This dissertation discusses the development and successful implementation of high-accuracy EUV interferometric techniques. Proof-of-principle experiments with a prototype EUV point-diffraction interferometer for themore » measurement of Fresnel zoneplate lenses first demonstrated sub-wavelength EUV interferometric capability. These experiments spurred the development of the superior phase-shifting point-diffraction interferometer (PS/PDI), which has been implemented for the testing of an all-reflective lithographic-quality EUV optical system. Both systems rely on pinhole diffraction to produce spherical reference wavefronts in a common-path geometry. Extensive experiments demonstrate EUV wavefront-measuring precision beyond 0.02 waves RMS. EUV imaging experiments provide verification of the high-accuracy of the point-diffraction principle, and demonstrate the utility of the measurements in successfully predicting imaging performance. Complementary to the experimental research, several areas of theoretical investigation related to the novel PS/PDI system are presented. First-principles electromagnetic field simulations of pinhole diffraction are conducted to ascertain the upper limits of measurement accuracy and to guide selection of the pinhole diameter. Investigations of the relative merits of different PS/PDI configurations accompany a general study of the most significant sources of systematic measurement errors. To overcome a variety of experimental difficulties, several new methods in interferogram analysis and phase-retrieval were developed: the Fourier-Transform Method of Phase-Shift Determination, which uses Fourier-domain analysis to improve the accuracy of phase-shifting interferometry; the Fourier-Transform Guided Unwrap Method, which was developed to overcome difficulties associated with a high density of mid-spatial-frequency blemishes and which uses a low-spatial-frequency approximation to the measured wavefront to guide the phase unwrapping in the presence of noise; and, finally, an expedient method of Gram-Schmidt orthogonalization which facilitates polynomial basis transformations in wave-front surface fitting procedures.« less

[Application of Fourier transform infrared spectroscopy in identification of wine spoilage].

PubMed

Zhao, Xian-De; Dong, Da-Ming; Zheng, Wen-Gang; Jiao, Lei-Zi; Lang, Yun

2014-10-01

In the present work, fresh and spoiled wine samples from three wines produced by different companies were studied u- sing Fourier transform infrared (FTIR) spectroscopy. We analyzed the physicochemical property change in the process of spoil- age, and then, gave out the attribution of some main FTIR absorption peaks. A novel determination method was explored based on the comparisons of some absorbance ratios at different wavebands although the absorbance ratios in this method were relative. Through the compare of the wine spectra before and after spoiled, the authors found that they were informative at the bands of 3,020~2,790, 1,760~1,620 and 1,550~800 cm(-1). In order to find the relation between these informative spectral bands and the wine deterioration and achieve the discriminant analysis, chemometrics methods were introduced. Principal compounds analysis (PCA) and soft independent modeling of class analogy (SIMCA) were used for classifying different-quality wines. And partial least squares discriminant analysis (PLS-DA) was applied to identify spoiled wines and good wines. Results showed that FTIR technique combined with chemometrics methods could effectively distinguish spoiled wines from fresh samples. The effect of classification at the wave band of 1 550-800 cm(-1) was the best. The recognition rate of SIMCA and PLSDA were respectively 94% and 100%. This study demonstrates that Fourier transform infrared spectroscopy is an effective tool for monitoring red wine's spoilage and provides theoretical support for developing early-warning equipments.

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

Fan filters, the 3-D Radon transform, and image sequence analysis.

PubMed

Marzetta, T L

1994-01-01

This paper develops a theory for the application of fan filters to moving objects. In contrast to previous treatments of the subject based on the 3-D Fourier transform, simplicity and insight are achieved by using the 3-D Radon transform. With this point of view, the Radon transform decomposes the image sequence into a set of plane waves that are parameterized by a two-component slowness vector. Fan filtering is equivalent to a multiplication in the Radon transform domain by a slowness response function, followed by an inverse Radon transform. The plane wave representation of a moving object involves only a restricted set of slownesses such that the inner product of the plane wave slowness vector and the moving object velocity vector is equal to one. All of the complexity in the application of fan filters to image sequences results from the velocity-slowness mapping not being one-to-one; therefore, the filter response cannot be independently specified at all velocities. A key contribution of this paper is to elucidate both the power and the limitations of fan filtering in this new application. A potential application of 3-D fan filters is in the detection of moving targets in clutter and noise. For example, an appropriately designed fan filter can reject perfectly all moving objects whose speed, irrespective of heading, is less than a specified cut-off speed, with only minor attenuation of significantly faster objects. A simple geometric construction determines the response of the filter for speeds greater than the cut-off speed.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

PubMed Central

Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

2017-01-01

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

A Reduced-Order Model for Evaluating the Dynamic Response of Multilayer Plates to Impulsive Loads

DTIC Science & Technology

2016-04-12

01-0307 4UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited SAE INTERNATIONAL Based on the concepts of...Apply double Fourier Transform on the wave equations: 2� 2 + 2 � = 0 ; 2� 2 + 2 � = 0 Where ...into 2x2 matrices, and the source vector 0 ≠ 0 if loads apply on top surface. • Construct a 4Nx4N global scattering matrix for entire

Discriminating Sea Spikes in Incoherent Radar Measurements of Sea Clutter

DTIC Science & Technology

2008-03-01

het detecteren echter niet te verwachten dat bet gebruik van sea spikes te onderzoeken. Een van deze modellen zal leiden tot een Auteur (s) dergelijk...report I TNO-DV 2008 A067 6/33 Abbreviations CFAR Constant False-Alarm Rate CST Composite Surface Theory FFT Fast Fourier Transform PDF Probability Density...described by the composite surface theory (CST). This theory describes the sea surface as small Bragg-resonant capillary waves riding on top of

Fourier transform millimeter-wave spectroscopy of the ethyl radical in the electronic ground state.

PubMed

Kim, Eunsook; Yamamoto, Satoshi

2004-02-15

The pure rotational spectrum of the ethyl radical (C2H5) has been detected for the first time with the Fourier transform millimeter-wave spectrometer. The ethyl radical is produced by discharging the C2H5I gas diluted in Ar. The 1(01)-0(00) rotational transition of the ethyl radical is observed in the frequency range from 43,680 to 43,780 MHz. The observed spectrum shows a very complicated pattern of the fine and hyperfine structures of a doublet radical with the nuclear spins of five protons. The fine and hyperfine components are assigned with the aid of measurements of the Zeeman splittings. As a result, the 22 lines are ascribed to the transitions in the ground vibronic state (A2"). The rotational constant, the spin-rotation interaction constant, and hyperfine interaction constants are determined by the least-squares fit. The Fermi contact term of the alpha-proton is determined to be -64.1654 MHz in the gas phase, indicating that the structure of the -CH2 is essentially planar. The present rotational spectroscopic study further supports that the methyl group of the ethyl radical can be regarded as a nearly free internal rotor with a low energy barrier. A few unassigned lines still remain, which may be vibrational satellites of the internal rotation mode. Copyright 2004 American Institute of Physics

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

NASA Astrophysics Data System (ADS)

Ba, Zhenning; Kang, Zeqing; Liang, Jianwen

2018-04-01

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic (TI) half-space. The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces, which are then applied to the total system with the opposite sign. By adding solutions restricted in the loaded layer to solutions from the reaction forces, the global solutions in the wavenumber domain are obtained, and the dynamic Green's functions in the space domain are recovered by the inverse Fourier transform. The presented formulations can be reduced to the isotropic case developed by Wolf (1985), and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI half-space subjected to horizontally distributed loads which are special cases of the more general problem addressed. The deduced Green's functions, in conjunction with boundary element methods, will lead to significant advances in the investigation of a variety of wave scattering, wave radiation and soil-structure interaction problems in a layered TI site. Selected numerical results are given to investigate the influence of material anisotropy, frequency of excitation, inclination angle and layered on the responses of displacement and stress, and some conclusions are drawn.

Thz and Long Path Fourier Transform Spectroscopy of Methanol; Torsionally Coupled High-K Levels

NASA Astrophysics Data System (ADS)

Pearson, John C.; Yu, Shanshan; Drouin, Brian J.; Lees, Ronald M.; Xu, Li-Hong; Billinghurst, Brant E.

2012-06-01

Methanol is nearly ubiquitous in the interstellar gas. The presence of both a-type and b-type dipole moments, asymmetry, and internal rotation assure that any small astronomical observation window will contain multiple methanol transitions. This often allows a great deal about the local physical conditions to be deduced, but only insofar as the spectra are characterized. The Herschel Space Observatory has detected numerous, clearly beam diluted, methanol transitions with quanta surpassing J = 35 in many regions. Unfortunately, observations of methanol often display strong non-thermal behavior whose modeling requires many additional levels to be included in a radiative transfer analysis. Additionally, the intensities of many more highly excited transitions are strongly dependent on the accuracy of the wave functions used in the calculation. We report a combined Fourier Transform Infrared and THz study targeting the high J and K transitions in the ground torsional manifold. Microwave accuracy energy levels have been derived to J > 40 and K as high as 20. These levels illuminate a number of strongly resonant torsional interactions that dominate the high K spectrum of the molecule. Comparison with levels calculated from the rho-axis method Hamiltonian suggest that the rho-axis method should be able to model v_t = 0, 1 and probably v_t = 2 to experimental accuracy. The challenges in determining methanol wave functions to experimental accuracy will be discussed.

Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Osborne, A. R.

2014-01-01

Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum annd continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in Earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum and continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Optical spatial heterodyne interferometric Fourier transform technique (OSHIFT) and a resulting interferometer

NASA Astrophysics Data System (ADS)

Georges, James A., III

2007-09-01

This article reports on the novel patent pending Optical Spatial Heterodyne Interferometric Fourier Transform Technique (the OSHIFT technique), the resulting interferometer also referred to as OSHIFT, and its preliminary results. OSHIFT was borne out of the following requirements: wavefront sensitivity on the order of 1/100 waves, high-frequency wavefront spatial sampling, snapshot 100Hz operation, and the ability to deal with discontinuous wavefronts. The first two capabilities lend themselves to the use of traditional interferometric techniques; however, the last two prove difficult for standard techniques, e.g., phase shifting interferometry tends to take a time sequence of images and most interferometers require estimation of a center fringe across wavefront discontinuities. OSHIFT overcomes these challenges by employing a spatial heterodyning concept in the Fourier (image) plane of the optic-under-test. This concept, the mathematical theory, an autocorrelation view of operation, and the design with results of OSHIFT will be discussed. Also discussed will be future concepts such as a sensor that could interrogate an entire imaging system as well as a methodology to create innovative imaging systems that encode wavefront information onto the image. Certain techniques and systems described in this paper are the subject of a patent application currently pending in the United States Patent Office.

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Validating data analysis of broadband laser ranging

NASA Astrophysics Data System (ADS)

Rhodes, M.; Catenacci, J.; Howard, M.; La Lone, B.; Kostinski, N.; Perry, D.; Bennett, C.; Patterson, J.

2018-03-01

Broadband laser ranging combines spectral interferometry and a dispersive Fourier transform to achieve high-repetition-rate measurements of the position of a moving surface. Telecommunications fiber is a convenient tool for generating the large linear dispersions required for a dispersive Fourier transform, but standard fiber also has higher-order dispersion that distorts the Fourier transform. Imperfections in the dispersive Fourier transform significantly complicate the ranging signal and must be dealt with to make high-precision measurements. We describe in detail an analysis process for interpreting ranging data when standard telecommunications fiber is used to perform an imperfect dispersive Fourier transform. This analysis process is experimentally validated over a 27-cm scan of static positions, showing an accuracy of 50 μm and a root-mean-square precision of 4.7 μm.

The morphing of geographical features by Fourier transformation.

PubMed

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets

ERIC Educational Resources Information Center

Singh, Iqbal; Kaur, Bikramjeet

2018-01-01

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

Applications of surface acoustic and shallow bulk acoustic wave devices

NASA Astrophysics Data System (ADS)

Campbell, Colin K.

1989-10-01

Surface acoustic wave (SAW) device coverage includes delay lines and filters operating at selected frequencies in the range from about 10 MHz to 11 GHz; modeling with single-crystal piezoelectrics and layered structures; resonators and low-loss filters; comb filters and multiplexers; antenna duplexers; harmonic devices; chirp filters for pulse compression; coding with fixed and programmable transversal filters; Barker and quadraphase coding; adaptive filters; acoustic and acoustoelectric convolvers and correlators for radar, spread spectrum, and packet radio; acoustooptic processors for Bragg modulation and spectrum analysis; real-time Fourier-transform and cepstrum processors for radar and sonar; compressive receivers; Nyquist filters for microwave digital radio; clock-recovery filters for fiber communications; fixed-, tunable-, and multimode oscillators and frequency synthesizers; acoustic charge transport; and other SAW devices for signal processing on gallium arsenide. Shallow bulk acoustic wave device applications include gigahertz delay lines, surface-transverse-wave resonators employing energy-trapping gratings, and oscillators with enhanced performance and capability.

Uncertainty principles for inverse source problems for electromagnetic and elastic waves

NASA Astrophysics Data System (ADS)

Griesmaier, Roland; Sylvester, John

2018-06-01

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

Crack Detection with Lamb Wave Wavenumber Analysis

NASA Technical Reports Server (NTRS)

Tian, Zhenhua; Leckey, Cara; Rogge, Matt; Yu, Lingyu

2013-01-01

In this work, we present our study of Lamb wave crack detection using wavenumber analysis. The aim is to demonstrate the application of wavenumber analysis to 3D Lamb wave data to enable damage detection. The 3D wavefields (including vx, vy and vz components) in time-space domain contain a wealth of information regarding the propagating waves in a damaged plate. For crack detection, three wavenumber analysis techniques are used: (i) two dimensional Fourier transform (2D-FT) which can transform the time-space wavefield into frequency-wavenumber representation while losing the spatial information; (ii) short space 2D-FT which can obtain the frequency-wavenumber spectra at various spatial locations, resulting in a space-frequency-wavenumber representation; (iii) local wavenumber analysis which can provide the distribution of the effective wavenumbers at different locations. All of these concepts are demonstrated through a numerical simulation example of an aluminum plate with a crack. The 3D elastodynamic finite integration technique (EFIT) was used to obtain the 3D wavefields, of which the vz (out-of-plane) wave component is compared with the experimental measurement obtained from a scanning laser Doppler vibrometer (SLDV) for verification purposes. The experimental and simulated results are found to be in close agreement. The application of wavenumber analysis on 3D EFIT simulation data shows the effectiveness of the analysis for crack detection. Keywords: : Lamb wave, crack detection, wavenumber analysis, EFIT modeling

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Virtual detector theory for strong-field atomic ionization

NASA Astrophysics Data System (ADS)

Wang, Xu; Tian, Justin; Eberly, J. H.

2018-04-01

A virtual detector (VD) is an imaginary device located at a fixed position in space that extracts information from the wave packet passing through it. By recording the particle momentum and the corresponding probability current at each time, the VDs can accumulate and build the differential momentum distribution of the particle, in a way that resembles real experiments. A mathematical proof is given for the equivalence of the differential momentum distribution obtained by the VD method and by Fourier transforming the wave function. In addition to being a tool for reducing the computational load, VDs have also been found useful in interpreting the ultrafast strong-field ionization process, especially the controversial quantum tunneling process.

FIBER AND INTEGRATED OPTICS. OTHER TOPICS IN QUANTUM ELECTRONICS: Increase of the bandwidth and of the efficiency of integrated optical traveling-wave modulators

NASA Astrophysics Data System (ADS)

Zolotov, Evgenii M.; Pelekhatyĭ, V. M.; Tavlykaev, R. F.

1990-05-01

A simultaneous increase in the frequency bandwidth and a reduction in the control (drive) power of integrated optical traveling-wave modulators can be achieved as a result of the electrooptic interaction in accordance with a linear frequency-modulated oscillatory law derived by inverse Fourier transformation of a rectangular amplitude-frequency characteristic and a quadratic phase-frequency characteristic of a modulator. This oscillatory law is realized using planar electrode structures with triangular or trapezoidal toothed edges. The tooth repetition frequency is governed by the linearly frequency-modulated oscillations and it rises on increase in the light modulation frequency.

Frequency-agile terahertz-wave parametric oscillator in a ring-cavity configuration.

PubMed

Minamide, Hiroaki; Ikari, Tomofumi; Ito, Hiromasa

2009-12-01

We demonstrate a frequency-agile terahertz wave parametric oscillator (TPO) in a ring-cavity configuration (ring-TPO). The TPO consists of three mirrors and a MgO:LiNbO(3) crystal under noncollinear phase-matching conditions. A novel, fast frequency-tuning method was realized by controlling a mirror of the three-mirror ring cavity. The wide tuning range between 0.93 and 2.7 THz was accomplished. For first demonstration using the ring-TPO, terahertz spectroscopy was performed as the verification of the frequency-agile performance, measuring the transmission spectrum of the monosaccharide glucose. The spectrum was obtained within about 8 s in good comparison to those of Fourier transform infrared spectrometer.

A pitfall of muting and removing bad traces in surface-wave analysis

NASA Astrophysics Data System (ADS)

Hu, Yue; Xia, Jianghai; Mi, Binbin; Cheng, Feng; Shen, Chao

2018-06-01

Multi-channel analysis of surface/Love wave (MASW/MALW) has been widely used to construct the shallow shear (S)-wave velocity profile. The key step in surface-wave analysis is to generate accurate dispersion energy and pick the dispersive curves for inversion along the peaks of dispersion energy at different frequencies. In near-surface surface-wave acquisition, bad traces are very common and inevitable due to the imperfections in the recording instruments or others. The existence of bad traces will cause some artifacts in the dispersion energy image. To avoid the interference of bad traces on the surface-wave analysis, the bad traces should be alternatively muted (zeroed) or removed (deleted) from the raw surface-wave data before dispersion measurement. Most geophysicists and civil engineers, however, are not aware of the differences and implications between muting and removing of bad traces in surface-wave analysis. A synthetic test and a real-world example demonstrate the potential pitfalls of applying muting and removing on bad traces when using different dispersion-imaging methods. We implement muting and removing on bad traces respectively before dispersion measurement, and compare the influence of the two operations on three dispersion-imaging methods, high-resolution linear Radon transform (HRLRT), f-k transformation, and phase shift method. Results indicate that when using the HRLRT to generate the dispersive energy, muting bad traces will cause an even more complicated and discontinuous dispersive energy. When f-k transformation is utilized to conduct dispersive analysis, bad traces should be muted instead of removed to generate an accurate dispersion image to avoid the uneven sampling problem in the Fourier transform. As for the phase shift method, the difference between the two operations is slight, but we suggest that removal should be chosen because the integral for the phase-shift operator of the zeroed traces would bring in the sloped aliasing. This study provides a pre-process guidance for the real-world surface-wave data processing when the recorded shot gather contains inevitable bad traces.

Research about vibration characteristics of timing chain system based on short-time Fourier transform

NASA Astrophysics Data System (ADS)

Xi, Jiaxin; Liu, Ning

2017-09-01

Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

Fourier transform mass spectrometry.

PubMed

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

Fourier Transform Mass Spectrometry

PubMed Central

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

The morphing of geographical features by Fourier transformation

PubMed Central

Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features’ continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable. PMID:29351344

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Heisler, R.

1978-01-01

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Measurement of wave-front aberration in a small telescope remote imaging system using scene-based wave-front sensing

DOEpatents

Poyneer, Lisa A; Bauman, Brian J

2015-03-31

Reference-free compensated imaging makes an estimation of the Fourier phase of a series of images of a target. The Fourier magnitude of the series of images is obtained by dividing the power spectral density of the series of images by an estimate of the power spectral density of atmospheric turbulence from a series of scene based wave front sensor (SBWFS) measurements of the target. A high-resolution image of the target is recovered from the Fourier phase and the Fourier magnitude.

Representation of Complex Spectra in Auditory Cortex

DTIC Science & Technology

1997-01-01

predict the response to any broadband dynamic sound. Fourier Transform Inverse Transform ∫ [.] exp(±2πjΩx±2πjwt) 2 1 2 / 1 1 a 2 1 2 / 1 1 a...Systems Research University of Maryland Spectro-Temporal Transform Ω wx = log f t w = “ripple velocity” Ω = “ripple frequency” Fourier Transform Inverse ... Transform ∫ [.] exp(±2πjΩx±2πjwt) Real functions in the spectro-temporal domain give rise to complex conjugate symmetric functions in the Fourier

A Thin Lens Model for Charged-Particle RF Accelerating Gaps

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

Allen, Christopher K.

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model aremore » presented.« less

On the solutions of fractional order of evolution equations

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-01-01

In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory.

PubMed

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-29

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory

NASA Astrophysics Data System (ADS)

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-01

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

Rapid-Scanning Fourier Transform Spectrometer for Studies of Propagation of Near-Millimeter-Wave Radiation through Clear Air and Fog.

DTIC Science & Technology

1988-03-01

parallel in the output beam . ’ , However, as will be seen, this function can be performed by auxiliary, non -moving mirrors. Our . design for a rapid... splitter used in our design is shown in Fig. 2. The mirror drive is somewhat novel for this type of interferometer in that one mirror in each beam . M3...features: * High interferometric efficiency, due to the Martin-Puplett type design 0 Ruggedness in photolithographically produced beam splitters

Windowing of Full Wavefield Data in Multiple Domains to Characterize Angle-Beam Shear Wave Scattering (Postprint)

DTIC Science & Technology

2017-02-01

OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YY) 2. REPORT TYPE 3 . DATES COVERED (From - To) 19...September 2016 Interim 3 March 2014 – 19 August 2016 4. TITLE AND SUBTITLE WINDOWING OF FULL WAVEFIELD DATA IIN MULTIPLE DOMAINS TO CHARACTERIZE...wavefield baseline subtraction before and after the introduction of a scatterer [2]. Next, a 3 -D Fourier transform is performed to convert the residual

Transient Gratings, Four-Wave Mixing and Polariton Effects in Nonlinear Optics

DTIC Science & Technology

1991-06-01

w, are. under some very general conditions, equal to the Fourier transform of the TG signal 1361. The possibility of exciton localization l37-3...which is tile analogue of the Anderson electron localization , could also be probed ideally by the grating technique 1401. In this review we develop a...often handled using, at mean-tield t heor ilie local -tield approximation) I 7). -lI. Our -,encral formialism reduce,, to these commnon procedureN xxci he

2008 Program of Study: Perspectives and Challenges in GFD (Geophysical Fluid Dynamics)

DTIC Science & Technology

2009-03-01

half of the complex k- plane , and Φ− is similarly well defined in the lower half of 338 PSfrag replacements Im k Re k−i +i Figure 2: Branch cuts in...domains ⊕ and , which include, respectively, the upper and lower half k- planes . The full Fourier transform of φ (and of h, d, etc.) is then well defined in...contour at infinity in the lower half k- plane ; the solution will only contain waves arising from poles located in the

[Optical-fiber Fourier transform spectrometer].

PubMed

Liu, Yong; Li, Bao-sheng; Liu, Yan; Zhai, Yu-feng; Wang, An

2006-10-01

A novel Fourier transform spectrum analyzer based on a single mode fiber Mach-Zehnder interferometer is reported. An optical fiber Fourier transform spectrometer, with bulk optics components replaced by fiber optical components and with the moving mirror replaced by a piezoelectric element fiber stretcher was constructed. The output spectrum of a LD below threshold was measured. Experiment result agrees with that by using grating spectrum analyzer, showing the feasibility of the optic fiber Fourier transform spectrometer for practical spectrum measurement. Spectrum resolution -7 cm(-1) was obtained in our experiment. The resolution can be further improved by increasing the maximum optical path difference.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

PubMed

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

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

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

Local Guided Wavefield Analysis for Characterization of Delaminations in Composites

NASA Technical Reports Server (NTRS)

Rogge, Matthew D.; Campbell Leckey, Cara A.

2012-01-01

Delaminations in composite laminates resulting from impact events may be accompanied by minimal indication of damage at the surface. As such, inspection techniques are required to ensure defects are within allowable limits. Conventional ultrasonic scanning techniques have been shown to effectively characterize the size and depth of delaminations but require physical contact with the structure. Alternatively, a noncontact scanning laser vibrometer may be used to measure guided wave propagation in the laminate structure. A local Fourier domain analysis method is presented for processing guided wavefield data to estimate spatially-dependent wavenumber values, which can be used to determine delamination depth. The technique is applied to simulated wavefields and results are analyzed to determine limitations of the technique with regards to determining defect size and depth. Finally, experimental wavefield data obtained in quasi-isotropic carbon fiber reinforced polymer (CFRP) laminates with impact damage is analyzed and wavenumber is measured to an accuracy of 8.5% in the region of shallow delaminations. Keywords: Ultrasonic wavefield imaging, Windowed Fourier transforms, Guided waves, Structural health monitoring, Nondestructive evaluation

The Fresnel Diffraction: A Story of Light and Darkness

NASA Astrophysics Data System (ADS)

Aime, C.; Aristidi, É.; Rabbia, Y.

2013-03-01

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given here. In a second part of the paper, the presentation turns into the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, giving thereby the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends up with a brief application to incoherent imaging in astronomy.

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

ERIC Educational Resources Information Center

LoPresto, Michael C.

2013-01-01

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Stability of the Superconducting d-Wave Pairing Toward the Intersite Coulomb Repulsion in CuO_2 Plane

NASA Astrophysics Data System (ADS)

Val'kov, V. V.; Dzebisashvili, D. M.; Korovushkin, M. M.; Barabanov, A. F.

2018-06-01

Taking into account the real crystalline structure of the CuO_2 plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction V_1 between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform V_q vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction V_2 of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of V_2.

Stability of the Superconducting d-Wave Pairing Toward the Intersite Coulomb Repulsion in CuO_2 Plane

NASA Astrophysics Data System (ADS)

Val'kov, V. V.; Dzebisashvili, D. M.; Korovushkin, M. M.; Barabanov, A. F.

2018-03-01

Taking into account the real crystalline structure of the CuO_2 plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction V_1 between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform V_q vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction V_2 of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of V_2.

Influence of viscoelastic property on laser-generated surface acoustic waves in coating-substrate systems

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

Sun Hongxiang; Faculty of Science, Jiangsu University, Zhenjiang 212013; Zhang Shuyi

2011-04-01

Taking account of the viscoelasticity of materials, the pulsed laser generation of surface acoustic waves in coating-substrate systems has been investigated quantitatively by using the finite element method. The displacement spectra of the surface acoustic waves have been calculated in frequency domain for different coating-substrate systems, in which the viscoelastic properties of the coatings and substrates are considered separately. Meanwhile, the temporal displacement waveforms have been obtained by applying inverse fast Fourier transforms. The numerical results of the normal surface displacements are presented for different configurations: a single plate, a slow coating on a fast substrate, and a fast coatingmore » on a slow substrate. The influences of the viscoelastic properties of the coating and the substrate on the attenuation of the surface acoustic waves have been studied. In addition, the influence of the coating thickness on the attenuation of the surface acoustic waves has been also investigated in detail.« less

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

NASA Technical Reports Server (NTRS)

Marko, H.

1978-01-01

A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.

Harmonic generation of Lamb waves

NASA Astrophysics Data System (ADS)

Ing, Ros Kiri

2002-11-01

Lamb waves are dispersive waves that propagate following a number of distinct modes that depend on the values of the central frequency and frequency band. According to such properties and using the time-reversal process, it is shown that the hyperfocusing effect may be experienced [R. K. Ing and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1032-1043 (1998)]. Such a focusing effect both relates the time recompression of the dispersive Lamb waves and constructive interference on the focus point of the modes involved. The hyperfocusing effect is interesting because it allows the amplitude of the Lamb waves to reach huge values on the focus point. In our experiments, Lamb waves with normal amplitudes of micrometer values have been achieved on the free surface of a Duralumin plate of 3 mm thickness. By analyzing the Lamb waves in the neighborhood of the focus point using the 2-D Fourier transform technique, a nonlinear process of harmonic generation is then observed--the fundamental frequency component is centered at 1.5 MHz. This nonlinear process is under study and quantified.

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Time-frequency representation of autoionization dynamics in helium

NASA Astrophysics Data System (ADS)

Busto, D.; Barreau, L.; Isinger, M.; Turconi, M.; Alexandridi, C.; Harth, A.; Zhong, S.; Squibb, R. J.; Kroon, D.; Plogmaker, S.; Miranda, M.; Jiménez-Galán, Á.; Argenti, L.; Arnold, C. L.; Feifel, R.; Martín, F.; Gisselbrecht, M.; L'Huillier, A.; Salières, P.

2018-02-01

Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light-matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wave packet. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wave packets emitted via the sp2+ and sp3+ resonances in helium. These measurements allow us to reconstruct the corresponding temporal profiles by Fourier transform. In addition, applying various time-frequency representations, we observe the build-up of the wave packets in the continuum, monitor the instantaneous frequencies emitted at any time and disentangle the dynamics of the direct and resonant ionization channels.

Multidimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rodrigues, M. M.; Vieira, N.

2012-11-01

This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form (CDt0+αu)(t,x) = iħ/2m(C∇βu)(t,x), with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here (CDt0+α,C∇β are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.

Guided wave mode selection for inhomogeneous elastic waveguides using frequency domain finite element approach.

PubMed

Chillara, Vamshi Krishna; Ren, Baiyang; Lissenden, Cliff J

2016-04-01

This article describes the use of the frequency domain finite element (FDFE) technique for guided wave mode selection in inhomogeneous waveguides. Problems with Rayleigh-Lamb and Shear-Horizontal mode excitation in isotropic homogeneous plates are first studied to demonstrate the application of the approach. Then, two specific cases of inhomogeneous waveguides are studied using FDFE. Finally, an example of guided wave mode selection for inspecting disbonds in composites is presented. Identification of sensitive and insensitive modes for defect inspection is demonstrated. As the discretization parameters affect the accuracy of the results obtained from FDFE, effect of spatial discretization and the length of the domain used for the spatial fast Fourier transform are studied. Some recommendations with regard to the choice of the above parameters are provided. Copyright © 2015 Elsevier B.V. All rights reserved.

Mid-infrared, long wave infrared (4-12 μm) molecular emission signatures from pharmaceuticals using laser-induced breakdown spectroscopy (LIBS).

PubMed

Yang, Clayton S-C; Brown, Ei E; Kumi-Barimah, Eric; Hommerich, Uwe H; Jin, Feng; Trivedi, Sudhir B; Samuels, Alan C; Snyder, A Peter

2014-01-01

In an effort to augment the atomic emission spectra of conventional laser-induced breakdown spectroscopy (LIBS) and to provide an increase in selectivity, mid-wave to long-wave infrared (IR), LIBS studies were performed on several organic pharmaceuticals. Laser-induced breakdown spectroscopy signature molecular emissions of target organic compounds are observed for the first time in the IR fingerprint spectral region between 4-12 μm. The IR emission spectra of select organic pharmaceuticals closely correlate with their respective standard Fourier transform infrared spectra. Intact and/or fragment sample molecular species evidently survive the LIBS event. The combination of atomic emission signatures derived from conventional ultraviolet-visible-near-infrared LIBS with fingerprints of intact molecular entities determined from IR LIBS promises to be a powerful tool for chemical detection.

Radar imaging using electromagnetic wave carrying orbital angular momentum

NASA Astrophysics Data System (ADS)

Yuan, Tiezhu; Cheng, Yongqiang; Wang, Hongqiang; Qin, Yuliang; Fan, Bo

2017-03-01

The concept of radar imaging based on orbital angular momentum (OAM) modulation, which has the ability of azimuthal resolution without relative motion, has recently been proposed. We investigate this imaging technique further in greater detail. We first analyze the principle of the technique, accounting for its resolving ability physically. The phase and intensity distributions of the OAM-carrying fields produced by phased uniform circular array antenna, which have significant effects on the imaging results, are investigated. The imaging model shows that the received signal has the form of inverse discrete Fourier transform with the use of OAM and frequency diversities. The two-dimensional Fourier transform is employed to reconstruct the target images in the case of large and small elevation angles. Due to the peculiar phase and intensity characteristics, the small elevation is more suitable for practical application than the large one. The minimum elevation angle is then obtained given the array parameters. The imaging capability is analyzed by means of the point spread function. All results are verified through numerical simulations. The proposed staring imaging technique can achieve extremely high azimuthal resolution with the use of plentiful OAM modes.

Research of transmissive near infrared spectroscopy for non-invasive blood glucose measurement

NASA Astrophysics Data System (ADS)

Yang, Wenming; Liao, Ningfang; Li, Yasheng; Shao, Liwei; Huang, Dehuang

2016-10-01

Near infrared (NIR) has prospectively applied in non-invasive blood glucose measurement due to glucose absorption among the 1.0-2.5m spectral bands. However, this significant technology is hard to be developed because of other blood components and low signal-to-noise ratio (SNR). In this work, we presented a non-invasive glucose measurement system using Fourier transform spectrometer which will work in fingertips or other human body tissues. A refrigerated InGaAs detector with high quantum efficiency performing well in the range of 1.0-1.7μm wavelength is used to acquire transmissive radiation. Preliminary experiment investigations were set up to test glucose levels of aqueous solutions with different concentrations. The analytical modeling of the interferogram data is based on arithmetic Fourier transform and supported by the curvilineal characterization. Experimental results show the variation of light intensity among different glucose concentrations and emphasize the obvious absorption of glucose in NIR wave-range. This study confirms the suitability that NIR can be developed in non-invasive glucose measurement.

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Accuracy & Computational Considerations for Wide--Angle One--way Seismic Propagators and Multiple Scattering by Invariant Embedding

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2004-12-01

Pseudodifferential operators (PSDOs) yield in principle exact one--way seismic wave equations, which are attractive both conceptually and for their promise of computational efficiency. The one--way operators can be extended to include multiple--scattering effects, again in principle exactly. In practice approximations must be made and, as an example, the variable--wavespeed Helmholtz equation for scalar waves in two space dimensions is here factorized to give the one--way wave equation. This simple case permits clear identification of a sequence of physically reasonable approximations to be used when the mathematically exact PSDO one--way equation is implemented on a computer. As intuition suggests, these approximations hinge on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow--angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so--called ``standard--ordering'' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane--wave synthesis lying at the heart of the calculations. The decision on whether a slow or a fast Fourier transform code should be used rests upon how many lateral model parameters are truly distinct. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one--way propagator for the laterally varying case, representing the intuitive extension of classical integral--transform solutions for a laterally homogeneous medium. This exponential propagator suggests the use of larger discrete step sizes, and it can also be used to approach phase--screen like approximations (though the latter are not the main interest here). Numerical comparisons with finite--difference solutions will be presented in order to assess the approximations being made and to gain an understanding of computation time differences. The ideas described extend to the three--dimensional, generally anisotropic case and to multiple scattering by invariant embedding.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates

PubMed Central

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

A Comparison of Optical versus Hardware Fourier Transforms.

DTIC Science & Technology

1983-10-31

AD- R136 223 A COMPRISON’OF OPTICAL ERSUS HARDWARE FOURIER i/i.TRANSFORMS(U) VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS S P...transform and its inverse filtered Fourier transform obtained with the Digital Image Processing (DIP) hardware system located at the School of Aerospace...transparencies, and provided to us by Dr. Ralph G. Allen, Director of the Laser Effects Branch (Division of Radiation Sciences). The DIP system consisted of: an

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

NASA Astrophysics Data System (ADS)

Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg

2017-03-01

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O ( N 4 ) , with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

Joint transform correlators with spatially incoherent illumination

NASA Astrophysics Data System (ADS)

Bykovsky, Yuri A.; Karpiouk, Andrey B.; Markilov, Anatoly A.; Rodin, Vladislav G.; Starikov, Sergey N.

1997-03-01

Two variants of joint transform correlators with monochromatic spatially incoherent illumination are considered. The Fourier-holograms of the reference and recognized images are recorded simultaneously or apart in a time on the same spatial light modulator directly by monochromatic spatially incoherent light. To create the signal of mutual correlation of the images it is necessary to execute nonlinear transformation when the hologram is illuminated by coherent light. In the first scheme of the correlator this aim was achieved by using double pas of a restoring coherent wave through the hologram. In the second variant of the correlator the non-linearity of the characteristic of the spatial light modulator for hologram recording was used. Experimental schemes and results on processing teste images by both variants of joint transform correlators with monochromatic spatially incoherent illumination. The use of spatially incoherent light on the input of joint transform correlators permits to reduce the requirements to optical quality of elements, to reduce accuracy requirements on elements positioning and to expand a number of devices suitable to input images in correlators.

The Filtered Abel Transform and Its Application in Combustion Diagnostics

NASA Technical Reports Server (NTRS)

Simons, Stephen N. (Technical Monitor); Yuan, Zeng-Guang

2003-01-01

Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to an integral transform of the original projection data with the kernel function being the Abel transform of the filtering function. The kernel function is independent of the projection data and can be obtained separately when the filtering function is selected. Users can select the best filtering function for a particular set of experimental data. When the kernal function is obtained, it can be used repeatedly to a number of projection data sets (rovs) from the same experiment. When an entire flame image that contains a large number of projection lines needs to be processed, the new approach significantly reduces computational effort in comparison with the conventional approach in which each projection data set is deconvoluted separately. Computer codes have been developed to perform the filter Abel transform for an entire flame field. Measured soot volume fraction data of a jet diffusion flame are processed as an example.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.

2016-04-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

Rapid update of discrete Fourier transform for real-time signal processing

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.; Kakad, Yogendra P.

2001-10-01

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Discrimination and prediction of the origin of Chinese and Korean soybeans using Fourier transform infrared spectrometry (FT-IR) with multivariate statistical analysis

PubMed Central

Lee, Byeong-Ju; Zhou, Yaoyao; Lee, Jae Soung; Shin, Byeung Kon; Seo, Jeong-Ah; Lee, Doyup; Kim, Young-Suk

2018-01-01

The ability to determine the origin of soybeans is an important issue following the inclusion of this information in the labeling of agricultural food products becoming mandatory in South Korea in 2017. This study was carried out to construct a prediction model for discriminating Chinese and Korean soybeans using Fourier-transform infrared (FT-IR) spectroscopy and multivariate statistical analysis. The optimal prediction models for discriminating soybean samples were obtained by selecting appropriate scaling methods, normalization methods, variable influence on projection (VIP) cutoff values, and wave-number regions. The factors for constructing the optimal partial-least-squares regression (PLSR) prediction model were using second derivatives, vector normalization, unit variance scaling, and the 4000–400 cm–1 region (excluding water vapor and carbon dioxide). The PLSR model for discriminating Chinese and Korean soybean samples had the best predictability when a VIP cutoff value was not applied. When Chinese soybean samples were identified, a PLSR model that has the lowest root-mean-square error of the prediction value was obtained using a VIP cutoff value of 1.5. The optimal PLSR prediction model for discriminating Korean soybean samples was also obtained using a VIP cutoff value of 1.5. This is the first study that has combined FT-IR spectroscopy with normalization methods, VIP cutoff values, and selected wave-number regions for discriminating Chinese and Korean soybeans. PMID:29689113

Time-dependent Electron Acceleration in Blazar Transients: X-Ray Time Lags and Spectral Formation

NASA Astrophysics Data System (ADS)

Lewis, Tiffany R.; Becker, Peter A.; Finke, Justin D.

2016-06-01

Electromagnetic radiation from blazar jets often displays strong variability, extending from radio to γ-ray frequencies. In a few cases, this variability has been characterized using Fourier time lags, such as those detected in the X-rays from Mrk 421 using BeppoSAX. The lack of a theoretical framework to interpret the data has motivated us to develop a new model for the formation of the X-ray spectrum and the time lags in blazar jets based on a transport equation including terms describing stochastic Fermi acceleration, synchrotron losses, shock acceleration, adiabatic expansion, and spatial diffusion. We derive the exact solution for the Fourier transform of the electron distribution and use it to compute the Fourier transform of the synchrotron radiation spectrum and the associated X-ray time lags. The same theoretical framework is also used to compute the peak flare X-ray spectrum, assuming that a steady-state electron distribution is achieved during the peak of the flare. The model parameters are constrained by comparing the theoretical predictions with the observational data for Mrk 421. The resulting integrated model yields, for the first time, a complete first-principles physical explanation for both the formation of the observed time lags and the shape of the peak flare X-ray spectrum. It also yields direct estimates of the strength of the shock and the stochastic magnetohydrodynamical wave acceleration components in the Mrk 421 jet.

Reduced-rank approximations to the far-field transform in the gridded fast multipole method

NASA Astrophysics Data System (ADS)

Hesford, Andrew J.; Waag, Robert C.

2011-05-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method.

PubMed

Hesford, Andrew J; Waag, Robert C

2011-05-10

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method

PubMed Central

Hesford, Andrew J.; Waag, Robert C.

2011-01-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly. PMID:21552350

Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Quirós-Pacheco, Fernando; Correia, Carlos; Esposito, Simone

The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.

Polarization Ratio Determination with Two Identical Linearly Polarized Antennas

DTIC Science & Technology

2017-01-17

Fourier transform analysis of 21 measurements with one of the antennas rotating about its axis a circular polarization ratio is derived which can be...deter- mined directly from a discrete Fourier transform (DFT) of (5). However, leakage between closely spaced DFT bins requires improving the... Fourier transform and a mechanical antenna rotation to separate the principal and opposite circular polarization components followed by a basis

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

Arterial waveguide model for shear wave elastography: implementation and in vitro validation

NASA Astrophysics Data System (ADS)

Vaziri Astaneh, Ali; Urban, Matthew W.; Aquino, Wilkins; Greenleaf, James F.; Guddati, Murthy N.

2017-07-01

Arterial stiffness is found to be an early indicator of many cardiovascular diseases. Among various techniques, shear wave elastography has emerged as a promising tool for estimating local arterial stiffness through the observed dispersion of guided waves. In this paper, we develop efficient models for the computational simulation of guided wave dispersion in arterial walls. The models are capable of considering fluid-loaded tubes, immersed in fluid or embedded in a solid, which are encountered in in vitro/ex vivo, and in vivo experiments. The proposed methods are based on judiciously combining Fourier transformation and finite element discretization, leading to a significant reduction in computational cost while fully capturing complex 3D wave propagation. The developed methods are implemented in open-source code, and verified by comparing them with significantly more expensive, fully 3D finite element models. We also validate the models using the shear wave elastography of tissue-mimicking phantoms. The computational efficiency of the developed methods indicates the possibility of being able to estimate arterial stiffness in real time, which would be beneficial in clinical settings.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations.

PubMed

McAleavey, Stephen

2011-01-01

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

Apparatus for direct-to-digital spatially-heterodyned holography

DOEpatents

Thomas, Clarence E.; Hanson, Gregory R.

2006-12-12

An apparatus operable to record a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis includes: a laser; a beamsplitter optically coupled to the laser; an object optically coupled to the beamsplitter; a focusing lens optically coupled to both the beamsplitter and the object; a digital recorder optically coupled to the focusing lens; and a computer that performs a Fourier transform, applies a digital filter, and performs an inverse Fourier transform. A reference beam and an object beam are focused by the focusing lens at a focal plane of the digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis which is recorded by the digital recorder, and the computer transforms the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes and shifts axes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam and cuts off signals around an original origin before performing the inverse Fourier transform.

Fourier transform imaging of impurities in the unit cells of crystals: Mn in GaAs

NASA Astrophysics Data System (ADS)

Lee, T.-L.; Bihler, C.; Schoch, W.; Limmer, W.; Daeubler, J.; Thieß, S.; Brandt, M. S.; Zegenhagen, J.

2010-06-01

The lattice sites of Mn in ferromagnetic (Ga,Mn)As thin films were imaged using the x-ray standing wave technique. The model-free images, obtained straightforwardly by Fourier inversion, disclose immediately that the Mn mostly substitutes the Ga with a small fraction residing on minority sites. The images further reveal variations in the Mn concentrations of the different sites upon post-growth treatments. Subsequent model refinement based on the directly reconstructed images resolves with high precision the complete Mn site distributions. It is found that post-growth annealing increases the fraction of substitutional Mn at the expense of interstitial Mn whereas hydrogenation has little influence on the Mn site distribution. Our study offers an element-specific high-resolution imaging approach for accurately determining the detailed site distributions of dilute concentrations of atoms in crystals.

Practical Sub-Nyquist Sampling via Array-Based Compressed Sensing Receiver Architecture

DTIC Science & Technology

2016-07-10

different array ele- ments at different sub-Nyquist sampling rates. Signal processing inspired by the sparse fast Fourier transform allows for signal...reconstruction algorithms can be computationally demanding (REF). The related sparse Fourier transform algorithms aim to reduce the processing time nec- essary to...compute the DFT of frequency-sparse signals [7]. In particular, the sparse fast Fourier transform (sFFT) achieves processing time better than the

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Study on ambient noise generated from breaking waves simulated by a wave maker in a tank

NASA Astrophysics Data System (ADS)

Wei, Ruey-Chang; Chan, Hsiang-Chih

2002-11-01

This paper studies ambient noise in the surf zone that was simulated by a piston-type wave maker in a tank. The experiment analyzed the bubbles of a breaking wave by using a hydrophone to receive the acoustic signal, and the images of bubbles were recorded by a digital video camera to observe the distribution of the bubbles. The slope of the simulated seabed is 1:5, and the dimensions of the water tank are 35 m x1 m x1.2 m. The studied parameters of ambient noise generated by breaking wave bubbles were wave height, period, and water depth. Short-time Fourier transform was applied to obtain the acoustic spectrum of bubbles, MATLAB programs were used to calculate mean sound pressure level, and determine the number of bubbles. Bubbles with resonant frequency from 0.5 to 10 kHz were studied, counted from peaks in the spectrum. The number of bubbles generated by breaking waves could be estimated by the bubbles energy distributions. The sound pressure level of ambient noise was highly related to the wave height and period, with correlation coefficient 0.7.

Analysis of Meniscus Fluctuation in a Continuous Casting Slab Mold

NASA Astrophysics Data System (ADS)

Zhang, Kaitian; Liu, Jianhua; Cui, Heng; Xiao, Chao

2018-06-01

A water model of slab mold was established to analyze the microscopic and macroscopic fluctuation of meniscus. The fast Fourier transform and wavelet entropy were adopted to analyze the wave amplitude, frequency, and components of fluctuation. The flow patterns under the meniscus were measured by using particle image velocimetry measurement and then the mechanisms of meniscus fluctuation were discussed. The results reflected that wavelet entropy had multi-scale and statistical properties, and it was suitable for the study of meniscus fluctuation details both in time and frequency domain. The basic wave, frequency of which exceeding 1 Hz in the condition of no mold oscillation, was demonstrated in this work. In fact, three basic waves were found: long-wave with low frequency, middle-wave with middle frequency, and short-wave with high frequency. In addition, the upper roll flow in mold had significant effect on meniscus fluctuation. When the position of flow impinged was far from the meniscus, long-wave dominated the fluctuation and the stability of meniscus was enhanced. However, when the velocity of flow was increased, the short-wave dominated the meniscus fluctuation and the meniscus stability was decreased.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Time-frequency energy density precipitation method for time-of-flight extraction of narrowband Lamb wave detection signals

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

Zhang, Y., E-mail: thuzhangyu@foxmail.com; Huang, S. L., E-mail: huangsling@tsinghua.edu.cn; Wang, S.

The time-of-flight of the Lamb wave provides an important basis for defect evaluation in metal plates and is the input signal for Lamb wave tomographic imaging. However, the time-of-flight can be difficult to acquire because of the Lamb wave dispersion characteristics. This work proposes a time-frequency energy density precipitation method to accurately extract the time-of-flight of narrowband Lamb wave detection signals in metal plates. In the proposed method, a discrete short-time Fourier transform is performed on the narrowband Lamb wave detection signals to obtain the corresponding discrete time-frequency energy density distribution. The energy density values at the center frequency formore » all discrete time points are then calculated by linear interpolation. Next, the time-domain energy density curve focused on that center frequency is precipitated by least squares fitting of the calculated energy density values. Finally, the peak times of the energy density curve obtained relative to the initial pulse signal are extracted as the time-of-flight for the narrowband Lamb wave detection signals. An experimental platform is established for time-of-flight extraction of narrowband Lamb wave detection signals, and sensitivity analysis of the proposed time-frequency energy density precipitation method is performed in terms of propagation distance, dispersion characteristics, center frequency, and plate thickness. For comparison, the widely used Hilbert–Huang transform method is also implemented for time-of-flight extraction. The results show that the time-frequency energy density precipitation method can accurately extract the time-of-flight with relative error of <1% and thus can act as a universal time-of-flight extraction method for narrowband Lamb wave detection signals.« less

Time-frequency energy density precipitation method for time-of-flight extraction of narrowband Lamb wave detection signals.

PubMed

Zhang, Y; Huang, S L; Wang, S; Zhao, W

2016-05-01

The time-of-flight of the Lamb wave provides an important basis for defect evaluation in metal plates and is the input signal for Lamb wave tomographic imaging. However, the time-of-flight can be difficult to acquire because of the Lamb wave dispersion characteristics. This work proposes a time-frequency energy density precipitation method to accurately extract the time-of-flight of narrowband Lamb wave detection signals in metal plates. In the proposed method, a discrete short-time Fourier transform is performed on the narrowband Lamb wave detection signals to obtain the corresponding discrete time-frequency energy density distribution. The energy density values at the center frequency for all discrete time points are then calculated by linear interpolation. Next, the time-domain energy density curve focused on that center frequency is precipitated by least squares fitting of the calculated energy density values. Finally, the peak times of the energy density curve obtained relative to the initial pulse signal are extracted as the time-of-flight for the narrowband Lamb wave detection signals. An experimental platform is established for time-of-flight extraction of narrowband Lamb wave detection signals, and sensitivity analysis of the proposed time-frequency energy density precipitation method is performed in terms of propagation distance, dispersion characteristics, center frequency, and plate thickness. For comparison, the widely used Hilbert-Huang transform method is also implemented for time-of-flight extraction. The results show that the time-frequency energy density precipitation method can accurately extract the time-of-flight with relative error of <1% and thus can act as a universal time-of-flight extraction method for narrowband Lamb wave detection signals.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

System and method for phase retrieval for radio telescope and antenna control

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2013-01-01

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for radio phase retrieval. A system practicing the method gathers first data from radio waves associated with an object observed via a first aperture, gathers second data from radio waves associated with the object observed via an introduced second aperture associated with the first aperture, generates reduced noise data by incoherently subtracting the second data from the first data, and performs phase retrieval for the radio waves by modeling the reduced noise data using a single Fourier transform. The first and second apertures are at different positions, such as side by side. This approach can include determining a value Q which represents a ratio of wavelength times a focal ratio divided by pixel spacing. This information can be used to accurately measure and correct alignment errors or other optical system flaws in the apertures.

Terahertz transmission properties of silicon wafers using continuous-wave terahertz spectroscopy

NASA Astrophysics Data System (ADS)

Kim, Chihoon; Ahn, Jae Sung; Ji, Taeksoo; Eom, Joo Beom

2017-04-01

We present the spectral properties of Si wafers using continuous-wave terahertz (CW-THz) spectroscopy. By using a tunable laser source and a fixed distributed-feedback laser diode (DFB-LD), a stably tunable beat source for CW-THz spectroscopy system can be implemented. THz radiation is generated in the frequency range of 100 GHz-800 GHz by photomixing in a photoconductive antenna. We also measured CW-THz waveforms by changing the beat frequency and confirmed repeatability through repeated measurement. We calculated the peaks of the THz frequency by taking fast Fourier transforms (FFTs) of measured THz waveforms. The feasibility of CW-THz spectroscopy is demonstrated by the THz spectra of Si wafers with different resistivities, mobilities, and carrier concentrations. The results show that Si wafers with a lower resistivity absorb more THz waves. Thus, we expect our CW-THz system to have the advantage of being able to perform fast non-destructive analysis.

Shape measurement and vibration analysis of moving speaker cone

NASA Astrophysics Data System (ADS)

Zhang, Qican; Liu, Yuankun; Lehtonen, Petri

2014-06-01

Surface three-dimensional (3-D) shape information is needed for many fast processes such as structural testing of material, standing waves on loudspeaker cone, etc. Usually measurement is done from limited number of points using electrical sensors or laser distance meters. Fourier Transform Profilometry (FTP) enables fast shape measurement of the whole surface. Method is based on angled sinusoidal fringe pattern projection and image capturing. FTP requires only one image of the deformed fringe pattern to restore the 3-D shape of the measured object, which makes real-time or dynamic data processing possible. In our experiment the method was used for loudspeaker cone distortion measurement in dynamic conditions. For sound quality issues it is important that the whole cone moves in same phase and there are no partial waves. Our imaging resolution was 1280x1024 pixels and frame rate was 200 fps. Using our setup we found unwanted spatial waves in our sample cone.

Mid-wave infrared narrow bandwidth guided mode resonance notch filter.

PubMed

Zhong, Y; Goldenfeld, Z; Li, K; Streyer, W; Yu, L; Nordin, L; Murphy, N; Wasserman, D

2017-01-15

We have designed, fabricated, and characterized a guided mode resonance notch filter operating in the technologically vital mid-wave infrared (MWIR) region of the electromagnetic spectrum. The filter provides a bandstop at λ≈4.1  μm, with a 12 dB extinction on resonance. In addition, we demonstrate a high transmission background (>80%), less than 6% transmission on resonance, and an ultra-narrow bandwidth transmission notch (10  cm^-1). Our filter is optically characterized using angle- and polarization-dependent Fourier transform infrared spectroscopy, and simulated using rigorous coupled-wave analysis (RCWA) with excellent agreement between simulations and our experimental results. Using our RCWA simulations, we are able to identify the optical modes associated with the transmission dips of our filter. The presented structure offers a potential route toward narrow-band laser filters in the MWIR.

Fourier Analysis and the Rhythm of Conversation.

ERIC Educational Resources Information Center

Dabbs, James M., Jr.

Fourier analysis, a common technique in engineering, breaks down a complex wave form into its simple sine wave components. Communication researchers have recently suggested that this technique may provide an index of the rhythm of conversation, since vocalizing and pausing produce a complex wave form pattern of alternation between two speakers. To…

An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.

Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid

NASA Astrophysics Data System (ADS)

Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

2017-04-01

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

Long wavelength identification of microcalcifications in breast cancer tissue using a quantum cascade laser and upconversion detection

NASA Astrophysics Data System (ADS)

Tseng, Y. P.; Bouzy, P.; Stone, N.; Pedersen, C.; Tidemand-Lichtenberg, P.

2018-02-01

Spectral imaging in the long-wave infrared regime has great potential for medical diagnostics. Breast cancer is the most common cancer amongst females in the US. The pathological features and the occurrence of the microcalcifications are still poorly understood. However, two types of microcalcifications have been identified as unique biomarkers: type I consisting of calcium oxalate (benign lesions) and type II composed of hydroxyapatite (benign or invasive lesions). In this study, we propose a new approach based on vibrational spectroscopy that is non-destructive, label-free and chemically specific for breast cancer detection. Long-wave infrared spectroscopy combining quantum cascade lasers (QCL) and upconversion detection, offer to improve signal-to-noise ratios compared to standard long-wave infrared spectroscopy. We demonstrated long-wave identification of synthetic samples of carbonated hydroxyapatite and of microcalcification in breast cancer tissue using upconversion detection. Absorbance spectra and upconverted images of in situ breast cancer biopsy are compared with that of Fourier-transform infrared (FTIR) spectroscopy.

Hair waving natural product: Dillenia indica seed sap.

PubMed

Saikia, Jyoti Prasad

2013-02-01

Knowing keratin is the main component and mechanical strength of hair a study was performed to evaluate whether Dillenia indica seed sap can affect molecular strength of hair or not. In the present study the human hair collected from barber shop waste were subjected to purified sap for 12 h and then analysed using Fourier transform infrared spectroscopy (FTIR) for documenting evidence for keratin degradation. Further the deterioration was confirmed by thermo gravimetric analysis (TGA) and scanning electron microscopy (SEM). Copyright © 2012 Elsevier B.V. All rights reserved.

Observations of earth eigen vibrations possibly excited by low frequency gravity waves

NASA Technical Reports Server (NTRS)

Tuman, V. S.

1971-01-01

A cryogenic gravity meter made of two parts, a magnetic suspension unit and a detection module, was used to monitor earth eigen vibrations. The magnetic field and field gradient are generated by energizing a set of superconducting coils made of niobium-zirconium alloy wire. The detection module is a double Josephson junction magnetometer. The output is printed on a chart recorder and later digitized using a computer; a Fourier transformation is performed on the accumulated data. The measurements of eigen vibrations are summarized in tabular and graphical representations.

Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs

DOE PAGES

Burghoff, David; Yang, Yang; Hayton, Darren J.; ...

2015-01-01

Recently, much attention has been focused on the generation of optical frequency combs from quantum cascade lasers. We discuss how fast detectors can be used to demonstrate the mutual coherence of such combs, and present an inequality that can be used to quantitatively evaluate their performance. We discuss several technical issues related to shifted wave interference Fourier Transform spectroscopy (SWIFTS), and show how such measurements can be used to elucidate the time-domain properties of such combs, showing that they can possess signatures of both frequency-modulation and amplitude-modulation.

Subwavelength Sensing Using Nonlinear Feedback in a Wave-Chaotic Cavity

DTIC Science & Technology

2013-01-01

r̃in and r̃in are the Fourier transforms of the input pulse and output pulse response, respectively. The magnitude and phase of Hcavity( f ) are plotted...function between its input and output voltages. But, as f increases (beyond ∼ 500 MHz), the amplitudes of the output signals decrease and the phase delay...coupled to free space where it is directed along two paths via a beam splitter (BS), where it is reflected of of mirrors (M1 and M2) that are attached to

Full-Wave Based Validation of Stripline Field Applicator For Low Frequency Material Measurements

DTIC Science & Technology

2009-03-01

16 3.3.1 Principal Solution. . . . . . . . . . . . . . . . . 17 3.3.2 Reflected Solution. . . . . . . . . . . . . . . . . 22 3.4 Applying...potential) [ 17 ]. The vector potential BCs are found to be Ax(x, y = ±h, z) = 0 ∀ x, z (3.2) ∂Ay(x, y = ±h, z) ∂y = 0 ∀ x, z (3.3) Az(x, y = ±h, z...solution at y = ±h, an inverse Fourier transform must be performed on the principal contribution 17 ηre ηim x x η-plane −jp jp Figure 3.2

A Methodology for the Parametric Reconstruction of Non-Steady and Noisy Meteorological Time Series

NASA Astrophysics Data System (ADS)

Rovira, F.; Palau, J. L.; Millán, M.

2009-09-01

Climatic and meteorological time series often show some persistence (in time) in the variability of certain features. One could regard annual, seasonal and diurnal time variability as trivial persistence in the variability of some meteorological magnitudes (as, e.g., global radiation, air temperature above surface, etc.). In these cases, the traditional Fourier transform into frequency space will show the principal harmonics as the components with the largest amplitude. Nevertheless, meteorological measurements often show other non-steady (in time) variability. Some fluctuations in measurements (at different time scales) are driven by processes that prevail on some days (or months) of the year but disappear on others. By decomposing a time series into time-frequency space through the continuous wavelet transformation, one is able to determine both the dominant modes of variability and how those modes vary in time. This study is based on a numerical methodology to analyse non-steady principal harmonics in noisy meteorological time series. This methodology combines both the continuous wavelet transform and the development of a parametric model that includes the time evolution of the principal and the most statistically significant harmonics of the original time series. The parameterisation scheme proposed in this study consists of reproducing the original time series by means of a statistically significant finite sum of sinusoidal signals (waves), each defined by using the three usual parameters: amplitude, frequency and phase. To ensure the statistical significance of the parametric reconstruction of the original signal, we propose a standard statistical t-student analysis of the confidence level of the amplitude in the parametric spectrum for the different wave components. Once we have assured the level of significance of the different waves composing the parametric model, we can obtain the statistically significant principal harmonics (in time) of the original time series by using the Fourier transform of the modelled signal. Acknowledgements The CEAM Foundation is supported by the Generalitat Valenciana and BANCAIXA (València, Spain). This study has been partially funded by the European Commission (FP VI, Integrated Project CIRCE - No. 036961) and by the Ministerio de Ciencia e Innovación, research projects "TRANSREG” (CGL2007-65359/CLI) and "GRACCIE” (CSD2007-00067, Program CONSOLIDER-INGENIO 2010).

An Investigation into the Use of Spatially-Filtered Fourier Transforms to Classify Mammary Lesions.

DTIC Science & Technology

difference in Fourier space between lesioned breast tissue which would enable accurate computer classification of benign and malignant lesions. Low...separate benign and malignant breast tissue. However, no success was achieved when using two-dimensional Fourier transform and power spectrum analysis. (Author)

Detection of Fast Moving and Accelerating Targets Compensating Range and Doppler Migration

DTIC Science & Technology

2014-06-01

Radon -Fourier transform has been introduced to realize long- term coherent integration of the moving targets with range migration [8, 9]. Radon ...2010) Long-time coherent integration for radar target detection base on Radon -Fourier transform, in Proceedings of the IEEE Radar Conference, pp...432–436. 9. Xu, J., Yu, J., Peng, Y. & Xia, X. (2011) Radon -Fourier transform for radar target detection, I: Generalized Doppler filter bank, IEEE

A Primer of Fourier Transform NMR.

ERIC Educational Resources Information Center

Macomber, Roger S.

1985-01-01

Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Damage Detection in Composite Structures with Wavenumber Array Data Processing

NASA Technical Reports Server (NTRS)

Tian, Zhenhua; Leckey, Cara; Yu, Lingyu

2013-01-01

Guided ultrasonic waves (GUW) have the potential to be an efficient and cost-effective method for rapid damage detection and quantification of large structures. Attractive features include sensitivity to a variety of damage types and the capability of traveling relatively long distances. They have proven to be an efficient approach for crack detection and localization in isotropic materials. However, techniques must be pushed beyond isotropic materials in order to be valid for composite aircraft components. This paper presents our study on GUW propagation and interaction with delamination damage in composite structures using wavenumber array data processing, together with advanced wave propagation simulations. Parallel elastodynamic finite integration technique (EFIT) is used for the example simulations. Multi-dimensional Fourier transform is used to convert time-space wavefield data into frequency-wavenumber domain. Wave propagation in the wavenumber-frequency domain shows clear distinction among the guided wave modes that are present. This allows for extracting a guided wave mode through filtering and reconstruction techniques. Presence of delamination causes spectral change accordingly. Results from 3D CFRP guided wave simulations with delamination damage in flat-plate specimens are used for wave interaction with structural defect study.

Wavelet-based automatic determination of the P- and S-wave arrivals

NASA Astrophysics Data System (ADS)

Bogiatzis, P.; Ishii, M.

2013-12-01

The detection of P- and S-wave arrivals is important for a variety of seismological applications including earthquake detection and characterization, and seismic tomography problems such as imaging of hydrocarbon reservoirs. For many years, dedicated human-analysts manually selected the arrival times of P and S waves. However, with the rapid expansion of seismic instrumentation, automatic techniques that can process a large number of seismic traces are becoming essential in tomographic applications, and for earthquake early-warning systems. In this work, we present a pair of algorithms for efficient picking of P and S onset times. The algorithms are based on the continuous wavelet transform of the seismic waveform that allows examination of a signal in both time and frequency domains. Unlike Fourier transform, the basis functions are localized in time and frequency, therefore, wavelet decomposition is suitable for analysis of non-stationary signals. For detecting the P-wave arrival, the wavelet coefficients are calculated using the vertical component of the seismogram, and the onset time of the wave is identified. In the case of the S-wave arrival, we take advantage of the polarization of the shear waves, and cross-examine the wavelet coefficients from the two horizontal components. In addition to the onset times, the automatic picking program provides estimates of uncertainty, which are important for subsequent applications. The algorithms are tested with synthetic data that are generated to include sudden changes in amplitude, frequency, and phase. The performance of the wavelet approach is further evaluated using real data by comparing the automatic picks with manual picks. Our results suggest that the proposed algorithms provide robust measurements that are comparable to manual picks for both P- and S-wave arrivals.

Polarization-phase tomography of biological fluids polycrystalline structure

NASA Astrophysics Data System (ADS)

Dubolazov, A. V.; Vanchuliak, O. Ya.; Garazdiuk, M.; Sidor, M. I.; Motrich, A. V.; Kostiuk, S. V.

2013-12-01

Our research is aimed at designing an experimental method of Fourier's laser polarization phasometry of the layers of human effusion for an express diagnostics during surgery and a differentiation of the degree of severity (acute - gangrenous) appendectomy by means of statistical, correlation and fractal analysis of the coherent scattered field. A model of generalized optical anisotropy of polycrystal networks of albumin and globulin of the effusion of appendicitis has been suggested and the method of Fourier's phasometry of linear (a phase shift between the orthogonal components of the laser wave amplitude) and circular (the angle of rotation of the polarization plane) birefringence with a spatial-frequency selection of the coordinate distributions for the differentiation of acute and gangrenous conditions have been analytically substantiated. Comparative studies of the efficacy of the methods of direct mapping of phase distributions and Fourier's phasometry of a laser radiation field transformed by the dendritic and spherolitic networks of albumin and globulin of the layers of effusion of appendicitis on the basis of complex statistical, correlation and fractal analysis of the structure of phase maps.

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

NASA Technical Reports Server (NTRS)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

2018-03-01

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

PubMed

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

[Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis].

PubMed

Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua

2014-10-01

The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

A BASIC program for the removal of noise from reaction traces using Fourier filtering.

PubMed

Brittain, T

1989-04-01

Software for the removal of noise from reaction curves using the principle of Fourier filtering has been written in BASIC to execute on a PC. The program inputs reaction traces which are subjected to a rotation-inversion process, to produce functions suitable for Fourier analysis. Fourier transformation into the frequency domain is followed by multiplication of the transform by a rectangular filter function, to remove the noise frequencies. Inverse transformation then yields a noise-reduced reaction trace suitable for further analysis. The program is interactive at each stage and could easily be modified to remove noise from a range of input data types.

Quantum Entanglement Molecular Absorption Spectrum Simulator

NASA Technical Reports Server (NTRS)

Nguyen, Quang-Viet; Kojima, Jun

2006-01-01

Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.

Measurement of fast-changing low velocities by photonic Doppler velocimetry

NASA Astrophysics Data System (ADS)

Song, Hongwei; Wu, Xianqian; Huang, Chenguang; Wei, Yangpeng; Wang, Xi

2012-07-01

Despite the increasing popularity of photonic Doppler velocimetry (PDV) in shock wave experiments, its capability of capturing low particle velocities while changing rapidly is still questionable. The paper discusses the performance of short time Fourier transform (STFT) and continuous wavelet transform (CWT) in processing fringe signals of fast-changing low velocities measured by PDV. Two typical experiments are carried out to evaluate the performance. In the laser shock peening test, the CWT gives a better interpretation to the free surface velocity history, where the elastic precursor, main plastic wave, and elastic release wave can be clearly identified. The velocities of stress waves, Hugoniot elastic limit, and the amplitude of shock pressure induced by laser can be obtained from the measurement. In the Kolsky-bar based tests, both methods show validity of processing the longitudinal velocity signal of incident bar, whereas CWT improperly interprets the radial velocity of the shocked sample at the beginning period, indicating the sensitiveness of the CWT to the background noise. STFT is relatively robust in extracting waveforms of low signal-to-noise ratio. Data processing method greatly affects the temporal resolution and velocity resolution of a given fringe signal, usually CWT demonstrates a better local temporal resolution and velocity resolution, due to its adaptability to the local frequency, also due to the finer time-frequency product according to the uncertainty principle.

Measurement of fast-changing low velocities by photonic Doppler velocimetry.

PubMed

Song, Hongwei; Wu, Xianqian; Huang, Chenguang; Wei, Yangpeng; Wang, Xi

2012-07-01

Despite the increasing popularity of photonic Doppler velocimetry (PDV) in shock wave experiments, its capability of capturing low particle velocities while changing rapidly is still questionable. The paper discusses the performance of short time Fourier transform (STFT) and continuous wavelet transform (CWT) in processing fringe signals of fast-changing low velocities measured by PDV. Two typical experiments are carried out to evaluate the performance. In the laser shock peening test, the CWT gives a better interpretation to the free surface velocity history, where the elastic precursor, main plastic wave, and elastic release wave can be clearly identified. The velocities of stress waves, Hugoniot elastic limit, and the amplitude of shock pressure induced by laser can be obtained from the measurement. In the Kolsky-bar based tests, both methods show validity of processing the longitudinal velocity signal of incident bar, whereas CWT improperly interprets the radial velocity of the shocked sample at the beginning period, indicating the sensitiveness of the CWT to the background noise. STFT is relatively robust in extracting waveforms of low signal-to-noise ratio. Data processing method greatly affects the temporal resolution and velocity resolution of a given fringe signal, usually CWT demonstrates a better local temporal resolution and velocity resolution, due to its adaptability to the local frequency, also due to the finer time-frequency product according to the uncertainty principle.

Measurement of fast-changing low velocities by photonic Doppler velocimetry

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

Song Hongwei; Wu Xianqian; Huang Chenguang

2012-07-15

Despite the increasing popularity of photonic Doppler velocimetry (PDV) in shock wave experiments, its capability of capturing low particle velocities while changing rapidly is still questionable. The paper discusses the performance of short time Fourier transform (STFT) and continuous wavelet transform (CWT) in processing fringe signals of fast-changing low velocities measured by PDV. Two typical experiments are carried out to evaluate the performance. In the laser shock peening test, the CWT gives a better interpretation to the free surface velocity history, where the elastic precursor, main plastic wave, and elastic release wave can be clearly identified. The velocities of stressmore » waves, Hugoniot elastic limit, and the amplitude of shock pressure induced by laser can be obtained from the measurement. In the Kolsky-bar based tests, both methods show validity of processing the longitudinal velocity signal of incident bar, whereas CWT improperly interprets the radial velocity of the shocked sample at the beginning period, indicating the sensitiveness of the CWT to the background noise. STFT is relatively robust in extracting waveforms of low signal-to-noise ratio. Data processing method greatly affects the temporal resolution and velocity resolution of a given fringe signal, usually CWT demonstrates a better local temporal resolution and velocity resolution, due to its adaptability to the local frequency, also due to the finer time-frequency product according to the uncertainty principle.« less

Various new applications of fiber optic infrared Fourier transform spectroscopy for dermatology

NASA Astrophysics Data System (ADS)

Bruch, Reinhard F.; Afanasyeva, Natalia I.; Sukuta, Sydney; Brooks, Angelique L.; Makhine, Volodymyr; Kolyakov, Sergei F.

1999-02-01

Fiberoptical evanescent wave Fourier transform infrared (FEW- FTIR) spectroscopy has been applied in the middle infrared (MIR) wavelength range (3 to 20 micrometer) to the in vivo diagnostics of normal skin tissue, acupuncture points as well as precancerous and cancerous conditions. The FTIR-FEW technique, using nontoxic unclad fibers, is suitable for noninvasive, sensitive investigations of skin tissue for various dermatological studies of skin caner, aging, laser treatment, cosmetics, skin allergies, etc. This method is direct, nondestructive, and fast (seconds). Our optical fibers are nonhygroscopic, flexible, and characterized by extremely low losses. In this study, we have noninvasively investigated more than 300 cases of normal skin, acupuncture points, precancerous and cancerous tissue in the range of 1400 to 1800 cm-1. The results of our analysis of skin and other tissue are discussed in terms of structural and mathematical similarities and differences on a molecular level. In addition, we have also performed cluster analysis, using principal component scores, to confirm pathological classifications and to discriminate between genders. We have found good agreement with prior pathological classifications for normal skin tissue and melanoma tumors and normal females were distinctly separate from males.

A method to measure the presampling MTF in digital radiography using Wiener deconvolution

NASA Astrophysics Data System (ADS)

Zhou, Zhongxing; Zhu, Qingzhen; Gao, Feng; Zhao, Huijuan; Zhang, Lixin; Li, Guohui

2013-03-01

We developed a novel method for determining the presampling modulation transfer function (MTF) of digital radiography systems from slanted edge images based on Wiener deconvolution. The degraded supersampled edge spread function (ESF) was obtained from simulated slanted edge images with known MTF in the presence of poisson noise, and its corresponding ideal ESF without degration was constructed according to its central edge position. To meet the requirements of the absolute integrable condition of Fourier transformation, the origianl ESFs were mirrored to construct the symmetric pattern of ESFs. Then based on Wiener deconvolution technique, the supersampled line spread function (LSF) could be acquired from the symmetric pattern of degraded supersampled ESFs in the presence of ideal symmetric ESFs and system noise. The MTF is then the normalized magnitude of the Fourier transform of the LSF. The determined MTF showed a strong agreement with the theoritical true MTF when appropriated Wiener parameter was chosen. The effects of Wiener parameter value and the width of square-like wave peak in symmetric ESFs were illustrated and discussed. In conclusion, an accurate and simple method to measure the presampling MTF was established using Wiener deconvolution technique according to slanted edge images.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

A method to improve the range resolution in stepped frequency continuous wave radar

NASA Astrophysics Data System (ADS)

Kaczmarek, Paweł

2018-04-01

In the paper one of high range resolution methods - Aperture Sampling - was analysed. Unlike MUSIC based techniques it proved to be very efficient in terms of achieving unambiguous synthetic range profile for ultra-wideband stepped frequency continuous wave radar. Assuming that minimal distance required to separate two targets in depth (distance) corresponds to -3 dB width of received echo, AS provided a 30,8 % improvement in range resolution in analysed scenario, when compared to results of applying IFFT. Output data is far superior in terms of both improved range resolution and reduced side lobe level than used typically in this area Inverse Fourier Transform. Furthermore it does not require prior knowledge or an estimate of number of targets to be detected in a given scan.

Active chiral control of GHz acoustic whispering-gallery modes

NASA Astrophysics Data System (ADS)

Mezil, Sylvain; Fujita, Kentaro; Otsuka, Paul H.; Tomoda, Motonobu; Clark, Matt; Wright, Oliver B.; Matsuda, Osamu

2017-10-01

We selectively generate chiral surface-acoustic whispering-gallery modes in the gigahertz range on a microscopic disk by means of an ultrafast time-domain technique incorporating a spatial light modulator. Active chiral control is achieved by making use of an optical pump spatial profile in the form of a semicircular arc, positioned on the sample to break the symmetry of clockwise- and counterclockwise-propagating modes. Spatiotemporal Fourier transforms of the interferometrically monitored two-dimensional acoustic fields measured to micron resolution allow individual chiral modes and their azimuthal mode order, both positive and negative, to be distinguished. In particular, for modes with 15-fold rotational symmetry, we demonstrate ultrafast chiral control of surface acoustic waves in a micro-acoustic system with picosecond temporal resolution. Applications include nondestructive testing and surface acoustic wave devices.

GIFTS SM EDU Data Processing and Algorithms

NASA Technical Reports Server (NTRS)

Tian, Jialin; Johnson, David G.; Reisse, Robert A.; Gazarik, Michael J.

2007-01-01

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation.

Improved quantitative visualization of hypervelocity flow through wavefront estimation based on shadow casting of sinusoidal gratings.

PubMed

Medhi, Biswajit; Hegde, Gopalakrishna M; Gorthi, Sai Siva; Reddy, Kalidevapura Jagannath; Roy, Debasish; Vasu, Ram Mohan

2016-08-01

A simple noninterferometric optical probe is developed to estimate wavefront distortion suffered by a plane wave in its passage through density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a continuous-tone sinusoidal grating. Through a geometrical optics, eikonal approximation to the distorted wavefront, a bilinear approximation to it is related to the location-dependent shift (distortion) suffered by the grating, which can be read out space-continuously from the projected grating image. The processing of the grating shadow is done through an efficient Fourier fringe analysis scheme, either with a windowed or global Fourier transform (WFT and FT). For comparison, wavefront slopes are also estimated from shadows of random-dot patterns, processed through cross correlation. The measured slopes are suitably unwrapped by using a discrete cosine transform (DCT)-based phase unwrapping procedure, and also through iterative procedures. The unwrapped phase information is used in an iterative scheme, for a full quantitative recovery of density distribution in the shock around the model, through refraction tomographic inversion. Hypersonic flow field parameters around a missile-shaped body at a free-stream Mach number of ∼8 measured using this technique are compared with the numerically estimated values. It is shown that, while processing a wavefront with small space-bandwidth product (SBP) the FT inversion gave accurate results with computational efficiency; computation-intensive WFT was needed for similar results when dealing with larger SBP wavefronts.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

Ground roll attenuation using polarization analysis in the t-f-k domain

NASA Astrophysics Data System (ADS)

Wang, C.; Wang, Y.

2017-07-01

S waves travel slower than P waves and have a lower dominant frequency. Therefore, applying common techniques such as time-frequency filtering and f-k filtering to separate S waves from ground roll is difficult because ground roll is also characterized by slow velocity and low frequency. In this study, we present a method for attenuating ground roll using a polarization filtering method based on the t-f-k transform. We describe the particle motion of the waves by complex vector signals. Each pair of frequency components, whose frequencies have the same absolute value but different signs, of the complex signal indicate an elliptical or linear motion. The polarization parameters of the elliptical or linear motion are explicitly related to the two Fourier coefficients. We then extend these concepts to the t-f-k domain and propose a polarization filtering method for ground roll attenuation based on the t-f-k transform. The proposed approach can define automatically the time-varying reject zones on the f-k panel at different times as a function of the reciprocal ellipticity. Four attributes, time, frequency, apparent velocity and polarization are used to identify and extract the ground roll simultaneously. Thus, the ground roll and body waves can be separated as long as they are dissimilar in one of these attributes. We compare our method with commonly used filtering techniques by applying the methods to synthetic and real seismic data. The results indicate that our method can attenuate ground roll while preserving body waves more effectively than the other methods.

Structural correlation of the chalcogenide Ge40Se60 glass

NASA Astrophysics Data System (ADS)

Moharram, A. H.

2017-01-01

Binary Ge40Se60 glass was prepared using the melt-quench technique. The total structure factors, S( K), are obtained using the X-ray diffraction in the wave vector interval 0.28 ≤ K ≤ 6.5 Å-1. The appearance of the first sharp diffraction peak (FSDP) in the structure factor indicates the presence of the intermediate range order. Radial distribution functions, RDF( r), have been obtained using either the conventional (Fourier) transformation or the Monte Carlo simulation of the experimental X-ray data. The short range order parameters deduced from the Monte Carlo total correlation, T( r), functions are better than those obtained from the conventional (Fourier) T( r) data. Gaussian analyses of the total correlation function show that Ge2(Se1/2)6 molecular units are the basic structural units for the investigated Ge40Se60 glass.

Fields of an ultrashort tightly focused radially polarized laser pulse in a linear response plasma

NASA Astrophysics Data System (ADS)

Salamin, Yousef I.

2017-10-01

Analytical expressions for the fields of a radially polarized, ultrashort, and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogeneous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First, the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated series (finite sum). The zeroth-order term in, for example, the axial electric field component is shown to model a pulse much better than its widely used paraxial approximation counterpart. Some of the propagation characteristics of the fields are discussed and all fields are shown to have manifested the expected limits for propagation in a vacuum.

2.5-D frequency-domain viscoelastic wave modelling using finite-element method

NASA Astrophysics Data System (ADS)

Zhao, Jian-guo; Huang, Xing-xing; Liu, Wei-fang; Zhao, Wei-jun; Song, Jian-yong; Xiong, Bin; Wang, Shang-xu

2017-10-01

2-D seismic modelling has notable dynamic information discrepancies with field data because of the implicit line-source assumption, whereas 3-D modelling suffers from a huge computational burden. The 2.5-D approach is able to overcome both of the aforementioned limitations. In general, the earth model is treated as an elastic material, but the real media is viscous. In this study, we develop an accurate and efficient frequency-domain finite-element method (FEM) for modelling 2.5-D viscoelastic wave propagation. To perform the 2.5-D approach, we assume that the 2-D viscoelastic media are based on the Kelvin-Voigt rheological model and a 3-D point source. The viscoelastic wave equation is temporally and spatially Fourier transformed into the frequency-wavenumber domain. Then, we systematically derive the weak form and its spatial discretization of 2.5-D viscoelastic wave equations in the frequency-wavenumber domain through the Galerkin weighted residual method for FEM. Fixing a frequency, the 2-D problem for each wavenumber is solved by FEM. Subsequently, a composite Simpson formula is adopted to estimate the inverse Fourier integration to obtain the 3-D wavefield. We implement the stiffness reduction method (SRM) to suppress artificial boundary reflections. The results show that this absorbing boundary condition is valid and efficient in the frequency-wavenumber domain. Finally, three numerical models, an unbounded homogeneous medium, a half-space layered medium and an undulating topography medium, are established. Numerical results validate the accuracy and stability of 2.5-D solutions and present the adaptability of finite-element method to complicated geographic conditions. The proposed 2.5-D modelling strategy has the potential to address modelling studies on wave propagation in real earth media in an accurate and efficient way.

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

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

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

PubMed

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

Fast Fourier Transform algorithm design and tradeoffs

NASA Technical Reports Server (NTRS)

Kamin, Ray A., III; Adams, George B., III

1988-01-01

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

TIME-DEPENDENT ELECTRON ACCELERATION IN BLAZAR TRANSIENTS: X-RAY TIME LAGS AND SPECTRAL FORMATION

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

Lewis, Tiffany R.; Becker, Peter A.; Finke, Justin D., E-mail: pbecker@gmu.edu, E-mail: tlewis13@gmu.edu, E-mail: justin.finke@nrl.navy.mil

2016-06-20

Electromagnetic radiation from blazar jets often displays strong variability, extending from radio to γ -ray frequencies. In a few cases, this variability has been characterized using Fourier time lags, such as those detected in the X-rays from Mrk 421 using Beppo SAX. The lack of a theoretical framework to interpret the data has motivated us to develop a new model for the formation of the X-ray spectrum and the time lags in blazar jets based on a transport equation including terms describing stochastic Fermi acceleration, synchrotron losses, shock acceleration, adiabatic expansion, and spatial diffusion. We derive the exact solution formore » the Fourier transform of the electron distribution and use it to compute the Fourier transform of the synchrotron radiation spectrum and the associated X-ray time lags. The same theoretical framework is also used to compute the peak flare X-ray spectrum, assuming that a steady-state electron distribution is achieved during the peak of the flare. The model parameters are constrained by comparing the theoretical predictions with the observational data for Mrk 421. The resulting integrated model yields, for the first time, a complete first-principles physical explanation for both the formation of the observed time lags and the shape of the peak flare X-ray spectrum. It also yields direct estimates of the strength of the shock and the stochastic magnetohydrodynamical wave acceleration components in the Mrk 421 jet.« less

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2013 CFR

2013-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2014 CFR

2014-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

3-Dimensional stereo implementation of photoacoustic imaging based on a new image reconstruction algorithm without using discrete Fourier transform

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu

2017-05-01

In this paper, we propose a new three-dimensional stereo image reconstruction algorithm for a photoacoustic medical imaging system. We also introduce and discuss a new theoretical algorithm by using the physical concept of Radon transform. The main key concept of proposed theoretical algorithm is to evaluate the existence possibility of the acoustic source within a searching region by using the geometric distance between each sensor element of acoustic detector and the corresponding searching region denoted by grid. We derive the mathematical equation for the magnitude of the existence possibility which can be used for implementing a new proposed algorithm. We handle and derive mathematical equations of proposed algorithm for the one-dimensional sensing array case as well as two dimensional sensing array case too. A mathematical k-wave simulation data are used for comparing the image quality of the proposed algorithm with that of general conventional algorithm in which the FFT should be necessarily used. From the k-wave Matlab simulation results, we can prove the effectiveness of the proposed reconstruction algorithm.

40 CFR Appendix B to Subpart Uuuuu - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2012 CFR

2012-07-01

... Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix B to... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

Time-localized frequency analysis of ultrasonic guided waves for nondestructive testing

NASA Astrophysics Data System (ADS)

Shin, Hyeon Jae; Song, Sung-Jin

2000-05-01

A time-localized frequency (TLF) analysis is employed for the guided wave mode identification and improved guided wave applications. For the analysis of time-localized frequency contents of digitized ultrasonic signals, TLF analysis consists of splitting the time domain signal into overlapping segments, weighting each with the hanning window, and forming the columns of discrete Fourier transforms. The result is presented by a frequency versus time domain diagram showing frequency variation along the signal arrival time. For the demonstration of the utility of TLF analysis, an experimental group velocity dispersion pattern obtained by TLF analysis is compared with the dispersion diagram obtained by theory of elasticity. Sample piping is carbon steel piping that is used for the transportation of natural gas underground. Guided wave propagation characteristic on the piping is considered with TLF analysis and wave structure concepts. TLF analysis is used for the detection of simulated corrosion defects and the assessment of weld joint using ultrasonic guided waves. TLF analysis has revealed that the difficulty of mode identification in multi-mode propagation could be overcome. Group velocity dispersion pattern obtained by TLF analysis agrees well with theoretical results.

Design of a CMOS integrated on-chip oscilloscope for spin wave characterization

NASA Astrophysics Data System (ADS)

Egel, Eugen; Meier, Christian; Csaba, György; Breitkreutz-von Gamm, Stephan

2017-05-01

Spin waves can perform some optically-inspired computing algorithms, e.g. the Fourier transform, directly than it is done with the CMOS logic. This article describes a new approach for on-chip characterization of spin wave based devices. The readout circuitry for the spin waves is simulated with 65-nm CMOS technology models. Commonly used circuits for Radio Frequency (RF) receivers are implemented to detect a sinusoidal ultra-wideband (5-50 GHz) signal with an amplitude of at least 15 μV picked up by a loop antenna. First, the RF signal is amplified by a Low Noise Amplifier (LNA). Then, it is down-converted by a mixer to Intermediate Frequency (IF). Finally, an Operational Amplifier (OpAmp) brings the IF signal to higher voltages (50-300 mV). The estimated power consumption and the required area of the readout circuit is approximately 55.5 mW and 0.168 mm2, respectively. The proposed On-Chip Oscilloscope (OCO) is highly suitable for on-chip spin wave characterization regarding the frequency, amplitude change and phase information. It offers an integrated low power alternative to current spin wave detecting systems.

Monitoring of corrosion damage using high-frequency guided ultrasonic waves

NASA Astrophysics Data System (ADS)

Chew, D.; Fromme, P.

2014-03-01

Due to adverse environmental conditions corrosion can develop during the life cycle of industrial structures, e.g., offshore oil platforms, ships, and desalination plants. Both pitting corrosion and generalized corrosion leading to wall thickness loss can cause the degradation of the integrity and load bearing capacity of the structure. Structural health monitoring of corrosion damage in difficult to access areas can in principle be achieved using high frequency guided waves propagating along the structure from accessible areas. Using standard ultrasonic transducers with single sided access to the structure, high frequency guided wave modes were generated that penetrate through the complete thickness of the structure. Wall thickness reduction was induced using accelerated corrosion in a salt water bath. The corrosion damage was monitored based on the effect on the wave propagation and interference of the different modes. The change in the wave interference was quantified based on an analysis in the frequency domain (Fourier transform) and was found to match well with theoretical predictions for the wall thickness loss. High frequency guided waves have the potential for corrosion damage monitoring at critical and difficult to access locations from a stand-off distance.

Monitoring of corrosion damage using high-frequency guided ultrasonic waves

NASA Astrophysics Data System (ADS)

Chew, D.; Fromme, P.

2015-03-01

Due to adverse environmental conditions corrosion can develop during the life cycle of industrial structures, e.g., offshore oil platforms, ships, and desalination plants. Both pitting corrosion and generalized corrosion leading to wall thickness loss can cause the degradation of the integrity and load bearing capacity of the structure. Structural health monitoring of corrosion damage in difficult to access areas can in principle be achieved using high frequency guided waves propagating along the structure from accessible areas. Using standard ultrasonic transducers with single sided access to the structure, high frequency guided wave modes were generated that penetrate through the complete thickness of the structure. Wall thickness reduction was induced using accelerated corrosion in a salt water bath. The corrosion damage was monitored based on the effect on the wave propagation and interference of the different modes. The change in the wave interference was quantified based on an analysis in the frequency domain (Fourier transform) and was found to match well with theoretical predictions for the wall thickness loss. High frequency guided waves have the potential for corrosion damage monitoring at critical and difficult to access locations from a stand-off distance.

Acquisition and analysis of angle-beam wavefield data

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

Dawson, Alexander J.; Michaels, Jennifer E.; Levine, Ross M.

2014-02-18

Angle-beam ultrasonic testing is a common practical technique used for nondestructive evaluation to detect, locate, and characterize a variety of material defects and damage. Greater understanding of the both the incident wavefield produced by an angle-beam transducer and the subsequent scattering from a variety of defects and geometrical features is anticipated to increase the reliability of data interpretation. The focus of this paper is on acquiring and analyzing propagating waves from angle-beam transducers in simple, defect-free plates as a first step in the development of methods for flaw characterization. Unlike guided waves, which excite the plate throughout its thickness, angle-beammore » bulk waves bounce back and forth between the plate surfaces, resulting in the well-known multiple “skips” or “V-paths.” The experimental setup consists of a laser vibrometer mounted on an XYZ scanning stage, which is programmed to move point-to-point on a rectilinear grid to acquire waveform data. Although laser vibrometry is now routinely used to record guided waves for which the frequency content is below 1 MHz, it is more challenging to acquire higher frequency bulk waves in the 1–10 MHz range. Signals are recorded on the surface of an aluminum plate that were generated from a 5 MHz, 65° refracted angle, shear wave transducer-wedge combination. Data are analyzed directly in the x-t domain, via a slant stack Radon transform in the τ-p (offset time-slowness) domain, and via a 2-D Fourier transform in the ω-k domain, thereby enabling identification of specific arrivals and modes. Results compare well to those expected from a simple ray tracing analysis except for the unexpected presence of a strong Rayleigh wave.« less

An Evaluation of the Environmental Fate and Behavior of Munitions Materiel (Tetryl and Polar Metabolites of TNT) in Soil and Plant Systems. Environmental Fate and Behavior of Tetryl

DTIC Science & Technology

1992-03-01

attempted to verify product identity and purity by GC with either Fourier transform infrared spectro.icopy (FTIR) or mass spectroscopy (MS) detection...ýl0 5 In-1 z U)-’i0oo -3g’i o -6o0 626o a i60 ito1 2i oo I ’ o [JfnVENUII8ER (cm- FIGURE 3,9. Fourier Transform Infrared Spectroscopy Spectrum of...Fourier Transform Infrared Spectroscopy Spectrum of Tetryl I-I F1U~IGUR Fourier Utransformlfret Spcrop S ectrum of TeasomtinPoutrl 0 , -39 i : : : -. . i

Modeling the effects of Multi-path propagation and scintillation on GPS signals

NASA Astrophysics Data System (ADS)

Habash Krause, L.; Wilson, S. J.

2014-12-01

GPS signals traveling through the earth's ionosphere are affected by charged particles that often disrupt the signal and the information it carries due to "scintillation", which resembles an extra noise source on the signal. These signals are also affected by weather changes, tropospheric scattering, and absorption from objects due to multi-path propagation of the signal. These obstacles cause distortion within information and fading of the signal, which ultimately results in phase locking errors and noise in messages. In this work, we attempted to replicate the distortion that occurs in GPS signals using a signal processing simulation model. We wanted to be able to create and identify scintillated signals so we could better understand the environment that caused it to become scintillated. Then, under controlled conditions, we simulated the receiver's ability to suppress scintillation in a signal. We developed a code in MATLAB that was programmed to: 1. Create a carrier wave and then plant noise (four different frequencies) on the carrier wave, 2. Compute a Fourier transform on the four different frequencies to find the frequency content of a signal, 3. Use a filter and apply it to the Fourier transform of the four frequencies and then compute a Signal-to-noise ratio to evaluate the power (in Decibels) of the filtered signal, and 4.Plot each of these components into graphs. To test the code's validity, we used user input and data from an AM transmitter. We determined that the amplitude modulated signal or AM signal would be the best type of signal to test the accuracy of the MATLAB code due to its simplicity. This code is basic to give students the ability to change and use it to determine the environment and effects of noise on different AM signals and their carrier waves. Overall, we were able to manipulate a scenario of a noisy signal and interpret its behavior and change due to its noisy components: amplitude, frequency, and phase shift.

Multi-wavelength Observations of Solar Acoustic Waves Near Active Regions

NASA Astrophysics Data System (ADS)

Monsue, Teresa; Pesnell, Dean; Hill, Frank

2018-01-01

Active region areas on the Sun are abundant with a variety of waves that are both acoustically helioseismic and magnetohydrodynamic in nature. The occurrence of a solar flare can disrupt these waves, through MHD mode-mixing or scattering by the excitation of these waves. We take a multi-wavelength observational approach to understand the source of theses waves by studying active regions where flaring activity occurs. Our approach is to search for signals within a time series of images using a Fast Fourier Transform (FFT) algorithm, by producing multi-frequency power map movies. We study active regions both spatially and temporally and correlate this method over multiple wavelengths using data from NASA’s Solar Dynamics Observatory. By surveying the active regions on multiple wavelengths we are able to observe the behavior of these waves within the Solar atmosphere, from the photosphere up through the corona. We are able to detect enhancements of power around active regions, which could be acoustic power halos and of an MHD-wave propagating outward by the flaring event. We are in the initial stages of this study understanding the behaviors of these waves and could one day contribute to understanding the mechanism responsible for their formation; that has not yet been explained.

Advanced satellite communication system

NASA Technical Reports Server (NTRS)

Staples, Edward J.; Lie, Sen

1992-01-01

The objective of this research program was to develop an innovative advanced satellite receiver/demodulator utilizing surface acoustic wave (SAW) chirp transform processor and coherent BPSK demodulation. The algorithm of this SAW chirp Fourier transformer is of the Convolve - Multiply - Convolve (CMC) type, utilizing off-the-shelf reflective array compressor (RAC) chirp filters. This satellite receiver, if fully developed, was intended to be used as an on-board multichannel communications repeater. The Advanced Communications Receiver consists of four units: (1) CMC processor, (2) single sideband modulator, (3) demodulator, and (4) chirp waveform generator and individual channel processors. The input signal is composed of multiple user transmission frequencies operating independently from remotely located ground terminals. This signal is Fourier transformed by the CMC Processor into a unique time slot for each user frequency. The CMC processor is driven by a waveform generator through a single sideband (SSB) modulator. The output of the coherent demodulator is composed of positive and negative pulses, which are the envelopes of the chirp transform processor output. These pulses correspond to the data symbols. Following the demodulator, a logic circuit reconstructs the pulses into data, which are subsequently differentially decoded to form the transmitted data. The coherent demodulation and detection of BPSK signals derived from a CMC chirp transform processor were experimentally demonstrated and bit error rate (BER) testing was performed. To assess the feasibility of such advanced receiver, the results were compared with the theoretical analysis and plotted for an average BER as a function of signal-to-noise ratio. Another goal of this SBIR program was the development of a commercial product. The commercial product developed was an arbitrary waveform generator. The successful sales have begun with the delivery of the first arbitrary waveform generator.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

PubMed

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

A Comparison of FTNMR and FTIR Techniques.

ERIC Educational Resources Information Center

Ahn, Myong-Ku

1989-01-01

Nuclear magnetic resonance and infrared are two spectroscopic methods that commonly use the Fourier transform technique. Discussed are the similarities and differences in the use of the Fourier transform in these two spectroscopic techniques. (CW)

Novel hybrid optical correlator: theory and optical simulation.

PubMed

Casasent, D; Herold, R L

1975-02-01

The inverse transform of the product of two Fourier transform holograms is analyzed and shown to contain the correlation of the two images from which the holograms were formed. The theory, analysis, and initial experimental demonstration of the feasibility of a novel correlation scheme using this multiplied Fourier transform hologram system are presented.

Fast algorithm for chirp transforms with zooming-in ability and its applications.

PubMed

Deng, X; Bihari, B; Gan, J; Zhao, F; Chen, R T

2000-04-01

A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10(-12) for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0 < or = z < d2/lambda. It compensates another algorithm for Fresnel diffraction that is limited to z > d2/lambdaN [J. Opt. Soc. Am. A 15, 2111 (1998)]. Experimental results from waveguide-output microcoupler diffraction are in good agreement with the calculations.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Holographic recording materials development. [using stilbene, indigo, and thioindigo derivatives

NASA Technical Reports Server (NTRS)

1975-01-01

The area of organic cis-trans photoisomerization systems for holographic memory applications was examined. Photochemical studies were made of stilbene, indigo, and thioindigo derivatives in solution and in a variety of polymer matrix materials, to optimize the photorefractive behavior of the chemical system as a whole. Lithium niobate was used to study the writing and reading efficiencies of thick phase holograms. Both phase-wave holograms and Fourier-transform holograms were employed, and a number of reconstruction techniques are discussed. The possibility of using cis-trans photoisomerization of appropriate organic chemicals as the basis for a holographic recording system is confirmed.

Application of a flight test and data analysis technique to flutter of a drone aircraft

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Abel, I.

1981-01-01

Modal identification results are presented that were obtained from recent flight flutter tests of a drone vehicle with a research wing equipped with an active flutter suppression system (FSS). Frequency and damping of several modes are determined by a time domain modal analysis of the impulse response function obtained by Fourier transformations of data from fast swept sine wave excitation by the FSS control surfaces on the wing. Flutter points are determined for two different altitudes with the FSS off. Data are given for near the flutter boundary with the FSS on.

Two-path plasmonic interferometer with integrated detector

DOEpatents

Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory

2016-03-29

An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Experimental image alignment system

NASA Technical Reports Server (NTRS)

Moyer, A. L.; Kowel, S. T.; Kornreich, P. G.

1980-01-01

A microcomputer-based instrument for image alignment with respect to a reference image is described which uses the DEFT sensor (Direct Electronic Fourier Transform) for image sensing and preprocessing. The instrument alignment algorithm which uses the two-dimensional Fourier transform as input is also described. It generates signals used to steer the stage carrying the test image into the correct orientation. This algorithm has computational advantages over algorithms which use image intensity data as input and is suitable for a microcomputer-based instrument since the two-dimensional Fourier transform is provided by the DEFT sensor.

Fourier-transform and global contrast interferometer alignment methods

DOEpatents

Goldberg, Kenneth A.

2001-01-01

Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.

A fast D.F.T. algorithm using complex integer transforms

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1978-01-01

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

PubMed

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances

NASA Technical Reports Server (NTRS)

Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.

2000-01-01

A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).

Technique for the metrology calibration of a Fourier transform spectrometer

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

Spencer, Locke D.; Naylor, David A

2008-11-10

A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, Charles L.

1996-01-01

An imaging Fourier transform spectrometer (10, 210) having a Fourier transform infrared spectrometer (12) providing a series of images (40) to a focal plane array camera (38). The focal plane array camera (38) is clocked to a multiple of zero crossing occurrences as caused by a moving mirror (18) of the Fourier transform infrared spectrometer (12) and as detected by a laser detector (50) such that the frame capture rate of the focal plane array camera (38) corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer (12). The images (40) are transmitted to a computer (45) for processing such that representations of the images (40) as viewed in the light of an arbitrary spectral "fingerprint" pattern can be displayed on a monitor (60) or otherwise stored and manipulated by the computer (45).

Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

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

Yükçü, Niyazi

Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Component analyses of urinary nanocrystallites of uric acid stone formers by combination of high-resolution transmission electron microscopy, fast Fourier transformation, energy dispersive X-ray spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy.

PubMed

Sun, Xin-Yuan; Xue, Jun-Fa; Xia, Zhi-Yue; Ouyang, Jian-Ming

2015-06-01

This study aimed to analyse the components of nanocrystallites in urines of patients with uric acid (UA) stones. X-ray diffraction (XRD), Fourier transform infrared spectroscopy, high-resolution transmission electron microscopy (HRTEM), fast Fourier transformation (FFT) of HRTEM, and energy dispersive X-ray spectroscopy (EDS) were performed to analyse the components of these nanocrystallites. XRD and FFT showed that the main component of urinary nanocrystallites was UA, which contains a small amount of calcium oxalate monohydrate and phosphates. EDS showed the characteristic absorption peaks of C, O, Ca and P. The formation of UA stones was closely related to a large number of UA nanocrystallites in urine. A combination of HRTEM, FFT, EDS and XRD analyses could be performed accurately to analyse the components of urinary nanocrystallites.

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

Etude de la Generation des Ultrasons Par Laser dans un Materiau Composite

NASA Astrophysics Data System (ADS)

Dubois, Marc

Laser generation of ultrasound is not a new subject. Many authors have proposed mathematical models of the thermoelastic process of generation of acoustic waves. However, none of those models, up to now, could take simultaneously the effects of the thermal conduction, the optical penetration, the anisotropy of the material and any time and surface profiles of the laser excitation into account. The model presented in this work takes all these parameters into consideration in the case of an infinite orthotropic plate. The mathematical approach used allows to obtain an analytical solution of the mechanical displacement field in the Laplace and two-dimensional (2-D) Fourier spaces. Numerical inverse Laplace and 2-D Fourier transformations bring the mechanical displacement field back into the normal spaces. The use of direct numerical transformations enables to consider almost any time and spatial distributions of the generation laser beam. The acoustic displacements calculated by this model have been compared to experimental displacements measured with a wide band optical detection system. The features of this system allow the quantitative measurement of the parallel and normal displacements to the surface of the sample. Hence, the calculated normal and parallel displacements have been compared to those experimentally measured at various locations on aluminum, glass and polymer samples. In all cases, the agreement between the calculated and experimentally measured displacements was good. The semi-analytical model having proved its validity, it has been used, in addition to a completely analytical one-dimensional model, to study the effects of the optical penetration and the laser pulse duration on the longitudinal acoustic wave generated. This study has established that a short enough laser pulse and a large irradiation with regard to the sample thickness allows to determine quantitatively, from the full width at half maximum of the acoustic pulse, the optical penetration depth at the wavelength of the generation laser inside the material. This semi-analytical model has also permitted to analyze the effects of the optical penetration on the directivity patterns of the longitudinal and shear waves generated by a thermoelastic source. This study has clearly shown that the optical penetration modifies significantly the longitudinal wave directivity pattern, but has only weak effects on the shear wave one. (Abstract shortened by UMI.).

A Two-Color Fourier Transform Mm-Wave Spectrometer for Gas Analysis Operating from 260-295 GHZ

NASA Astrophysics Data System (ADS)

Steber, Amanda L.; Harris, Brent J.; Lehmann, Kevin K.; Pate, Brooks H.

2013-06-01

We have designed a two-color mm-wave spectrometer for Fourier transform mm-wave spectroscopy that uses consumer level components for the tunable synthesizers, digital control of the pulse modulators, and digitization of the coherent free induction decay (FID). The excitation pulses are generated using an x24 active multiplier chain (AMC) that produces a peak power of 30 mW. The microwave input to the AMC is generated in a frequency up conversion circuit that accepts a microwave input frequency from about 2-4 GHz. This circuit also generates the input to the mm-wave subhamonic mixer that creates the local oscillator from a separate 2-4 GHz microwave input. Excitation pulses at two independently tunable frequencies are generated using a dual-channel source based on a low-cost, wideband synthesizer integrated circuit (Valon Technology Model 5008). The outputs of the synthesizer are pulse modulated using a PIN diode switch that is driven using the arbitrary waveform generator (AWG) output of a USB-controlled high-speed digitizer / arbitrary waveform generator combination unit (Tie Pie HS-5 530 XM). The two pulses are combined using a Wilkinson power divider before input to the up conversion circuit. The FID frequency is down converted in a two-stage mixing process to 65 MHz. The two LO frequencies used in the receiver are provided by a second Valon 5008. The FID is digitized at 200 MSamples/s using the 12-bit Tie Pie digitizer. The digital oscilloscope (and its AWG channel) and the two synthesizers use a 10 MHz reference signal from a Rubidium clock to permit time-domain signal averaging. A key feature of the digital oscilloscope is its deep memory of 32 Mpts (complemented by the 64 Mpt memory in the 240 MS/s AWG). This makes it possible to perform several one- and two-color coherent measurements, including pulse echoes and double-resonance spectroscopy, in a single "readout" experiment to speed the analysis of mm-wave rotational spectra. The spectrometer sensitivity and frequency accuracy are illustrated by high-speed measurements of OCS rotational transitions for low-abundance isotopes. Examples of pulse echo measurements to determine the collisional relaxation rate and two-color double-resonance measurements to confirm the presence of a molecular species will be illustrated using OCS as the room-temperature gas sample.

Snapshot Imaging Spectrometry in the Visible and Long Wave Infrared

NASA Astrophysics Data System (ADS)

Maione, Bryan David

Imaging spectrometry is an optical technique in which the spectral content of an object is measured at each location in space. The main advantage of this modality is that it enables characterization beyond what is possible with a conventional camera, since spectral information is generally related to the chemical composition of the object. Due to this, imaging spectrometers are often capable of detecting targets that are either morphologically inconsistent, or even under resolved. A specific class of imaging spectrometer, known as a snapshot system, seeks to measure all spatial and spectral information simultaneously, thereby rectifying artifacts associated with scanning designs, and enabling the measurement of temporally dynamic scenes. Snapshot designs are the focus of this dissertation. Three designs for snapshot imaging spectrometers are developed, each providing novel contributions to the field of imaging spectrometry. In chapter 2, the first spatially heterodyned snapshot imaging spectrometer is modeled and experimentally validated. Spatial heterodyning is a technique commonly implemented in non-imaging Fourier transform spectrometry. For Fourier transform imaging spectrometers, spatial heterodyning improves the spectral resolution trade space. Additionally, in this chapter a unique neural network based spectral calibration is developed and determined to be an improvement beyond Fourier and linear operator based techniques. Leveraging spatial heterodyning as developed in chapter 2, in chapter 3, a high spectral resolution snapshot Fourier transform imaging spectrometer, based on a Savart plate interferometer, is developed and experimentally validated. The sensor presented in this chapter is the highest spectral resolution sensor in its class. High spectral resolution enables the sensor to discriminate narrowly spaced spectral lines. The capabilities of neural networks in imaging spectrometry are further explored in this chapter. Neural networks are used to perform single target detection on raw instrument data, thereby eliminating the need for an explicit spectral calibration step. As an extension of the results in chapter 2, neural networks are once again demonstrated to be an improvement when compared to linear operator based detection. In chapter 4 a non-interferometric design is developed for the long wave infrared (wavelengths spanning 8-12 microns). The imaging spectrometer developed in this chapter is a multi-aperture filtered microbolometer. Since the detector is uncooled, the presented design is ultra-compact and low power. Additionally, cost effective polymer absorption filters are used in lieu of interference filters. Since, each measurement of the system is spectrally multiplexed, an SNR advantage is realized. A theoretical model for the filtered design is developed, and the performance of the sensor for detecting liquid contaminants is investigated. Similar to past chapters, neural networks are used and achieve false detection rates of less than 1%. Lastly, this dissertation is concluded with a discussion on future work and potential impact of these devices.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

PubMed

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Experimental Validation of a Forward Looking Interferometer for Detection of Clear Air Turbulence due to Mountain Waves

NASA Technical Reports Server (NTRS)

Schaffner, Philip R.; Daniels, Taumi S.; West, Leanne L.; Gimmestad, Gary G.; Lane, Sarah E.; Burdette, Edward M.; Smith, William L.; Kireev, Stanislav; Cornman, Larry; Sharman, Robert D.

2012-01-01

The Forward-Looking Interferometer (FLI) is an airborne sensor concept for detection and estimation of potential atmospheric hazards to aircraft. The FLI concept is based on high-resolution Infrared Fourier Transform Spectrometry technologies that have been developed for satellite remote sensing. The FLI is being evaluated for its potential to address multiple hazards, during all phases of flight, including clear air turbulence, volcanic ash, wake vortices, low slant range visibility, dry wind shear, and icing. In addition, the FLI is being evaluated for its potential to detect hazardous runway conditions during landing, such as wet or icy asphalt or concrete. The validation of model-based instrument and hazard simulation results is accomplished by comparing predicted performance against empirical data. In the mountain lee wave data collected in the previous FLI project, the data showed a damped, periodic mountain wave structure. The wave data itself will be of use in forecast and nowcast turbulence products such as the Graphical Turbulence Guidance and Graphical Turbulence Guidance Nowcast products. Determining how turbulence hazard estimates can be derived from FLI measurements will require further investigation.

Excited-State Vibrational Coherence in Perylene Bisimide Probed by Femtosecond Broadband Pump-Probe Spectroscopy.

PubMed

Son, Minjung; Park, Kyu Hyung; Yoon, Min-Chul; Kim, Pyosang; Kim, Dongho

2015-06-18

Broadband laser pulses with ultrashort duration are capable of triggering impulsive excitation of the superposition of vibrational eigenstates, giving rise to quantum beating signals originating from coherent wave packet motions along the potential energy surface. In this work, coherent vibrational wave packet dynamics of an N,N'-bis(2,6-dimethylphenyl)perylene bisimide (DMP-PBI) were investigated by femtosecond broadband pump-probe spectroscopy which features fast and balanced data acquisition with a wide spectral coverage of >200 nm. Clear modulations were observed in the envelope of the stimulated emission decay profiles of DMP-PBI with the oscillation frequencies of 140 and 275 cm(-1). Fast Fourier transform analysis of each oscillatory mode revealed characteristic phase jumps near the maxima of the steady-state fluorescence, indicating that the observed vibrational coherence originates from an excited-state wave packet motion. Quantum calculations of the normal modes at the low-frequency region suggest that low-frequency C-C (C═C) stretching motions accompanied by deformation of the dimethylphenyl substituents are responsible for the manifestation of such coherent wave packet dynamics.

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

Surface Green's function of a piezoelectric half-space.

PubMed

Laude, Vincent; Jerez-Hanckes, Carlos F; Ballandras, Sylvain

2006-02-01

The computation of the two-dimensional harmonic spatial-domain Green's function at the surface of a piezoelectric half-space is discussed. Starting from the known form of the Green's function expressed in the spectral domain, the singular contributions are isolated and treated separately. It is found that the surface acoustic wave contributions (i.e., poles in the spectral Green's function) give rise to an anisotropic generalization of the Hankel function H0(2), the spatial Green's function for the scalar two-dimensional wave equation. The asymptotic behavior at infinity and at the origin (for the electrostatic contribution) also are explicitly treated. The remaining nonsingular part of the spectral Green's function is obtained numerically by a combination of fast Fourier transform and quadrature. Illustrations are given in the case of a substrate of Y-cut lithium niobate.

THz holography in reflection using a high resolution microbolometer array.

PubMed

Zolliker, Peter; Hack, Erwin

2015-05-04

We demonstrate a digital holographic setup for Terahertz imaging of surfaces in reflection. The set-up is based on a high-power continuous wave (CW) THz laser and a high-resolution (640 × 480 pixel) bolometer detector array. Wave propagation to non-parallel planes is used to reconstruct the object surface that is rotated relative to the detector plane. In addition we implement synthetic aperture methods for resolution enhancement and compare Fourier transform phase retrieval to phase stepping methods. A lateral resolution of 200 μm and a relative phase sensitivity of about 0.4 rad corresponding to a depth resolution of 6 μm are estimated from reconstructed images of two specially prepared test targets, respectively. We highlight the use of digital THz holography for surface profilometry as well as its potential for video-rate imaging.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

NASA Astrophysics Data System (ADS)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Laser generated guided waves and finite element modeling for the thickness gauging of thin layers.

PubMed

Lefevre, F; Jenot, F; Ouaftouh, M; Duquennoy, M; Ourak, M

2010-03-01

In this paper, nondestructive testing has been performed on a thin gold layer deposited on a 2 in. silicon wafer. Guided waves were generated and studied using a laser ultrasonic setup and a two-dimensional fast Fourier transform technique was employed to obtain the dispersion curves. A gold layer thickness of 1.33 microm has been determined with a +/-5% margin of error using the shape of the two first propagating modes, assuming for the substrate and the layer an uncertainty on the elastic parameters of +/-2.5%. A finite element model has been implemented to validate the data post-treatment and the experimental results. A good agreement between the numerical simulation, the analytical modeling and the experimentations has been observed. This method was considered suitable for thickness layer higher than 0.7 microm.

The Microwave Spectroscopy Study of 1,2-DIMETHOXYETHANE

NASA Astrophysics Data System (ADS)

Li, Weixing; Vigorito, Annalisa; Calabrese, Camilla; Evangelisti, Luca; Favero, Laura B.; Maris, Assimo; Melandri, Sonia

2017-06-01

With Pulsed-Jet Fourier Transform MicroWave (PJ-FTMW) spectroscopy and Stark modulated Free Jet Millimeter-Wave absorption (FJ-AMMW) spectroscopy, the rotational spectra of two conformers of 1,2-Dimethoxyethane were identified and characterized. Besides the normal species, the spectra of all the mono-substituted ^{13}C isotopologues in natural abundance were also measured. By fitting the rotational transitions split by the methyl internal rotations using both XIAM and ERHAM programs, the spectroscopic parameters were obtained and compared. The rotational constants indicated the conformers to be TGT and TGG', respectively. With the rotational constants of the normal and ^{13}C species, the coordinates of the substituted carbon atoms could be calculated with Kraitchmann's equations. The carbon-frameworks further confirmed the assignment of the two conformations. The V_{3} barriers of the two methyl groups' internal rotations were also experimentally determined.

A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment

NASA Astrophysics Data System (ADS)

Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin

2015-03-01

The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

2.5-D poroelastic wave modelling in double porosity media

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua

2011-09-01

To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.

Detection of cerebral ischemia using the power spectrum of the pulse wave measured by near-infrared spectroscopy.

PubMed

Ebihara, Akira; Tanaka, Yuichi; Konno, Takehiko; Kawasaki, Shingo; Fujiwara, Michiyuki; Watanabe, Eiju

2013-10-01

The diagnosis and medical treatment of cerebral ischemia are becoming more important due to the increase in the prevalence of cerebrovascular disease. However, conventional methods of evaluating cerebral perfusion have several drawbacks: they are invasive, require physical restraint, and the equipment is not portable, which makes repeated measurements at the bedside difficult. An alternative method is developed using near-infrared spectroscopy (NIRS). NIRS signals are measured at 44 positions (22 on each side) on the fronto-temporal areas in 20 patients with cerebral ischemia. In order to extract the pulse-wave component, the raw total hemoglobin data recorded from each position are band-pass filtered (0.8 to 2.0 Hz) and subjected to a fast Fourier transform to obtain the power spectrum of the pulse wave. The ischemic region is determined by single-photon emission computed tomography. The pulse-wave power in the ischemic region is compared with that in the symmetrical region on the contralateral side. In 17 cases (85%), the pulse-wave power on the ischemic side is significantly lower than that on the contralateral side, which indicates that the transmission of the pulse wave is attenuated in the region with reduced blood flow. Pulse-wave power might be useful as a noninvasive marker of cerebral ischemia.

Identifying Wave-Particle Interactions in the Solar Wind using Statistical Correlations

NASA Astrophysics Data System (ADS)

Broiles, T. W.; Jian, L. K.; Gary, S. P.; Lepri, S. T.; Stevens, M. L.

2017-12-01

Heavy ions are a trace component of the solar wind, which can resonate with plasma waves, causing heating and acceleration relative to the bulk plasma. While wave-particle interactions are generally accepted as the cause of heavy ion heating and acceleration, observations to constrain the physics are lacking. In this work, we statistically link specific wave modes to heavy ion heating and acceleration. We have computed the Fast Fourier Transform (FFT) of transverse and compressional magnetic waves between 0 and 5.5 Hz using 9 days of ACE and Wind Magnetometer data. The FFTs are averaged over plasma measurement cycles to compute statistical correlations between magnetic wave power at each discrete frequency, and ion kinetic properties measured by ACE/SWICS and Wind/SWE. The results show that lower frequency transverse oscillations (< 0.2 Hz) and higher frequency compressional oscillations (> 0.4 Hz) are positively correlated with enhancements in the heavy ion thermal and drift speeds. Moreover, the correlation results for the He2+ and O6+ were similar on most days. The correlations were often weak, but most days had some frequencies that correlated with statistical significance. This work suggests that the solar wind heavy ions are possibly being heated and accelerated by both transverse and compressional waves at different frequencies.

Bound states and propagating modes in quantum wires with sharp bends and/or constrictions

NASA Astrophysics Data System (ADS)

Razavy, M.

1997-06-01

A number of interesting problems of quantum wires with different geometries can be studied with the help of conformal mapping. These include crossed wires, twisting wires, conductors with constrictions, and wires with a bend. Here the Helmholz equation with Dirichlet boundary condition on the surface of the wire is transformed to a Schröautdinger-like equation with an energy-dependent nonseparable potential but with boundary conditions given on two straight lines. By expanding the wave function in terms of the Fourier series of one of the variables one obtains an infinite set of coupled ordinary differential equations. Only the propagating modes plus a few of the localized modes contribute significantly to the total wave function. Once the problem is solved, one can express the results in terms of the original variables using the inverse conformal mapping. As an example, the total wave function, the components of the current density, and the bound-state energy for a Γ-shaped quantum wire is calculated in detail.

On the accuracy and precision of numerical waveforms: effect of waveform extraction methodology

NASA Astrophysics Data System (ADS)

Chu, Tony; Fong, Heather; Kumar, Prayush; Pfeiffer, Harald P.; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela

2016-08-01

We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and cover mass ratios 1-3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities e\\lt {10}-4. A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio q = 10. Gravitational waveforms at asymptotic infinity are computed with two independent techniques: extrapolation and Cauchy characteristic extraction. An error analysis based on noise-weighted inner products is performed. We find that numerical truncation error, error due to gravitational wave extraction, and errors due to the Fourier transformation of signals with finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors dominating at noise-weighted mismatches of ˜ 3× {10}-4. This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: experimental characterization.

PubMed

Pisano, Giampaolo; Savini, Giorgio; Ade, Peter A R; Haynes, Vic; Gear, Walter K

2006-09-20

An achromatic half-wave plate (HWP) to be used in millimeter cosmic microwave background (CMB) polarization experiments has been designed, manufactured, and tested. The design is based on the 5-plates Pancharatnam recipe and it works in the frequency range 85-185 GHz. A model has been used to predict the transmission, reflection, absorption, and phase shift as a function of frequency. The HWP has been tested by using coherent radiation from a back-wave oscillator to investigate its modulation efficiency and with incoherent radiation from a polarizing Fourier transform spectrometer (FTS) to explore its frequency behavior. The FTS measurements have been fitted with an optical performance model which is in excellent agreement with the data. A detailed analysis of the data also allows a precise determination of the HWP fast and slow axes in the frequency band of operation. A list of the HWP performance characteristics is reported including estimates of its cross polarization.

Discrete Fourier Transform Analysis in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Instrument Line Shape Modeling and Correction for Off-Axis Detectors in Fourier Transform Spectrometry

NASA Technical Reports Server (NTRS)

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Fourier Transform Mass Spectrometry.

ERIC Educational Resources Information Center

Gross, Michael L.; Rempel, Don L.

1984-01-01

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.

ERIC Educational Resources Information Center

Perkins, W. D.

1987-01-01

This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

22 July 2009 total solar eclipse induced gravity waves in ionosphere as inferred from GPS observations over EIA

NASA Astrophysics Data System (ADS)

Kumar, K. Vijay; Maurya, Ajeet K.; Kumar, Sanjay; Singh, Rajesh

2016-11-01

In the present contribution we investigate the variation in the Global Positioning System (GPS) derived ionospheric Total Electron Content (TEC) over Equatorial Ionization Anomaly (EIA) region on the rare occasional astronomical phenomenon of total solar eclipse of 22 July 2009. The aim is to study and identify the wave like structure enumerated due to solar eclipse induced gravity waves in the F-region ionosphere altitude. The work is aimed to understand features of horizontal and vertical variation of atmospheric gravity waves (AGWs) properties over the Equatorial Ionization Anomaly (EIA) region in Indian low latitude region. The ionospheric observations is from the site of Allahabad (lat 25.4° N; lon. 81.9° E; dip 38.6° N) located at the fringe of eclipse totality path. The estimated vertical electron density profile from FORMOSAT-3/COSMIC GPS-RO satellite, considering all the satellite line of sight around the time of eclipse totality shows maximum depletion of 43%. The fast fourier transform and wavelet transform of GPS DTEC data from Allahabad station (Allahabad: lat 25.4 N; lon. 81.9 E) shows the presence of periodic waves of ∼20 to 45 min and ∼70 to 90 min period at F-region altitude. The shorter period correspond to the sunrise time morning terminator and longer period can be associated with solar eclipse generated AGWs. The most important result obtained is that our results along with previous result for wave like signatures in D-region ionosphere from Allahabad station show that AGWs generated by sunrise time terminator have similarity in the D and F region of the ionosphere but solar eclipse induced AGWs show higher period in the F-region compared to D-region ionosphere.

Heliospheric Modulation of Galactic Cosmic Rays; Diurnal Variability Abstract Details

NASA Astrophysics Data System (ADS)

Kalu, D. F.; Okpala, K. C.

2017-12-01

We have studied the variability of Cosmic rays flux during solar quiet days at mid and high latitudes in the Northern Hemisphere. By using the five (5) quietest days for each month and the five disturbed days for each month, the monthly mean diurnal variation of cosmic ray anisotropy have been derived for the period 1999-2015, which covers part of cycles 23, and cycle 24. This study seeks to understand the heliospheric contribution to the variation of these Cosmic rays on quietest days, three stations (Inuvik, Moscow, Rome) Neutron Monitors were employed. This study seeks to understand the important features of the high latitude and mid latitude diurnal wave, and how solar and geomagnetic activity may be influencing the wave characteristics. Cosmic ray wave characteristics were obtained by discrete Fourier transform (DFT). The mean, diurnal amplitude, phase and dispersion for each month's diurnal wave were calculated and profiled. There was clear indication that the terrestrial effect on the variability of the monthly mean was more associated with geomagnetic activity rather than rigidity of the cosmic rays. Correlation of the time series of these wave characteristic with solar and geomagnetic activity index showed better association with solar activity.

Observation of the dispersion of wedge waves propagating along cylinder wedge with different truncations by laser ultrasound technique

NASA Astrophysics Data System (ADS)

Jia, Jing; Zhang, Yu; Han, Qingbang; Jing, Xueping

2017-10-01

The research focuses on study the influence of truncations on the dispersion of wedge waves propagating along cylinder wedge with different truncations by using the laser ultrasound technique. The wedge waveguide models with different truncations were built by using finite element method (FEM). The dispersion curves were obtained by using 2D Fourier transformation method. Multiple mode wedge waves were observed, which was well agreed with the results estimated from Lagasse's empirical formula. We established cylinder wedge with radius of 3mm, 20° and 60°angle, with 0μm, 5μm, 10μm, 20μm, 30μm, 40μm, and 50μm truncations, respectively. It was found that non-ideal wedge tip caused abnormal dispersion of the mode of cylinder wedge, the modes of 20° cylinder wedge presents the characteristics of guide waves which propagating along hollow cylinder as the truncation increasing. Meanwhile, the modes of 60° cylinder wedge with truncations appears the characteristics of guide waves propagating along hollow cylinder, and its mode are observed clearly. The study can be used to evaluate and detect wedge structure.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Generalized fiber Fourier optics.

PubMed

Cincotti, Gabriella

2011-06-15

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.

Use of the Wigner-Ville distribution in interpreting and identifying ULF waves in triaxial magnetic records

NASA Astrophysics Data System (ADS)

Chi, P. J.; Russell, C. T.

2008-01-01

Magnetospheric ultra-low-frequency (ULF) waves (f = 1 mHz to 1 Hz) exhibit highly time-dependent characteristics due to the dynamic properties of these waves and, for observations in space, the spacecraft motion. These time-dependent features may not be properly resolved by conventional Fourier techniques. In this study we examine how the Wigner-Ville distribution (WVD) can be used to analyze ULF waves. We find that this approach has unique advantages over the conventional Fourier spectrograms and wavelet scalograms. In particular, for Pc1 wave packets, field line/cavity mode resonances in the Pc 3-4 band, and Pi2 pulsations, the start and end times of each wave packet can be well identified and the frequency better defined. In addition, we demonstrate that the Wigner-Ville distribution can be used to calculate the polarization of wave signals in triaxial magnetic field data in a way analogous to Fourier analysis. Motivated by the large amount of ULF wave observations, we have also developed a WVD-based algorithm to identify ULF waves as a way to facilitate the rapid processing of the data collected by satellite missions and the vast network of ground magnetometers.

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

EPA Science Inventory

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

Classification and modeling of human activities using empirical mode decomposition with S-band and millimeter-wave micro-Doppler radars

NASA Astrophysics Data System (ADS)

Fairchild, Dustin P.; Narayanan, Ram M.

2012-06-01

The ability to identify human movements can be an important tool in many different applications such as surveillance, military combat situations, search and rescue operations, and patient monitoring in hospitals. This information can provide soldiers, security personnel, and search and rescue workers with critical knowledge that can be used to potentially save lives and/or avoid a dangerous situation. Most research involving human activity recognition is focused on using the Short-Time Fourier Transform (STFT) as a method of analyzing the micro-Doppler signatures. Because of the time-frequency resolution limitations of the STFT and because Fourier transform-based methods are not well-suited for use with non-stationary and nonlinear signals, we have chosen a different approach. Empirical Mode Decomposition (EMD) has been shown to be a valuable time-frequency method for processing non-stationary and nonlinear data such as micro-Doppler signatures and EMD readily provides a feature vector that can be utilized for classification. For classification, the method of a Support Vector Machine (SVMs) was chosen. SVMs have been widely used as a method of pattern recognition due to their ability to generalize well and also because of their moderately simple implementation. In this paper, we discuss the ability of these methods to accurately identify human movements based on their micro-Doppler signatures obtained from S-band and millimeter-wave radar systems. Comparisons will also be made based on experimental results from each of these radar systems. Furthermore, we will present simulations of micro-Doppler movements for stationary subjects that will enable us to compare our experimental Doppler data to what we would expect from an "ideal" movement.

[Research on spatially modulated Fourier transform imaging spectrometer data processing method].

PubMed

Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan

2010-03-01

Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies

NASA Astrophysics Data System (ADS)

Leśniewska, Danuta

2017-06-01

Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Numerous applications of fiber optic evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy for subsurface structural analysis

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.; Welser, Leslie; Bruch, Reinhard F.; Kano, Angelique; Makhine, Volodymyr

1999-10-01

A new infrared (IR) interferometric method has been developed in conjunction with low-loss, flexible optical fibers, sensors, and probes. This combination of fiber optical sensors and Fourier Transform (FT) spectrometers can be applied to many fields, including (1) noninvasive medical diagnostics of cancer and other different diseases in vivo, (2) minimally invasive bulk diagnostics of tissue, (3) remote monitoring of tissue, chemical processes, and environment, (4) surface analysis of polymers and other materials, (5) characterization of the quality of food, pharmacological products, cosmetics, paper, and other wood-related products, as well as (6) agricultural, forensic, geological, mining, and archeological field measurements. In particular, our nondestructive, fast, compact, portable, remote and highly sensitive diagnostics tools are very promising for subsurface analysis at the molecular level without sample preparation. For example, this technique is ideal for different types of soft porous foams, rough polymers, and rock surfaces. Such surfaces, as well as living tissue, are very difficult to investigate by traditional FTIR methods. We present here FEW-FTIR spectra of polymers, banana and grapefruit peels, and living tissues detected directly at surfaces. In addition, results on the vibrational spectral analysis of normal and pathological skin tissue in the region of 850 - 4000 cm-1 are discussed.

Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

PubMed

Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu

2017-06-21

For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

Simplified signal processing for impedance spectroscopy with spectrally sparse sequences

NASA Astrophysics Data System (ADS)

Annus, P.; Land, R.; Reidla, M.; Ojarand, J.; Mughal, Y.; Min, M.

2013-04-01

Classical method for measurement of the electrical bio-impedance involves excitation with sinusoidal waveform. Sinusoidal excitation at fixed frequency points enables wide variety of signal processing options, most general of them being Fourier transform. Multiplication with two quadrature waveforms at desired frequency could be easily accomplished both in analogue and in digital domains, even simplest quadrature square waves can be considered, which reduces signal processing task in analogue domain to synchronous switching followed by low pass filter, and in digital domain requires only additions. So called spectrally sparse excitation sequences (SSS), which have been recently introduced into bio-impedance measurement domain, are very reasonable choice when simultaneous multifrequency excitation is required. They have many good properties, such as ease of generation and good crest factor compared to similar multisinusoids. Typically, the usage of discrete or fast Fourier transform in signal processing step is considered so far. Usage of simplified methods nevertheless would reduce computational burden, and enable simpler, less costly and less energy hungry signal processing platforms. Accuracy of the measurement with SSS excitation when using different waveforms for quadrature demodulation will be compared in order to evaluate the feasibility of the simplified signal processing. Sigma delta modulated sinusoid (binary signal) is considered to be a good alternative for a synchronous demodulation.

Wave propagation model of heat conduction and group speed

NASA Astrophysics Data System (ADS)

Zhang, Long; Zhang, Xiaomin; Peng, Song

2018-03-01

In view of the finite relaxation model of non-Fourier's law, the Cattaneo and Vernotte (CV) model and Fourier's law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier's law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.

Multi-scale structures of turbulent magnetic reconnection

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

Nakamura, T. K. M., E-mail: takuma.nakamura@oeaw.ac.at; Nakamura, R.; Narita, Y.

2016-05-15

We have analyzed data from a series of 3D fully kinetic simulations of turbulent magnetic reconnection with a guide field. A new concept of the guide filed reconnection process has recently been proposed, in which the secondary tearing instability and the resulting formation of oblique, small scale flux ropes largely disturb the structure of the primary reconnection layer and lead to 3D turbulent features [W. Daughton et al., Nat. Phys. 7, 539 (2011)]. In this paper, we further investigate the multi-scale physics in this turbulent, guide field reconnection process by introducing a wave number band-pass filter (k-BPF) technique in whichmore » modes for the small scale (less than ion scale) fluctuations and the background large scale (more than ion scale) variations are separately reconstructed from the wave number domain to the spatial domain in the inverse Fourier transform process. Combining with the Fourier based analyses in the wave number domain, we successfully identify spatial and temporal development of the multi-scale structures in the turbulent reconnection process. When considering a strong guide field, the small scale tearing mode and the resulting flux ropes develop over a specific range of oblique angles mainly along the edge of the primary ion scale flux ropes and reconnection separatrix. The rapid merging of these small scale modes leads to a smooth energy spectrum connecting ion and electron scales. When the guide field is sufficiently weak, the background current sheet is strongly kinked and oblique angles for the small scale modes are widely scattered at the kinked regions. Similar approaches handling both the wave number and spatial domains will be applicable to the data from multipoint, high-resolution spacecraft observations such as the NASA magnetospheric multiscale (MMS) mission.« less

Multi-scale structures of turbulent magnetic reconnection

NASA Astrophysics Data System (ADS)

Nakamura, T. K. M.; Nakamura, R.; Narita, Y.; Baumjohann, W.; Daughton, W.

2016-05-01

We have analyzed data from a series of 3D fully kinetic simulations of turbulent magnetic reconnection with a guide field. A new concept of the guide filed reconnection process has recently been proposed, in which the secondary tearing instability and the resulting formation of oblique, small scale flux ropes largely disturb the structure of the primary reconnection layer and lead to 3D turbulent features [W. Daughton et al., Nat. Phys. 7, 539 (2011)]. In this paper, we further investigate the multi-scale physics in this turbulent, guide field reconnection process by introducing a wave number band-pass filter (k-BPF) technique in which modes for the small scale (less than ion scale) fluctuations and the background large scale (more than ion scale) variations are separately reconstructed from the wave number domain to the spatial domain in the inverse Fourier transform process. Combining with the Fourier based analyses in the wave number domain, we successfully identify spatial and temporal development of the multi-scale structures in the turbulent reconnection process. When considering a strong guide field, the small scale tearing mode and the resulting flux ropes develop over a specific range of oblique angles mainly along the edge of the primary ion scale flux ropes and reconnection separatrix. The rapid merging of these small scale modes leads to a smooth energy spectrum connecting ion and electron scales. When the guide field is sufficiently weak, the background current sheet is strongly kinked and oblique angles for the small scale modes are widely scattered at the kinked regions. Similar approaches handling both the wave number and spatial domains will be applicable to the data from multipoint, high-resolution spacecraft observations such as the NASA magnetospheric multiscale (MMS) mission.

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.

Fourier transform spectroscopy of cotton and cotton trash

USDA-ARS?s Scientific Manuscript database

Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...

The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.

ERIC Educational Resources Information Center

King, Roy W.; Williams, Kathryn R.

1989-01-01

Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

EPA Science Inventory

Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

A method to perform a fast fourier transform with primitive image transformations.

PubMed

Sheridan, Phil

2007-05-01

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

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

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fouriermore » transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.« less

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

Development of a High-Throughput Microwave Imaging System for Concealed Weapons Detection

DTIC Science & Technology

2016-07-15

hardware. Index Terms—Microwave imaging, multistatic radar, Fast Fourier Transform (FFT). I. INTRODUCTION Near-field microwave imaging is a non-ionizing...configuration, but its computational demands are extreme. Fast Fourier Transform (FFT) imaging has long been used to efficiently construct images sampled with...Simulated image of 25 point scatterers imaged at range 1.5m, with array layout depicted in Fig. 3. Left: image formed with Equation (5) ( Fourier