Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers.
Zhao, Xinyu; Gang, Tie
2009-01-01
A nonparaxial multi-Gaussian beam model is proposed in order to overcome the limitation that paraxial Gaussian beam models lose accuracy in simulating the beam steering behavior of phased array transducers. Using this nonparaxial multi-Gaussian beam model, the focusing and steering sound fields generated by an ultrasonic linear phased array transducer are calculated and compared with the corresponding results obtained by paraxial multi-Gaussian beam model and more exact Rayleigh-Sommerfeld integral model. In addition, with help of this novel nonparaxial method, an ultrasonic measurement model is provided to investigate the sensitivity of linear phased array transducers versus steering angles. Also the comparisons of model predictions with experimental results are presented to certify the accuracy of this provided measurement model.
NASA Astrophysics Data System (ADS)
Wu, Guohua; Dai, Wen; Tang, Hua; Guo, Hong
2015-02-01
Beam wander of random electromagnetic Gaussian-Shell model (EGSM) vortex beams propagating through atmospheric turbulence is investigated. We develop the expression for beam wander of random EGSM vortex beams in theory. The effects of topological charge, turbulence strength, initial spatially coherent length, transverse scale, and wavelength on beam wander are illustrated numerically. The numerical results show that vortex beams with both positive and negative topological charges have the same beam wander, decreasing the coherent length and decreasing the transverse scale, or increasing the topological charge, can decrease the beam wander. In free-space optical (FSO) communication, we can choose beams with smaller coherent length, smaller wavelength, and larger topological charge to reduce beam wander.
Lee, E.P.
1982-11-03
The growth rate of the hose instability is derived for a beam with Gaussian radial profile, using the spread mass model of phase mix damping. It is found that the maximum growth rate of a convecting wave packet is 49% larger than that derived for a beam with the Bennett profile, and the inverse group velocity (dz/d tau) is also increased by about this amount. A general discussion of spread mass models is presented along with an explanation of the regurgitation phenomena seen in their numerical treatment.
Zhou, Yuan; Yuan, Yangsheng; Qu, Jun; Huang, Wei
2016-05-16
Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M^{2}-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choosing appropriate beam or turbulence parameter values. It is also found that the LGCSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation. Our results will have some theoretical reference value for optical communications.
Simulation of ultrasonic surface waves with multi-Gaussian and point source beam models
Zhao, Xinyu; Schmerr, Lester W. Jr.; Li, Xiongbing; Sedov, Alexander
2014-02-18
In the past decade, multi-Gaussian beam models have been developed to solve many complicated bulk wave propagation problems. However, to date those models have not been extended to simulate the generation of Rayleigh waves. Here we will combine Gaussian beams with an explicit high frequency expression for the Rayleigh wave Green function to produce a three-dimensional multi-Gaussian beam model for the fields radiated from an angle beam transducer mounted on a solid wedge. Simulation results obtained with this model are compared to those of a point source model. It is shown that the multi-Gaussian surface wave beam model agrees well with the point source model while being computationally much more efficient.
Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Li, Ye; Hu, Zhengda
2016-07-01
For Gaussian-Schell model beams propagating in the isotropic turbulent ocean, theoretical expression of beam wander is derived based on the extended Huygens-Fresnel principle. The spatial coherence radius of spherical waves propagating in the paraxial channel of turbulent ocean including inner scale is also developed. Our results show that the beam wander decreases with the increasing rate of dissipation of kinetic energy per unit mass of fluid ɛ, but it increases as the increasing of the dissipation rate of temperature variance χt and the relative strength of temperature and salinity fluctuations ϖ. The salinity fluctuation has greater influence on the beam wander than that of temperature fluctuations. The model can be evaluated submarine-to-submarine/ship optical wireless communication performance.
Evaluation of the gaussian beam model for prediction of LDV fringe fields
Miles, P.C.; Witze, P.O.
1996-12-31
A simple model is developed to estimate the fringe field geometry at the intersection of two Gaussian laser beams. Comparison of the model results to experimentally measured fringe spacing demonstrates that while the model predicts the fringe geometry well when the beam waists are far from the intersection volume, it performs poorly under nominally ideal conditions- when the beam waists are located at the intersection. Data obtained with two different laser sources indicate that the discrepancies between the theory and experiment are likely due to deviations of the laser beam from an ideal Gaussian beam. With a high quality laser, the details of the fringe field geometry are still not well duplicated by the Gaussian beam model, although the magnitude of the variation in fringe spacing and the effect of the controlling system parameters are correctly predicted.
Born modeling for heterogeneous media using the Gaussian beam summation based Green's function
NASA Astrophysics Data System (ADS)
Huang, Xingguo; Sun, Hui; Sun, Jianguo
2016-08-01
Born approximation is a commonly used approximation in the simulation of seismic wave propagation. Calculation of the Green's function in Born approximation integral is essential for Born modeling. We derive a new Born formula based on the Gaussian beam representations of Green's functions. This procedure can be used to mitigate the problems like the caustic, shadow region, and multivalued traveltime caused by multipathing that traditional geometric ray theory cannot deal with. However, due to the characteristic of complex traveltime in the Gaussian beam, we present a new isochronous stack method for Gaussian beam based Born modeling. Additionally, two basic issues, background velocity and integral region selection, are discussed. Numerical results demonstrate the accuracy and efficiency of the Gaussian beam based Born theory and implementation.
Discrete Frame-Based Gaussian Beam Methods for Seismic Modeling and Imaging
NASA Astrophysics Data System (ADS)
Li, C.; Nowack, R. L.
2004-12-01
In this presentation we describe the use of discrete frame-based Gaussian beam summation methods with application to modeling and imaging. In this approach a windowed expansion is used where the individual functions are matched to paraxial Gaussian beams which are then propagated into the medium. The Gaussian windowed expansion is performed on an over-sampled position-wavenumber lattice where over-sampling is required for stability. The only window-based transform allowing critical sampling is a Wilson basis or local cosine transform which requires Gaussian beams to be launched in pairs losing some of localization properties of the method. For over-sampled Gaussian windowed expansions, dual functions must be computed to reconstruct the field, but for sufficiently high over-sampling the dual function becomes closer to a Gaussian function. An early application of windowed expansions using Gaussian beams was given by Hill (1990) for seismic migration. He also derived early sampling criteria for the expansion. Here we will give applications of the method to forward modeling including waves in a layer over half-space for a range of beam parameters. We also provide several applications of seismic imaging using surface sources and teleseismic waves incident from below.
Structure of the transverse profile of Gaussian-model non-paraxial electromagnetic beams
NASA Astrophysics Data System (ADS)
Martínez-Herrero, R.; Mejías, P. M.; Bosch, S.; Carnicer, A.
2006-06-01
Starting from the (inexact) Gaussian beam model, and on the basis of a plane-wave spectrum representation of non-paraxial electromagnetic fields, three free-propagating exact solutions of the Maxwell equations are investigated. The transverse part of one of these solutions is shown to closely resemble both the beam profile irradiance and the polarization distribution of a typical Gaussian beam. A limit has also been established for the validity of the paraxial regime, particularly for focused beams whose size at the waist approaches the light wavelength.
GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
On stochastic complex beam beam interaction models with Gaussian colored noise
NASA Astrophysics Data System (ADS)
Xu, Yong; Zhang, Huiqing; Xu, Wei
2007-10-01
This paper is to continue our study on complex beam-beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam-beam interaction model with random forcing [Physica A 336 (2004) 347-360]. The random noise is taken as the form of exponentially correlated Gaussian colored noise, and the transition probability density function is obtained in terms of a perturbation expansion of the parameter. Then the method of stochastic averaging based on perturbation technique is used to derive a Fokker-Planck equation for the transition probability density function. The solvability condition and the general transforms using the method of characteristics are proposed to obtain the approximate expressions of probability density function to order ε. Also the exact stationary probability density and the first and second moments of the amplitude are obtained, and one can find when the correlation time equals to zero, the result is identical to that derived from the Stratonovich-Khasminskii theorem for the same model under a broad-band excitation in our previous work.
Fast Pencil Beam Dose Calculation for Proton Therapy Using a Double-Gaussian Beam Model
da Silva, Joakim; Ansorge, Richard; Jena, Rajesh
2015-01-01
The highly conformal dose distributions produced by scanned proton pencil beams (PBs) are more sensitive to motion and anatomical changes than those produced by conventional radiotherapy. The ability to calculate the dose in real-time as it is being delivered would enable, for example, online dose monitoring, and is therefore highly desirable. We have previously described an implementation of a PB algorithm running on graphics processing units (GPUs) intended specifically for online dose calculation. Here, we present an extension to the dose calculation engine employing a double-Gaussian beam model to better account for the low-dose halo. To the best of our knowledge, it is the first such PB algorithm for proton therapy running on a GPU. We employ two different parameterizations for the halo dose, one describing the distribution of secondary particles from nuclear interactions found in the literature and one relying on directly fitting the model to Monte Carlo simulations of PBs in water. Despite the large width of the halo contribution, we show how in either case the second Gaussian can be included while prolonging the calculation of the investigated plans by no more than 16%, or the calculation of the most time-consuming energy layers by about 25%. Furthermore, the calculation time is relatively unaffected by the parameterization used, which suggests that these results should hold also for different systems. Finally, since the implementation is based on an algorithm employed by a commercial treatment planning system, it is expected that with adequate tuning, it should be able to reproduce the halo dose from a general beam line with sufficient accuracy. PMID:26734567
Fast Pencil Beam Dose Calculation for Proton Therapy Using a Double-Gaussian Beam Model.
da Silva, Joakim; Ansorge, Richard; Jena, Rajesh
2015-01-01
The highly conformal dose distributions produced by scanned proton pencil beams (PBs) are more sensitive to motion and anatomical changes than those produced by conventional radiotherapy. The ability to calculate the dose in real-time as it is being delivered would enable, for example, online dose monitoring, and is therefore highly desirable. We have previously described an implementation of a PB algorithm running on graphics processing units (GPUs) intended specifically for online dose calculation. Here, we present an extension to the dose calculation engine employing a double-Gaussian beam model to better account for the low-dose halo. To the best of our knowledge, it is the first such PB algorithm for proton therapy running on a GPU. We employ two different parameterizations for the halo dose, one describing the distribution of secondary particles from nuclear interactions found in the literature and one relying on directly fitting the model to Monte Carlo simulations of PBs in water. Despite the large width of the halo contribution, we show how in either case the second Gaussian can be included while prolonging the calculation of the investigated plans by no more than 16%, or the calculation of the most time-consuming energy layers by about 25%. Furthermore, the calculation time is relatively unaffected by the parameterization used, which suggests that these results should hold also for different systems. Finally, since the implementation is based on an algorithm employed by a commercial treatment planning system, it is expected that with adequate tuning, it should be able to reproduce the halo dose from a general beam line with sufficient accuracy.
Propagation properties of Gaussian Schell-model array beams in non-Kolmogorov turbulence
NASA Astrophysics Data System (ADS)
Song, Zhenzhen; Liu, Zhengjun; Zhou, Keya; Sun, Qiongge; Liu, Shutian
2016-10-01
A stochastic beam generated by a recently introduced Gaussian Schell-model array (GSMA) source (2015 Opt. Lett. 40 5662) is investigated. We derive the analytical propagation formulae for the spectral density and the propagation factor in non-Kolmogorov turbulence by utilizing the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function. Numerical results show that the lattice patterns of GSMA beams, which keep propagation-invariant in free space, are destroyed by the turbulence at sufficiently large distances. The GSMA beams have significant advantage over the Gaussian Schell-model beam in the robustness of the destructive effect of non-Kolmogorov turbulence, especially for the GSMA beam with more lattice elements and bigger relative separation distance of each lattice element. The effects of beam parameters and non-Kolmogorov turbulence on the propagation factor are analyzed in detail.
NASA Astrophysics Data System (ADS)
Chen, Xudong; Zhao, Daomu
2016-08-01
A model of electromagnetic rectangular multi-Gaussian Schell-model (ERMGSM) beams is introduced. Its analytic expression for the elements of the cross-spectral density matrix of such beams passing through oceanic turbulence is derived. It is shown that the rectangular shape of the ERMGSM beams holds a small distance on propagation in oceanic turbulence. The spectral density, the degree of coherence and the degree of polarization of ERMGSM beams are also studied in detail. The results will be helpful for underwater communication by using ERMGSM beams.
Chen, Chunyi; Yang, Huamin
2013-06-01
The temporal spectrum of beam wander is formulated by considering a Gaussian Schell-model beam passing through atmospheric turbulence with a finite outer scale. Two simpler asymptotic formulas for the temporal spectrum of beam wander within the high- and low-frequency ranges are derived, respectively. Based on the formulations, the effects of the initial partial coherence of the beam, finite outer scale of turbulence, initial beam radius, and initial phase front radius of curvature on the temporal spectrum of beam wander are analyzed by numerical examples.
Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence.
Xu, Hua-Feng; Zhang, Zhou; Qu, Jun; Huang, Wei
2014-09-22
Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.
Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence.
Mei, Zhangrong; Korotkova, Olga
2013-11-01
A recently introduced class of scalar cosine-Gaussian Schell-Model [CGSM] beams is generalized to electromagnetic theory. The realizability conditions and the beam conditions on the source parameters are derived. Analytical formulas for the cross-spectral density matrix elements of the electromagnetic cosine-Gaussian Schell-model [EM CGSM] beams propagating in isotropic random medium are derived. It is found that the EM CGSM beams possess single-ring or double-ring intensity profiles, depending of source parameters. As two examples, the statistical characteristics of the EM CGSM beams propagating in free space and non-Kolmogorov turbulent atmosphere are studied numerically. The effects of the fractal constant of the atmospheric spectrum and the refractive-index structure constant on such characteristics are analyzed in detail.
NASA Astrophysics Data System (ADS)
Li, Ya-Qing; Wu, Zhen-Sen
2012-05-01
On the basis of the extended Huygens—Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector, the characteristics of the partially coherent Gaussian Schell-model (GSM) beams propagating in slanted atmospheric turbulence are studied. Using the cross- spectral density function (CSDF), we derive the expressions for the effective beam radius, the spreading angle, and the average intensity. The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically. The influences of the coherence degree, the propagation distance, the propagation height, and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.
NASA Astrophysics Data System (ADS)
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence.
Wang, Xiaoyang; Yao, Mingwu; Qiu, Zhiliang; Yi, Xiang; Liu, Zengji
2015-05-18
The analytical expressions for the spectral degree of coherence, the effective radius of curvature and the propagation factor of the Bessel-Gaussian Schell-model (BGSM) beam in turbulent atmosphere are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The evolution properties of BGSM beams propagating in non-Kolmogorov turbulence are investigated by a set of numerical examples. It is demonstrated that the spectral degree of coherence of the BGSM beam evolves into Gaussian profile twice with the increasing of the propagation distance. The turbulence-induced degradation can be remarkably reduced by using the BGSM beam with the proper source parameters. The effects that the generalized refractive-index structure constant, outer and inner scales, and the spectral index of spatial power spectrum of atmospheric turbulence have on the evolution properties of BGSM beams are also discussed in detail.
Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime environment
NASA Astrophysics Data System (ADS)
Nelson, C.; Avramov-Zamurovic, S.; Korotkova, O.; Guth, S.; Malek-Madani, R.
2016-04-01
Irradiance fluctuations of a pseudo Multi-Gaussian Schell Model beam propagating in the maritime environment is explored as a function of spatial light modulator cycling rate and estimated atmospheric turnover rate. Analysis of the data demonstrates a strong negative correlation between the scintillation index of received optical intensity and cycling speed for the estimated atmospheric turnover rate.
Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Zhu, Yun; Hu, Zhengda
2016-09-01
The effect of anisotropic turbulence on the spreading and wandering of Gaussian-Schell model (GSM) laser beams propagating in an ocean is studied. The long-term spreading of a GSM beam propagating through the paraxial channel of a turbulent ocean is also developed. Expressions of random wander for such laser beams are derived in an anisotropic turbulent ocean based on the extended Huygens-Fresnel principle. We investigate the influence of parameters in a turbulent ocean on the beam wander and spreading. Our results indicate that beam spreading and random beam wandering are smaller without considering the anisotropy of turbulence in the oceanic channel. Salinity fluctuation has a greater contribution to both the beam spreading and beam wander than that of temperature fluctuations in a turbulent ocean. Our results could be helpful for designing a free-space optical wireless communication system in an oceanic environment.
Gaussian-Beam Laser-Resonator Program
NASA Technical Reports Server (NTRS)
Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman
1989-01-01
Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).
Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere.
Chen, Rong; Liu, Lin; Zhu, Shijun; Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-01-27
Laguerre-Gaussian Schell-model (LGSM) beam was proposed in theory [Opt. Lett.38, 91 (2013 Opt. Lett.38, 1814 (2013)] just recently. In this paper, we study the propagation of a LGSM beam in turbulent atmosphere. Analytical expressions for the cross-spectral density and the second-order moments of the Wigner distribution function of a LGSM beam in turbulent atmosphere are derived. The statistical properties, such as the degree of coherence and the propagation factor, of a LGSM beam in turbulent atmosphere are studied in detail. It is found that a LGSM beam with larger mode order n is less affected by turbulence than a LGSM beam with smaller mode order n or a GSM beam under certain condition, which will be useful in free-space optical communications.
NASA Astrophysics Data System (ADS)
Li, Jinhong; Lü, Baida
2009-04-01
Taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the analytical expressions for the cross-spectral density, average intensity and root mean square (rms) width of a GSM vortex beam with topological charge m = ± 1 propagating through atmospheric turbulence are derived, which enable us to study the propagation properties of GSM vortex beams through atmospheric turbulence and evolution behavior of their coherent vortices. The propagation of GSM vortex beams undergoes several stages of evolution of the intensity profile in both free space and turbulence, and is different from that of GSM non-vortex beams. An increase of the refraction index structure constant Cn2 and a decrease of the spatial correlation length σ0 speed up the evolution process. The beam-width spreading of GSM vortex beams is less than that of GSM non-vortex beams. The smaller the correlation length σ0 is, the less the beam-width spreading of GSM vortex beams is affected by turbulence. The position and number of coherent vortices depend on the structure constant Cn2, correlation length σ0 and topological charge m. The smaller Cn2 and larger σ0 result in a larger propagation distance for the conservation of the topological charge in turbulence.
Improved Gaussian Beam-Scattering Algorithm
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng
2011-09-12
In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.
Achromatic doublets for Gaussian beams
NASA Astrophysics Data System (ADS)
Biraud, F.; Daigne, G.
1991-04-01
The properties of doublets of thin lenses in the Gaussian optics approximation were investigated. Two different ways for such a doublet to give strictly achromatic images of the input beam waist were found. Both solutions may be useful in a variety of applications, one being the possibility of shaping asymmetrical beams for fan beam antennas illumination. Using modes higher than the fundamental mode will allow the design of more realistic focal systems.
Hirayama, S; Takayanagi, T; Fujii, Y; Fujimoto, R; Fujitaka, S; Umezawa, M; Nagamine, Y; Hosaka, M; Yasui, K; Toshito, T
2014-06-15
Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distribution in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.
Accurately modeling Gaussian beam propagation in the context of Monte Carlo techniques
NASA Astrophysics Data System (ADS)
Hokr, Brett H.; Winblad, Aidan; Bixler, Joel N.; Elpers, Gabriel; Zollars, Byron; Scully, Marlan O.; Yakovlev, Vladislav V.; Thomas, Robert J.
2016-03-01
Monte Carlo simulations are widely considered to be the gold standard for studying the propagation of light in turbid media. However, traditional Monte Carlo methods fail to account for diffraction because they treat light as a particle. This results in converging beams focusing to a point instead of a diffraction limited spot, greatly effecting the accuracy of Monte Carlo simulations near the focal plane. Here, we present a technique capable of simulating a focusing beam in accordance to the rules of Gaussian optics, resulting in a diffraction limited focal spot. This technique can be easily implemented into any traditional Monte Carlo simulation allowing existing models to be converted to include accurate focusing geometries with minimal effort. We will present results for a focusing beam in a layered tissue model, demonstrating that for different scenarios the region of highest intensity, thus the greatest heating, can change from the surface to the focus. The ability to simulate accurate focusing geometries will greatly enhance the usefulness of Monte Carlo for countless applications, including studying laser tissue interactions in medical applications and light propagation through turbid media.
NASA Astrophysics Data System (ADS)
Kono, N.; Baba, A.
2008-02-01
Phased array ultrasonic testing techniques have been applied to sizing of cracks in welds, especially stainless steels and nickel based alloys welds. Ultrasonic phased array probes are capable of providing high SN ratio and high resolution by means of focal beams with various depths, positions, and angles. In this study, a simple design method using numerical analysis is proposed to optimize parameters on array probes. Acoustical fields of array probes are calculated approximately based on a multi-Gaussian beam modeling for single transducers. Calculation results are compared with experimental data with a laser interferometer. Validity of the modeling for the acoustical fields of the array probes is confirmed by good agreement between simulations and experiments. In order to design array probes that satisfy inspection requirements, e.g. range and resolution, an index of focusing (focusing factor) is important in addition to the parameters of array probes. Specifications of array probes are discussed for two kinds of requirements, wide range and high resolution.
Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence.
Mei, Zhangrong; Schchepakina, Elena; Korotkova, Olga
2013-07-29
A stochastic beam generated by a recently introduced source of Schell type with cosine-Gaussian spectral degree of coherence is shown to possess interesting novel features on propagation in isotropic and homogeneous atmospheric turbulence with general non-Kolmogorov power spectrum. It is shown that while at small distances from the source the beam's intensity exhibits annular profile with adjustable area of the dark region, the center disappears at sufficiently large distances and the beam's intensity tends to Gaussian form. Hence the 3D bottle beam is produced by the cumulative effect of the random source and the atmosphere. The distances at which the on-axis beam intensity has local minima and maxima are shown to have analytic dependence on the source and the atmospheric parameters. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on beam characteristics is analyzed in depth. The novel double-cycle qualitative change in the degree of coherence is shown to occur on atmospheric propagation which was not previously known for any other beams.
Semi-analytical model of arrayed waveguide grating in SOI using Gaussian beam approximation.
Sidharth, R; Das, B K
2015-03-10
The arrayed waveguide grating structure can be used as an important component in high-speed CMOS optical interconnects in silicon-on-insulator (SOI) platform. However, the performance of such device is found to be extremely sensitive to the fabrication-related errors in defining the critical features. In the absence of an appropriate analytical model, one needs to rely on numerical computation to analyze the device characteristics and fabrication tolerances. Because compact design of such a device structure has foot-print ∼mm^{2} and the smallest features can be as small as ∼500 nm×220 nm (waveguide cross section), it demands a huge computational budget to optimize the design parameters. A semi-analytical model using Gaussian beam approximation of guided mode profiles has been developed to analyze the output spectrum of arrayed waveguide grating and to estimate the phase errors due to waveguide inhomogeneities. This model has been validated with existing numerical methods and published experimental results. It has been observed that a probabilistic waveguide width variations of ΔW∼5 nm can cause a cross-talk degradation of about 40 dB (25 dB) for a device (operating at λ∼1550 nm) fabricated on SOI substrate with 220 nm (2 μm) device layer thickness.
A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems
NASA Astrophysics Data System (ADS)
Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain
2016-08-01
In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread function is relevant.
Yu, Jiayi; Chen, Yahong; Liu, Lin; Liu, Xianlong; Cai, Yangjian
2015-05-18
Elegant Hermite-Gaussian correlated Schell-model (EHGCSM) beam was introduced in theory and generated in experiment just recently [Phys. Rev. A 91, 013823 (2015)]. In this paper, we study the propagation properties of an EHGCSM beam in turbulent atmosphere with the help of the extended Huygens-Fresnel integral. Analytical expressions for the cross-spectral density and the propagation factors of an EHGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factors, of an EHGCSM beam in Kolmogorov and non-Kolmogorov turbulence are illustrated numerically. It is found that an EHGCSM beam exhibits splitting and combing properties in turbulent atmosphere, and an EHGCSM beam with large mode orders is less affected by turbulence than an EHGCSM beam with small mode orders or a Gaussian Schell-model beam or a Gaussian beam, which will be useful in free-space optical communications.
Li, Ye; Zhang, Yixin; Zhu, Yun; Chen, Minyu
2016-07-01
Based on the spatial power spectrum of the refractive index of anisotropic turbulence, the average polarizability of the Gaussian Schell-model quantized beams and lateral coherence length of the spherical wave propagating through the ocean water channel are derived. Numerical results show that, in strong temperature fluctuation, the depolarization effects of anisotropic turbulence are inferior to isotropic turbulence, as the other parameters of two links are the same. The depolarization effects of salinity fluctuation are less than the effects of the temperature fluctuation; the average polarizability of beams increases when increasing the inner scale of turbulence and the source's transverse size; and the larger rate of dissipation of kinetic energy per unit mass of fluid enhances the average polarizability of beams. The region of the receiving radius is smaller than the characteristic radius and the average polarizability of beams in isotropy turbulence is smaller than that of beams in anisotropy turbulence. However, the receiving radius region is larger than a characteristic radius and the average polarizability of beams in isotropy turbulence is larger than that of beams in anisotropy turbulence.
Li, Ye; Zhang, Yixin; Zhu, Yun; Chen, Minyu
2016-07-01
Based on the spatial power spectrum of the refractive index of anisotropic turbulence, the average polarizability of the Gaussian Schell-model quantized beams and lateral coherence length of the spherical wave propagating through the ocean water channel are derived. Numerical results show that, in strong temperature fluctuation, the depolarization effects of anisotropic turbulence are inferior to isotropic turbulence, as the other parameters of two links are the same. The depolarization effects of salinity fluctuation are less than the effects of the temperature fluctuation; the average polarizability of beams increases when increasing the inner scale of turbulence and the source's transverse size; and the larger rate of dissipation of kinetic energy per unit mass of fluid enhances the average polarizability of beams. The region of the receiving radius is smaller than the characteristic radius and the average polarizability of beams in isotropy turbulence is smaller than that of beams in anisotropy turbulence. However, the receiving radius region is larger than a characteristic radius and the average polarizability of beams in isotropy turbulence is larger than that of beams in anisotropy turbulence. PMID:27409215
Modeling focusing Gaussian beams in a turbid medium with Monte Carlo simulations.
Hokr, Brett H; Bixler, Joel N; Elpers, Gabriel; Zollars, Byron; Thomas, Robert J; Yakovlev, Vladislav V; Scully, Marlan O
2015-04-01
Monte Carlo techniques are the gold standard for studying light propagation in turbid media. Traditional Monte Carlo techniques are unable to include wave effects, such as diffraction; thus, these methods are unsuitable for exploring focusing geometries where a significant ballistic component remains at the focal plane. Here, a method is presented for accurately simulating photon propagation at the focal plane, in the context of a traditional Monte Carlo simulation. This is accomplished by propagating ballistic photons along trajectories predicted by Gaussian optics until they undergo an initial scattering event, after which, they are propagated through the medium by a traditional Monte Carlo technique. Solving a known problem by building upon an existing Monte Carlo implementation allows this method to be easily implemented in a wide variety of existing Monte Carlo simulations, greatly improving the accuracy of those models for studying dynamics in a focusing geometry.
Propagation properties of cylindrical sinc Gaussian beam
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil T.; Bayraktar, Mert
2016-09-01
We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.
Wang, Jing; Zhu, Shijun; Wang, Haiyan; Cai, Yangjian; Li, Zhenhua
2016-05-30
Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications. PMID:27410089
Optimization of Gaussian beam widths in acoustic propagation
NASA Astrophysics Data System (ADS)
Gordon, D. F.
1989-10-01
The use of Gaussian beams to compute wave propagation phenomena is a field of current interest and activity. Porter and Bucker (1987) supply an extensive list of references. More recent references can be found in Benites and Aki (1989). Gaussian beams can be traced as rays in range-dependent media providing not only propagation loss, but travel times, multipath structure, and frequency dependence. The well-known ray theory problems of caustics and shadow zones are treated automatically. A beam width minimization technique applied to a Gaussian beam model developed by Dr. H. P. Bucker, is outlined. Porter and Bucker (1987) gives the formulation upon which the techniques is built. A free parameter E is usually determined in a heuristic manner. Here, it is shown that the minimization of beam width assigns a precise value to E. Examples are given showing that the minimized beams give good propagation losses in some cases. A case also shown in the standard Gaussian beams give poor results and the minimized beams give even worse results. The problem appears to arise in beams that pass near boundaries. This problem will have to be corrected before a final judgment can be made on the validity of minimum-width beams.
Eyyuboğlu, Halil T
2014-06-10
Using the random phase screen approach, we carry out a simulation analysis of the probability of error performance of Gaussian, annular Gaussian, cos Gaussian, and cosh Gaussian beams. In our scenario, these beams are intensity-modulated by the randomly generated binary symbols of an electrical message signal and then launched from the transmitter plane in equal powers. They propagate through a turbulent atmosphere modeled by a series of random phase screens. Upon arriving at the receiver plane, detection is performed in a circuitry consisting of a pin photodiode and a matched filter. The symbols detected are compared with the transmitted ones, errors are counted, and from there the probability of error is evaluated numerically. Within the range of source and propagation parameters tested, the lowest probability of error is obtained for the annular Gaussian beam. Our investigation reveals that there is hardly any difference between the aperture-averaged scintillations of the beams used, and the distinctive advantage of the annular Gaussian beam lies in the fact that the receiver aperture captures the maximum amount of power when this particular beam is launched from the transmitter plane.
Computational aspects of Gaussian beam migration
Hale, D.
1992-01-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Computational aspects of Gaussian beam migration
Hale, D.
1992-08-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.
Dennis, Mark R; Ring, James D
2013-09-01
We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.
Scintillations of partially coherent Laguerre Gaussian beams
NASA Astrophysics Data System (ADS)
Yüceer, M.; Eyyuboğlu, H. T.; Lukin, I. P.
2010-12-01
Scintillations of Laguerre-Gaussian (LG) beams for weak atmospheric turbulence conditions are derived for on-axis receiver positions by using Huygens-Fresnel (HF) method in semi-analytic fashion. Numerical evaluations indicate that at the fully coherent limit, higher values of radial mode numbers will give rise to more scintillations, at medium and low partial coherence levels, particularly at longer propagation distances, scintillations will fall against rises in radial mode numbers. At small source sizes, the scintillations of LG beams having full coherence will initially rise, reaching saturation at large source sizes. For LG beams with low partial coherence levels, a steady fall toward the larger source sizes is observed. Partially coherent beams of medium levels generally exhibit a rising trend toward the large source sizes, also changing the respective positions of the related curves. Beams of low coherence levels will be less affected by the variations in the refractive index structure constant.
Beam-Beam Simulations with the Gaussian Code TRS
Matter, Regina S.
2000-06-26
The authors have summarized the main features of the beam-beam simulation code TRS and presented two sample applications to the PEP-II collider. The code has been successfully tested against analytic results and against other simulation codes whenever such comparisons are meaningful. The soft-gaussian approximation is believed to represent reliably incoherent beam-beam effects. The code has been used to perform studies for the PEP-II collider. For example, simulated tune scans reveal undesirable operating points due to beam blowup from synchrotron sidebands. The dynamical beta effect, clearly seen in these simulations, also influences the choice of a working point. The code has been used to establish the adequate beam separation at the parasitic collision points [24], and has been applied to the proposed muon collider [25], including the effects from the instability of the muon.
NASA Astrophysics Data System (ADS)
Inaniwa, T.; Kanematsu, N.; Hara, Y.; Furukawa, T.; Fukahori, M.; Nakao, M.; Shirai, T.
2014-09-01
Challenging issues in treatment planning for scanned carbon-ion (C-ion) therapy are (i) accurate calculation of dose distribution, including the contribution of large angle-scattered fragments, (ii) reduction in the memory space required to store the dose kernel of individual pencil beams and (iii) shortening of computation time for dose optimization and calculation. To calculate the dose contribution from fragments, we modeled the transverse dose profile of the scanned C-ion beam with the superposition of three Gaussian distributions. The development of pencil beams belonging to the first Gaussian component was calculated analytically based on the Fermi-Eyges theory, while those belonging to the second and third components were transported empirically using the measured beam widths in a water phantom. To reduce the memory space for the kernels, we stored doses only in the regions of interest considered in the dose optimization. For the final dose calculation within the patient’s whole body, we applied a pencil beam redefinition algorithm. With these techniques, the triple Gaussian beam model can be applied not only to final dose calculation but also to dose optimization in treatment planning for scanned C-ion therapy. To verify the model, we made treatment plans for a homogeneous water phantom and a heterogeneous head phantom. The planned doses agreed with the measurements within ±2% of the target dose in both phantoms, except for the doses at the periphery of the target with a high dose gradient. To estimate the memory space and computation time reduction with these techniques, we made a treatment plan for a bone sarcoma case with a target volume of 1.94 l. The memory space for the kernel and the computation time for final dose calculation were reduced to 1/22 and 1/100 of those without the techniques, respectively. Computation with the triple Gaussian beam model using the proposed techniques is rapid, accurate and applicable to dose optimization and
High-order pseudo-Gaussian scalar acoustical beams.
Mitri, Farid
2014-01-01
Exact solutions of the scalar Helmholtz equation describing tightly spherically-focused beams are introduced without any approximations using the complex source point method in spherical coordinates. The generalized solutions, valid for any integer degree n and order m, describe high-order pseudo-Gaussian vortex, intermediate (vortex), hollow (nonvortex), and trigonometric (non-vortex) beams having an arbitrary beam waist w0. A very useful property of these beams is the efficient and fast computational modeling of tightly focused or quasi-collimated wave-fronts depending on the dimensionless waist parameter kw0, where k is the wave number of the acoustical radiation. Examples that illustrate hollow vortex and non-vortex beams are provided, and numerical simulations for the magnitude, isosurface, and phase plots of the pressure wave field of higher-order quasi-Gaussian beams are evaluated with particular emphasis on kw0 for strongly (kw0 = 3) to weakly focused (i.e., quasi-collimated) beams (kw0 = 7). Potential applications are in beam-forming design, imaging, particle sizing and manipulation in acoustical tweezers, and phenomena related to scattering, radiation force, and torque.
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
NASA Astrophysics Data System (ADS)
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
Yu, Hao; Rossi, Giammarco; Braglia, Andrea; Perrone, Guido
2016-08-10
The paper presents the development of a tool based on a back-propagation artificial neural network to assist in the accurate positioning of the lenses used to collimate the beam from semiconductor laser diodes along the so-called fast axis. After training using a Gaussian beam ray-equivalent model, the network is capable of indicating the tilt, decenter, and defocus of such lenses from the measured field distribution, so the operator can determine the errors with respect to the actual lens position and optimize the diode assembly procedure. An experimental validation using a typical configuration exploited in multi-emitter diode module assembly and fast axis collimating lenses with different focal lengths and numerical apertures is reported.
Yu, Hao; Rossi, Giammarco; Braglia, Andrea; Perrone, Guido
2016-08-10
The paper presents the development of a tool based on a back-propagation artificial neural network to assist in the accurate positioning of the lenses used to collimate the beam from semiconductor laser diodes along the so-called fast axis. After training using a Gaussian beam ray-equivalent model, the network is capable of indicating the tilt, decenter, and defocus of such lenses from the measured field distribution, so the operator can determine the errors with respect to the actual lens position and optimize the diode assembly procedure. An experimental validation using a typical configuration exploited in multi-emitter diode module assembly and fast axis collimating lenses with different focal lengths and numerical apertures is reported. PMID:27534506
BER of flat-topped Gaussian beam in slant path turbulent atmosphere
NASA Astrophysics Data System (ADS)
Lu, Fang; Han, Yanyan; Han, Xiang-e.; Yang, Rui-ke
2013-08-01
Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is dependent on altitude, the on-axis scintillation index of the flat-topped Gaussian beam at the receiver plane in slant path turbulence was given by using Kolmogorov atmospheric turbulence power spectrum model. The influences of the link altitudes, atmospheric refractive index structure constant C0 at the ground，the source size and the beam order on scintillation index of the flat-topped Gaussian beam are discussed in detail. The result shows that the scintillation index increased first and then decreased with the increase of the beam order. The advantage of a flat-topped Gaussian beam over a single Gaussian beam is restricted to small source sizes, which is consistent with the case of the horizontal path. To find the average bit error rate under weak slant path turbulence, the log-normal distribution model of the intensity fluctuation was used. The influence of beam order and source size on BER was discussed. The result indicates that the smaller sized flat-topped Gaussian beam will bring average bit error rate advantage over the same size Gaussian beam. Our results correctly reduce to the result of the horizontal path with atmospheric structure constant fixed.
Fractionalization of optical beams: II. Elegant Laguerre Gaussian modes
NASA Astrophysics Data System (ADS)
Gutiérrez-Vega, Julio C.
2007-05-01
We apply the tools of fractional calculus to introduce new fractional-order solutions of the paraxial wave equation that smoothly connect the elegant Laguerre-Gaussian beams of integral-order. The solutions are characterized in general by two fractional indices and are obtained by fractionalizing the creation operators used to create elegant Laguerre-Gauss beams from the fundamental Gaussian beam. The physical and mathematical properties of the circular fractional beams are discussed in detail. The orbital angular momentum carried by the fractional beam is a continuous function of the angular mode index and it is not restricted to take only discrete values.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
NASA Astrophysics Data System (ADS)
Kotlyar, V. V.; Kovalev, A. A.; Porfirev, A. P.
2016-07-01
We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.
Propagation of a Gaussian beam in a nonhomogeneous plasma
Mazzucato, E.
1989-06-01
The asymptotic theory of Choudhary and Felsen on the propagation of scalar inhomogeneous waves in two-dimensional isotropic media is extended to the case of three-dimensional vector fields. The theory is applied to the propagation of Gaussian beams in nonhomogeneous media. The wave trajectory equations are then reformulated for anisotropic media and used for tracking a Gaussian beam in a tokamak plasma. 14 refs., 5 figs.
Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer
NASA Astrophysics Data System (ADS)
Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre–Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.
Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer
NASA Astrophysics Data System (ADS)
Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre-Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.
Single-beam interference from plain Gaussian and OAM wavefronts
NASA Astrophysics Data System (ADS)
Popov, S.; Favier, M.
2016-03-01
We implement an SLM to generate laser beams of variable orbital angular momentum, also referred as Laguerre- Gaussian beams. Input beam polarization takes into account a local birefringence of each pixel of the SLM. We identify the beam polarization eigenstates allowing generate L-G beams of different order via matching variable birefringence of every separate pixels. Zero-order beam passing through the SLM can interact with a generated OAM beam to create an interference pattern. Experimental results demonstrate good agreement with simulations.
Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam
Wen, Wei; Chu, Xiuxiang
2015-09-15
The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airy beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.
Diffraction of Gaussian beams on intracavity Bragg gratings
NASA Astrophysics Data System (ADS)
Bitauld, David; Menez, Ludivine; Zaquine, Isabelle; Maruani, Alain; Frey, Robert
2005-06-01
The diffraction of Gaussian beams on intracavity Bragg gratings is analyzed theoretically. For reasonable waists the associated beam divergence does not significantly influence the diffraction efficiency of such devices. Nevertheless, the tilt angle of the incident beam, imposed by the Bragg resonance condition, strongly reduces the diffraction efficiency at short grating periods. However, the angular selectivity can be maintained if the Fabry-Perot cavity is tuned to the incident beam direction, which allows the use of small-volume holograms together with a dense angular multiplex. This theoretical analysis can be applied to the optimization of the diffraction properties of Gaussian beams on any intracavity Bragg grating, which could then be used for free-space parallel signal processing.
A new method for generating a hollow Gaussian beam
NASA Astrophysics Data System (ADS)
Wei, Cun; Lu, Xingyuan; Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-04-01
Hollow Gaussian beam (HGB) was introduced 10 years ago (Cai et al. in Opt Lett 28:1084, 2003). In this paper, we introduce a new method for generating a HGB through transforming a Laguerre-Gaussian beam with radial index 0 and azimuthal index l into a HGB with mode n = l/2. Furthermore, we report experimental generation of a HGB based on the proposed method, and we carry out experimental study of the focusing properties of the generated HGB. Our experimental results agree well with the theoretical predictions.
Non-gaussian statistics of pencil beam surveys
NASA Technical Reports Server (NTRS)
Amendola, Luca
1994-01-01
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.
Gaussian beam scattering by a gyrotropic anisotropic object
NASA Astrophysics Data System (ADS)
Chen, Zhenzhen; Zhang, Huayong; Wu, Xianliang; Huang, Zhixiang
2016-09-01
An exact semi-analytical solution is presented to the scattering of an on-axis Gaussian beam incident on a gyrotropic anisotropic object. The on-axis incident Gaussian beam, scattered fields as well as internal fields are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients of the scattered fields are determined by virtue of Schelkunoff's equivalence theorem and electromagnetic boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.
Comparison between Bessel and Gaussian beam propagation for in-depth optogenetic stimulation
NASA Astrophysics Data System (ADS)
Tejeda, Hector; Li, Ting; Mohanty, Samarendra
2013-03-01
Optogenetics technology has opened new landscapes for neuroscience research. Due to its non-diffracting and selfhealing nature, Bessel beam has potential to improve in-depth optogenetic stimulation. A detailed understanding of Bessel beam propagation, as well as its superiority over commonly used Gaussian beam, is essential for delivery and control of light irradiation for optogenetics and other light stimulation approaches. We developed an algorithm for modeling Bessel beam propagation and then compared both beam propagations in two-layered mice brain under variance of multiple variables (i.e., wavelength, numerical aperture, and beam size). These simulations show that Bessel beam is significantly advantageous over Gaussian beam for in-depth optogenetic stimulation, leading to development of lessinvasive probes. While experimental measurements using single-photon Bessel-Gauss beam generated by axicon-tip fiber did not show improved stimulation-depth, near-infrared Bessel beam generated using free-space optics and an axicon led to better penetration than near-infrared Gaussian beam.
Propagation of Airy Gaussian vortex beams in uniaxial crystals
NASA Astrophysics Data System (ADS)
Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng
2016-04-01
The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).
Propagation of Airy Gaussian vortex beams in uniaxial crystals
NASA Astrophysics Data System (ADS)
Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng
2016-04-01
The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).
Gaussian beam scintillation on ground-to-space paths: the importance of beam wander
NASA Astrophysics Data System (ADS)
Baker, Gary J.; Benson, Robert S.
2004-10-01
Predictions of scintillation for ground to space collimated Gaussian beams generated from a numerical wave optics simulation are compared with recent weak scintillation theory developed from the Rytov perturbation approach (L.C. Andrews, R.L. Phillips, P.T. Yu, Ap Opt 34, p 7742-7751, 1995; J.D. Shelton, JOSA A 12, p 2172-2181, 1995). Significant discrepancies are revealed for intermediate-sized beams, defined as beams whose initial diameters place the near ground turbulence in the transmitter near field and the remote space target in the transmitter far field. By adding wander tracking to the wave optics simulation, and by developing a separate analytic model of the beam wander scintillation mechanism, we show that the scintillation for intermediate-sized beams is dominated by turbulence-induced beam wander at the target, and that the results from the wave optics simulation are accurate. We conclude that the analytic theory"s treatment of beam wander is incomplete, leading to the output of incorrect predictions for the second moment of irradiance. The error is most severe at the target point on the transmitter"s optical axis.
Chen, Carl G; Konkola, Paul T; Ferrera, Juan; Heilmann, Ralf K; Schattenburg, Mark L
2002-02-01
The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.
Non-Gaussian beam dynamics in low energy antiproton storage rings
NASA Astrophysics Data System (ADS)
Resta-López, J.; Hunt, J. R.; Welsch, C. P.
2016-10-01
In low energy antiproton facilities, where electron cooling is fundamental, the cooling forces together with heating phenomena causing emittance blow-up, such as Intra Beam Scattering (IBS), result in highly non-Gaussian beam distributions. In these cases, a precise simulation of IBS effects is essential to realistically evaluate the long term beam evolution, taking into account the non-Gaussian characteristics of the beam. Here, we analyse the beam dynamics in the Extra Low ENergy Antiproton ring (ELENA), which is a new small synchrotron currently being constructed at CERN to decelerate antiprotons to energies as low as 100 keV. Simulations are performed using the code BETACOOL, comparing different models of IBS.
Scattering of Gaussian beams by disordered particulate media
NASA Astrophysics Data System (ADS)
Mishchenko, Michael I.; Dlugach, Janna M.
2016-11-01
A frequently observed characteristic of electromagnetic scattering by a disordered particulate medium is the absence of pronounced speckles in angular patterns of the scattered light. It is known that such diffuse speckle-free scattering patterns can be caused by averaging over randomly changing particle positions and/or over a finite spectral range. To get further insight into the possible physical causes of the absence of speckles, we use the numerically exact superposition T-matrix solver of the Maxwell equations and analyze the scattering of plane-wave and Gaussian beams by representative multi-sphere groups. We show that phase and amplitude variations across an incident Gaussian beam do not serve to extinguish the pronounced speckle pattern typical of plane-wave illumination of a fixed multi-particle group. Averaging over random particle positions and/or over a finite spectral range is still required to generate the classical diffuse speckle-free regime.
Interpretation of Extinction in Gaussian-Beam Scattering
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.
Gras, S.; Blair, D. G.; Ju, L.
2010-02-15
To reduce the thermal noise in the future generation of gravitational wave detectors, flat-top beams have been proposed to replace conventional Gaussian beams, so as to obtain better averaging over the Brownian motion of the test masses. Here, we present a detailed investigation of the unwanted opto-acoustic interactions in such interferometers, which can lead to the phenomenon of parametric instability. Our results show that the increased overlap of the Mesa beams with the test masses leads to approximately 3 times as many unstable modes in comparison to a similar interferometer with Gaussian beams.
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-01
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs. PMID:27607713
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-01
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.
Reflection of a Gaussian beam from a nonlinear interface.
Marcuse, D
1980-09-15
A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.
Transmission of a Gaussian beam by a Fizeau interferential wedge.
Stoykova, Elena
2005-12-01
Analysis of transmission of a finite-diameter Gaussian beam by a Fizeau interferential wedge is presented. The fringe calculation is based on angular spectrum expansion of the complex amplitude of the incident wave field. The developed approach is applicable to any beam diameter and wedge thickness at any distance from the wedge and yields as a boundary case the fringes at plane-wave illumination. The spatial region of resonant transmission on the wedge surface is given by the width of the transmitted peak for plane-wave illumination. At higher coating reflectivity, the direction of the transmitted beam is deviated with respect to that of the incident beam. Evaluation of the spectral response based on the spectral width of the transmitted power curve is introduced as more realistic for a correct description of the application of a Fizeau wedge as an interferential selector in laser resonators. PMID:16396037
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing
2016-08-01
Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing
2016-08-01
Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics. PMID:27505641
Light steering of Air-Gaussian beam in Nonlocal Nonlinear Medium
NASA Astrophysics Data System (ADS)
Chen, Ran; Zhang, Xiaping
2016-07-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results show that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Espesically, by tuning the phase difference between the two beams, we can steer the centre of the bound AiG beams in nonlocal nonlinear media.
Gaussian beam profile shaping apparatus, method therefor and evaluation thereof
Dickey, Fred M.; Holswade, Scott C.; Romero, Louis A.
1999-01-01
A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system.
Gaussian beam profile shaping apparatus, method therefore and evaluation thereof
Dickey, F.M.; Holswade, S.C.; Romero, L.A.
1999-01-26
A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system. 27 figs.
Optimal focusing conditions of lenses using Gaussian beams
NASA Astrophysics Data System (ADS)
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; Mourad, Idir
2016-07-01
By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. We show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used in wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.
Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
Bao, Gang; Lai, Jun; Qian, Jianliang
2014-03-15
Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, we have to take into account reflecting multiscale Gaussian beams, which are accomplished by enforcing reflecting boundary conditions during beam propagation and carrying out suitable reflecting beam summation. To propagate multiscale beams efficiently, we prove that the ratio of the squared magnitude of beam amplitude and the beam width is roughly conserved, and accordingly we propose an effective indicator to identify significant beams. We also prove that the resulting multiscale Gaussian beam methods converge asymptotically. Numerical examples demonstrate the accuracy and efficiency of the method.
Gaussian beam scattering from arbitrarily shaped objects with rough surfaces
NASA Astrophysics Data System (ADS)
Chen, Hui; Wu, Zhensen; Yang, Ruike; Bai, Lu
2004-07-01
The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 µm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.
Beam-beam simulations with non-Gaussian distributions for SLC and SLC-2000
Bane, K.L.F.; Chen, P.; Zimmermann, F.
1997-05-01
Due to various upstream beam manipulations, the longitudinal bunch shape at the interactions point of the Stanford Linear Collider (SLC) is highly non-Gaussian. In this paper, we report beam-beam simulations with realistic longitudinal bunch shapes for the present SLC parameters and for the SLC-2000 luminosity upgrade. The simulation results allow us to estimate the luminosity enhancement due to the pinch effect and to find optimum parameter settings for the bunch compressor and the linac.
Hermite-Gaussian beams with self-forming spiral phase distribution
NASA Astrophysics Data System (ADS)
Zinchik, Alexander A.; Muzychenko, Yana B.
2014-05-01
Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).
A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam
NASA Astrophysics Data System (ADS)
F, Khannous; A, A. A. Ebrahim; A, Belafhal
2016-04-01
Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.
Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere.
Chu, Xiuxiang
2007-12-24
The propagation of a cosh-Gaussian beam through an arbitrary ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity at any receiver plane are obtained. As an elementary example, the average intensity and its radius at the image plane of a cosh-Gaussian beam through a thin lens are studied. To show the effects of a lens on the average intensity and the intensity radius of the laser beam in turbulent atmosphere, the properties of a collimated cosh-Gaussian beam and a focused cosh-Gaussian beam for direct propagation in turbulent atmosphere are studied and numerically calculated. The average intensity profiles of a cosh-Gaussian beam through a lens can have a shape similar to that of the initial beam for a longer propagation distance than that of a collimated cosh-Gaussian beam for direct propagation. With the increment in the propagation distance, the average intensity radius at the image plane of a cosh-Gaussian beam through a thin lens will be smaller than that at the focal plane of a focused cosh-Gaussian beam for direct propagation. Meanwhile, the intensity distributions at the image plane of a cosh-Gaussian beam through a lens with different w(0) and Omega(0) are also studied.
Second and third harmonic waves excited by focused Gaussian beams.
Levy, Uri; Silberberg, Yaron
2015-10-19
Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1). PMID:26480441
NASA Astrophysics Data System (ADS)
Khaled, E. E. M.; Aly, M. E. M.
2011-02-01
Scattering of an on- or off-axis focused Gaussian beam by a dielectric spherical or a spheroidal particle with a nonconcentric spherical core is presented. The plane wave spectrum method is used to model the beam. The electric field intensities are calculated at any point using the T-matrix method, which is modified for the cases studied here. The calculated angular scattering intensities are shown for different cases of the core's offsets and for different cases of the beam-focusing positions with respect to the particle. The technique is applicable to a large-sized parameter particle with nonconcentric layers of different shapes illuminated with an arbitrarily shaped laser beam. Although the technique is applicable to a beam propagating in any direction and to an arbitrary shift of the core, all the calculations shown here are for an offset core and a beam propagating in the z-direction.
Double pulse laser induced breakdown spectroscopy with Gaussian and multimode beams
NASA Astrophysics Data System (ADS)
Lednev, V. N.; Pershin, S. M.; Bunkin, A. F.; Samokhvalov, A. A.; Veiko, V. P.; Kudryashov, S. I.; Ionin, A. A.
2016-10-01
Single vs multimode laser beams were compared for double pulse laser ablation, plasma properties and laser induced breakdown spectroscopy (LIBS) analytical capabilities. Laser beams with Gaussian and multimode profiles were generated within the same Nd:YAG laser in single and double pulse regimes. Gaussian beam produced a small and deep crater while multimode beam formed a wide shallow crater. Greater double pulse enhancement of ablated material and plasma volume were observed for Gaussian beam sampling. The higher intensity for atomic/ionic lines in the plasma spectra was observed for multimode beam sampling due to greater laser pulse energy and larger ablated mass. Interestingly, spectra line intensity enhancement for double pulse ablation was 2-3 times greater for Gaussian than for multimode beam ablation. Background emission decreased for plasma induced by multimode beam when using double pulse mode while for Gaussian beam an opposite dependence was observed. Surprisingly, higher peak fluence at sample surface for Gaussian beam didn't provide higher plasma temperature and electron density for double pulse ablation. Analytical capabilities of LIBS method were compared for double pulse plasma induced by Gaussian and multimode beam in terms of precision, sensitivity and linearity of calibration curves. It was observed that Gaussian beam sampling leads to improvement of analysis precision while sensitivity was element dependent.
Leung Shingyu; Qian Jianliang
2010-11-20
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Self-trapped elliptical super-Gaussian beam in cubic-quintic media
NASA Astrophysics Data System (ADS)
Jana, Soumendu; Singh, Ajitpal; Porsezian, K.; Mithun, T.
2014-12-01
We find self-trapped propagation of elliptical super-Gaussian beam in cubic-quintic nonlinear media. The soliton beam preserves its shape and size during propagation in Kerr media. Both defocusing and focusing quintic nonlinearities are considered. In a cubic (focusing)-quintic (defocusing) media breather like beam propagation with intriguing beam width oscillation is observed. The influence of beam ellipticity, super-Gaussian nature and quintic nonlinearity on self-trapping has been studied. A formula for critical power for self-focusing has been derived and it readily agrees with the results obtained by variational method. In Kerr and focusing quintic media beam collapse occurs quicker for higher order super-Gaussian beam. The critical power of self-focusing in defocusing (focusing) quintic medium prominently increases (decreases) with increasing strength of quintic nonlinearity. This variation rate is greater for higher order super Gaussian beam. A beam with greater ellipticity requires larger power for self-trapping.
Composite vortex beams by coaxial superposition of Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Huang, Sujuan; Miao, Zhuang; He, Chao; Pang, Fufei; Li, Yingchun; Wang, Tingyun
2016-03-01
We propose the generation of novel composite vortex beams by coaxial superposition of Laguerre-Gaussian (LG) beams with common waist position and waist parameter. Computer-generated holography by conjugate-symmetric extension is applied to produce the holograms of several composite vortex beams. Utilizing the holograms, fantastic light modes including optical ring lattice, double dark-ring and double bright-ring composite vortex beams etc. are numerically reconstructed. The generated composite vortex beams show diffraction broadening with some of them showing dynamic rotation around beam centers while propagating. Optical experiments based on a computer-controlled spatial light modulator (SLM) verify the numerical results. These novel composite vortex beams possess more complicated distribution and more controllable parameters for their potential application in comparison to conventional optical ring lattice.
Gong, Cheng; Li, ZiXi; Hua, LinQiang; Quan, Wei; Liu, XiaoJun
2016-09-15
Filamentation dynamics in fused silica are investigated using an Airy pattern and a Gaussian laser beam. The angle-resolved conical emission spectra are measured and compared with the predictions of several models. Our experimental observations are consistent with the X-waves model in both cases. This indicates that both laser beams spontaneously evolve into nonlinear X-waves and suggests a universal evolution of filaments in fused silica, regardless of the initial laser beam profile. PMID:27628383
Abd El-Maksoud, Rania H
2016-02-20
In this paper, a methodology is developed to model and analyze the effect of undesired (ghost) reflections of Gaussian beams that are produced by anamorphic optical systems. The superposition of these beams with the nominal beam modulates the nominal power distribution at the recording plane. This modulation may cause contrast reduction, veiling parts of the nominal image, and/or the formation of spurious interference fringes. The developed methodology is based on synthesizing the beam optical paths into nominal and ghost optical beam paths. Similar to the nominal beam, we present the concept that each ghost beam is characterized by a beam size, wavefront radius of curvature, and Gouy phase in the paraxial regime. The nominal and ghost beams are sequentially traced through the system and formulas for estimating the electric field magnitude and phase of each ghost beam at the recording plane are presented. The effective electric field is the addition of the individual nominal and ghost electric fields. Formulas for estimating Gouy phase, the shape of the interference fringes, and the central interference order are introduced. As an application, the theory of the formation of the interference fringes by Michelson interferometer is presented. This theory takes into consideration the ghost reflections that are formed by the beam splitter. To illustrate the theory and to show its wide applicability, simulation examples that include a Mangin mirror, a Michelson interferometer, and a black box optical system are provided. PMID:26906582
Evolution of a Gaussian laser beam in warm collisional magnetoplasma
NASA Astrophysics Data System (ADS)
Jafari, M. J.; Jafari Milani, M. R.; Niknam, A. R.
2016-07-01
In this paper, the spatial evolution of an intense circularly polarized Gaussian laser beam propagated through a warm plasma is investigated, taking into account the ponderomotive force, Ohmic heating, external magnetic field, and collisional effects. Using the momentum transfer and energy equations, both modified electron temperature and electron density in plasma are obtained. By introducing the complex dielectric permittivity of warm magnetized plasma and using the complex eikonal function, coupled differential equations for beam width parameter are established and solved numerically. The effects of polarization state of laser and magnetic field on the laser spot size evolution are studied. It is observed that in case of the right-handed polarization, an increase in the value of external magnetic field causes an increase in the strength of the self-focusing, especially in the higher values, and consequently, the self-focusing occurs in shorter distance of propagation. Moreover, the results demonstrate the existence of laser intensity and electron temperature ranges where self-focusing can occur, while the beam diverges outside of these regions; meanwhile, in these intervals, there exists a turning point for each of intensity and temperature in which the self-focusing process has its strongest strength. Finally, it is found that the self-focusing effect can be enhanced by increasing the plasma frequency (plasma density).
NASA Astrophysics Data System (ADS)
Xiang, NingJing; Wu, ZhenSen; Wang, MingJun
2014-10-01
The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function (MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, Yaochuan; Yin, Hongming
2016-04-01
The partially coherent four-petal Gaussian vortex beam is introduced and described by analytical expressions. The analytical propagation equation for partially coherent four-petal Gaussian vortex beam in turbulent atmosphere is derived by using the extended Huygens-Fresnel diffraction integral formula. The influences of refraction index structure, beam order n, topological charge M and the coherence length on the average intensity distributions of beam are investigated by numerical examples.
Xu, Yonggen; Li, Yude; Zhao, Xile
2015-09-01
Propagation properties of partially coherent elegant Laguerre-Gaussian beam (PC-eLGB) and partially coherent standard Laguerre-Gaussian beam (PC-sLGB) through the turbulent atmosphere are studied. Analytical formulas for the intensity and effective beam width (EBW) of the PC-eLGB and PC-sLGB through the turbulent atmosphere are derived based on the extended Huygens-Fresnel principle. The propagation properties of PC-eLGB and PC-sLGB through the turbulent atmosphere are studied numerically and comparatively. It is shown that the intensities of the PC-eLGB and PC-sLGB are less affected by the turbulent atmosphere than the fully coherent Laguerre-Gaussian beam. The spreading (EBW and divergent angle of the far field) of PC-eLGB and PC-sLGB with the different mode orders (m,n) is slower in the free space than in the turbulent atmosphere, and the PC-sLGB spreads more rapidly than the PC-eLGB through the free space and the turbulent atmosphere. The study results will be useful for free space optical communications.
Propagation characteristics of a Gaussian laser beam in plasma with modulated collision frequency
Wang Ying; Yuan Chengxun; Zhou Zhongxiang; Gao Ruilin; Li Lei; Du Yanwei
2012-08-15
The propagation characteristics of a Gaussian laser beam in cold plasma with the electron collision frequency modulated by laser intensity are presented. The nonlinear dynamics of the ponderomotive force, which induce nonlinear self-focusing as opposed to spatial diffraction, are considered. The effective dielectric function of the Drude model and complex eikonal function are adopted in deriving coupled differential equations of the varying laser beam parameters. In the framework of ponderomotive nonlinearity, the frequency of electron collision in plasmas, which is proportional to the spatial electron density, is strongly interrelated with the laser beam propagation characteristics. Hence, the propagation properties of the laser beam and the modulated electron collision frequency distribution in plasma were studied and explained in depth. Employing this self-consistent method, the obtained simulation results approach practical conditions, which is of significance to the study of laser-plasma interactions.
Terahertz generation by two cross focused Gaussian laser beams in magnetized plasma
Singh, Ram Kishor Sharma, R. P.
2014-11-15
This paper presents a theoretical model for terahertz (THz) radiation generation by two cross-focused Gaussian laser beams in a collisionless magnetoplasma. The plasma is redistributed due to the ponderomotive nonlinearity which leads to the cross focusing of the laser beams. The focusing of the copropagating laser beams increases with increasing the externally applied static magnetic field which is perpendicular to the wave propagation direction. The nonlinear current at THz frequency arises on account of nonlinear ponderomotive force as a result of beating of the two lasers. The generated THz radiation amplitude increases significantly with increasing magnetic field. The cross focusing of two laser beams enhances the THz yield. Optimization of laser-plasma parameters gives the radiated normalized THz power of the order of 10 kW.
Scattering of a Hermite-Gaussian beam field by a chiral sphere.
Yokota, M; He, S; Takenaka, T
2001-07-01
Scattering of a Hermite-Gaussian beam field by a chiral sphere is analyzed. A Hermite-Gaussian beam field is expressed as a superposition of multipole fields at complex-source points. Electromagnetic fields are expanded in terms of the spherical vector wave functions. The unknown expansion coefficients for the scattered field and the internal field are determined by the boundary conditions. As numerical examples, the scattered near fields of the beam incidence are calculated, and the effects of the chirality and the radius of the chiral sphere on the fields are examined. The results for a Gaussian beam incidence are also compared with those of a plane-wave incidence.
Scattering of an oblique incident focused Gaussian beam by a spheroidal particle
NASA Astrophysics Data System (ADS)
Zhao, Wenjuan; Han, Yiping; Han, Lu
2014-09-01
Based on the expansion of a Gaussian beam in spheroidal coordinates in general case of oblique illumination, a theoretical procedure to determine the scattered fields of spheroid obliquely illuminated by a Gaussian beam is presented. Specific attention is paid to the study of scattering properties of a spheroidal particle from an obliquely incident Gaussian beam. The calculated results for spheroid are compared with those from the surface integral equation method, and very good agreements are observed. Numerical results concerning the influences of shaped beam parameters (beam waist radius, incident angle) as well as spheroid parameters (major axis, minor axis, refractive index, size parameter) on the scattering properties are presented. These results can be used as a reference for other numerical methods to analyze the light scattering by non-spherical particles illuminated by Gaussian beam.
Optical Gaussian beam interaction with one-dimensional thermal wave in the Raman-Nath configuration.
Bukowski, Roman J
2009-03-01
Optical Gaussian beam interaction with a one-dimensional temperature field in the form of a thermal wave in the Raman-Nath configuration is analyzed. For the description of the Gaussian beam propagation through the nonstationary temperature field the complex geometric optics method was used. The influence of the refractive coefficient modulation by thermal wave on the complex ray phase, path, and amplitude was taken into account. It was assumed that for detection of the modulated Gaussian beam parameters two types of detector can be used: quadrant photodiodes or centroidal photodiodes. The influence of such parameters as the size and position of the Gaussian beam waist, the laser-screen (detector) distance, the thermal wave beam position and width, as well as thermal wave frequency and the distance between the probing optical beam axis and source of thermal waves on the so-called normal signal was taken into account.
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam
Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu
2016-01-01
We introduce a method for modulating the Gaussian beam by means of sine-azimuthal wavefront and carry out the experimental generation. The analytical propagation formula of such a beam passing through a paraxial ABCD optical system is derived, by which the intensity properties of the sine-azimuthal wavefront modulated Gaussian (SWMG) beam are examined both theoretically and experimentally. Both of the experimental and theoretical results show that the SWMG beam goes through the process from beam splitting to a Gaussian-like profile, which is closely determined by the phase factor and the propagation distance. Appropriate phase factor and short distance are helpful for the splitting of beam. However, in the cases of large phase factor and focal plane, the intensity distributions tend to take a Gaussian form. Such unique features may be of importance in particle trapping and medical applications. PMID:27443798
Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures.
Gao, Yanqi; Zhu, Baoqiang; Liu, Daizhong; Lin, Zunqi
2009-07-20
A general model for different apertures and flat-topped laser beams based on the multi-Gaussian function is developed. The general analytical expression for the propagation of a flat-topped beam through a general double-lens system with apertures is derived using the above model. Then, the propagation characteristics of the flat-topped beam through a spatial filter are investigated by using a simplified analytical expression. Based on the Fluence beam contrast and the Fill factor, the influences of a pinhole size on the propagation of the flat-topped multi-Gaussian beam (FMGB) through the spatial filter are illustrated. An analytical expression for the propagation of the FMGB through the spatial filter with a misaligned pinhole is presented, and the influences of the pinhole offset are evaluated.
Anupriya, J.; Ram, Nibedita; Pattabiraman, M.
2010-04-15
We describe a computational and experimental study on Hanle electromagnetically induced transparency and absorption resonance line shapes with a Laguerre Gaussian (LG) beam. It is seen that the LG beam profile brings about a significant narrowing in the line shape of the Hanle resonance and ground-state Zeeman coherence in comparison to a Gaussian beam. This narrowing is attributed to the azimuthal mode index of the LG field.
Davydovskaya, V V; Shepelevich, V V; Matusevich, V; Kisling, A; Kovarshik, R
2010-12-09
Propagation and interaction of orthogonally polarised two-dimensional super-Gaussian light beams is studied theoretically in a 4mm-symmetry photorefractive crystal in the drift regime when the external electric field is applied to the crystal in the direction of the optical axis. The output beams displaced with respect to each other in directions parallel and perpendicular to the direction of the external electric field strength vector are considered. It is shown that an auxiliary light beam polarised orthogonally to the fundamental light beam makes it possible to carry out efficiently address localisation of the fundamental beam propagating in a quasi-soliton regime. The crystal thicknesses are found, which are optimal from the viewpoint of maximisation of the fundamental light beam deviation. It is shown that 'square' super-Gaussian beams in the near-field diffraction region are focused at smaller values of the external electric field than those of the Gaussian beams. (nonlinear optical phenomena)
Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
Lukin, Igor P
2016-04-20
The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
NASA Astrophysics Data System (ADS)
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
Gaussian Confinement in a Jkj Decay Model
NASA Astrophysics Data System (ADS)
da Silva, Mario L. L.; Hadjimichef, Dimiter; Vasconcellos, Cesar A. Z.
In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.
Analytical structure of the TE and TM terms of paraxial Gaussian beam in the near field
NASA Astrophysics Data System (ADS)
Zhou, Guoquan; Zhu, Kaicheng; Liu, Fengqin
2007-08-01
The description of paraxial Gaussian beam is directly started from the Maxwell's equations. According to the vector plane wave spectrum representation of Maxwell's equations and the vectorial structure of electromagnetic beam, the analytical TE and TM terms of paraxial Gaussian beam are presented by means of mathematical techniques in the near field. The influence of linearly polarized angle on the components of the TE and TM terms is investigated. The structural light intensities are depicted in the near field. As the vectorial structures are not orthogonal in the near field, there is a crossed light intensity in the paraxial Gaussian beam. This research reveals the abundant internal structure of paraxial Gaussian beam in the near field.
Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere.
Zhou, Guoquan
2011-02-28
The propagation of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a higher-order cosh-Gaussian in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere are also examined in detail.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Video compressive sensing using Gaussian mixture models.
Yang, Jianbo; Yuan, Xin; Liao, Xuejun; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2014-11-01
A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.
Waveform synthesis of surface waves in a laterally heterogeneous earth by the Gaussian beam method
NASA Technical Reports Server (NTRS)
Yomogida, K.; Aki, K.
1985-01-01
The present investigation is concerned with an application of the Gaussian beam method to surface waves in the laterally heterogeneous earth. The employed method has been developed for ray tracing and synthesizing seismograms of surface waves in cases involving the laterally heterogeneous earth. The procedure is based on formulations derived by Yomogida (1985). Vertical structure of the wave field is represented by the eigenfunctions of normal mode theory, while lateral variation is expressed by the parabolic equation as in two-dimensional acoustic waves or elastic body waves. It is demonstrated that a large-amplitude change can result from a slight perturbation in the phase velocity model.
Gaussian versus flat-top spatial beam profiles for optical stimulation of the prostate nerves
NASA Astrophysics Data System (ADS)
Tozburun, Serhat; Lagoda, Gwen A.; Burnett, Arthur L.; Fried, Nathaniel M.
2010-02-01
The cavernous nerves (CN) course along the prostate surface and are responsible for erectile function. Improved identification and preservation of the CN's is critical to maintaining sexual potency after prostate cancer surgery. Noncontact optical nerve stimulation (ONS) of the CN's was recently demonstrated in a rat model, in vivo, as a potential alternative to electrical nerve stimulation (ENS) for identification of the CN's during prostate surgery. However, the therapeutic window for ONS is narrow, so optimal design of the fiber optic delivery system is critical for safe, reproducible stimulation. This study describes modeling, assembly, and testing of an ONS probe for delivering a small, collimated, flat-top laser beam for uniform CN stimulation. A direct comparison of the magnitude and response time of the intracavernosal pressure (ICP) for both Gaussian and flat-top spatial beam profiles was performed. Thulium fiber laser radiation (λ=1870 nm) was delivered through a 200-μm fiber, with distal fiber tip chemically etched to convert a Gaussian to flat-top beam profile. The laser beam was collimated to a 1-mm-diameter spot using an aspheric lens. Computer simulations of light propagation were used to optimize the probe design. The 10-Fr (3.4-mm-OD) laparoscopic probe provided a constant radiant exposure at the CN surface. The probe was tested in four rats, in vivo. ONS of the CN's was performed with a 1-mm-diameter spot, 5-ms pulse duration, and pulse rate of 20 Hz for a duration of 15-30 s. The flat-top laser beam profile consistently produced a faster and higher ICP response at a lower radiant exposure than the Gaussian beam profile due, in part, to easier alignment of the more uniform beam with nerve. The threshold for ONS was approximately 0.14 J/cm2, corresponding to a temperature increase of 6-8°C at the CN surface after a stimulation time of 15 s. With further development, ONS may be used as a diagnostic tool for identification of CN's during prostate
Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence.
Xu, Huafeng; Cui, Zhifeng; Qu, Jun
2011-10-24
The analytical formulas for the average intensity and the beam width of the elegant Laguerre-Gaussian beam (ELGB) in non-Kolmogorov turbulence have been derived based on the extended Huygens-Fresnel principle. Numerical results reveal that the ELGB converts to Gaussian form quicker for smaller values of beam order and for smaller wavelengths. The root-mean-square (rms) beam width of ELGB increases markedly with the propagation distance for higher beam order, smaller waist width, and larger wavelength. Furthermore, discussions of the influence of ELGB by the non-Kolmogorov turbulence reveal that the normalized intensity distribution of ELGB converts into Gaussian form more quickly and that the rms beam width of ELGB increases more rapidly in non-Kolmogorov turbulence with smaller parameter α, larger outer scale, smaller inner scale and larger structure constant.
Average spreading of a radial gaussian beam array in non-Kolmogorov turbulence.
Tang, Hua; Ou, Baolin; Luo, Bin; Guo, Hong; Dang, Anhong
2011-06-01
The analytical expression for the rms beam width of the radial gaussian beam array propagating in non-Kolmogorov turbulence is derived, where the coherent combination is considered. The influences of the beam number, the generalized exponent, and the ring radius on the rms beam width are investigated. The results indicate that the rms beam width depends greatly on the generalized exponent and the beam number. Further, an optimum ring radius, which leads to a minimum beam width, is proved to exist within a certain traveling distance and the optimum ring radius increases when the beam number increases.
Scattering by a spheroidal particle illuminated with a couple of on-axis Gaussian beams
NASA Astrophysics Data System (ADS)
Wang, Haihua; Sun, Xianming; Zhang, Huayong
2012-07-01
An on-axis Gaussian beam for any angle of incidence is expanded in terms of the spheroidal vector wave functions. With such an expansion, the problem of interaction between a couple of on-axis Gaussian beams and a spheroidal particle is studied in the framework of the generalized Lorenz-Mie theory (GLMT). The scattering characteristics are described in detail, and numerical results of the normalized differential scattering cross section are presented.
Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.
Eyyuboğlu, Halil Tanyer
2005-08-01
Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.
Generalised Hermite-Gaussian beams and mode transformations
NASA Astrophysics Data System (ADS)
Wang, Yi; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-05-01
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function α, which can be used to unite conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function α. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.
Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.
Mitri, Farid G
2015-10-01
Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation. PMID:26470046
Propagation properties of quantized Laguerre-Gaussian beams in atmospheric turbulence
NASA Astrophysics Data System (ADS)
Saito, Aya; Tanabe, Ayano; Kurihara, Makoto; Hashimoto, Nobuyuki; Ogawa, Kayo
2016-03-01
Effect of scintillations is serious problems in optical systems which require the atmospheric propagation, the optimization of optical system to minimize the effects of scintillation have been examined using the simulation of propagation in atmospheric turbulence. The analytic studies of scintillation index of LG beams show that LG beams have less scintillation than Gaussian beams. However, in these researches, the diameter of receiving aperture was set as point receiver without considering the effects of aperture averaging, which is phenomenon that reduced scintillations over finite aperture. In this paper, considering size of a receiving aperture, the propagation losses and the scintillation index of LG beams are simulated. Also, for practical applications, propagation properties of "quantized" LG(5,1) beams simulated. As a result of the examination, the propagation losses and the scintillation index of LG beams is smaller than those of Gaussian beams. By applying LG beams for optical wireless communications, it is expected to improve better the effect of scintillations than using Gaussian beams. The result is that the scintillation index of quantized LG beams is equal to those of LG beams, and it suggested that quantized LG beams can be treat the quantized LG beams the same as LG beams.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : {mathbb{Z}^2tomathbb{Z}}} a probability proportional to {exp(-β mathcal{H}(η))}, where {β} is the inverse-temperature and {mathcal{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Lloglog L}}. The key is a large deviation estimate for the height at the origin in {mathbb{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
Xiao, Xifeng; Voelz, David G; Toselli, Italo; Korotkova, Olga
2016-05-20
Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.
NASA Astrophysics Data System (ADS)
Ruffato, G.; Carli, M.; Massari, M.; Romanato, F.
2015-03-01
The work of design, fabrication and characterization of spiral phase plates for the generation of Laguerre-Gaussian (LG) beams with non-null radial index is presented. Samples were fabricated by electron beam lithography on polymethylmethacrylate layers over glass substrates. The optical response of these phase optical elements was measured and the purity of the experimental beams was investigated in terms of Laguerre-Gaussian modes contributions. The farfield intensity pattern was compared with theoretical models and numerical simulations, while the expected phase features were confirmed by interferometric analyses. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order Laguerre-Gaussian beams. A novel application consisting in the design of computer-generated holograms encoding information for light beams carrying phase singularities is shown. A numerical code based on iterative Fourier transform algorithm has been developed for the computation of the phase pattern of phase-only diffractive optical element for illumination under LG beams. Numerical analysis and preliminary experimental results confirm the applicability of these devices as high-security optical elements.
Scattering of a focused Laguerre-Gaussian beam by a spheroidal particle
NASA Astrophysics Data System (ADS)
Jiang, Yuesong; Shao, Yuwei; Qu, Xiaosheng; Ou, Jun; Hua, Houqiang
2012-12-01
A focused Laguerre-Gaussian beam scattered by a homogeneous prolate spheroidal particle is studied for on-axis incidence. An approach to expanding a focused Laguerre-Gaussian beam in terms of the spheroidal wavefunctions in spheroidal coordinates is presented. By using the localized approximations method, the beam-shape coefficients are evaluated and the results agree with the cases of on-axis incidence. Calculations of the far-field scattering intensity are performed to study the shaped beam scattered by a spheroid, which has different size parameters and eccentricities.
Procedures for the measurement of the extinction cross section of one particle using a Gaussian beam
NASA Astrophysics Data System (ADS)
Bosch, Salvador; Sancho-Parramon, Jordi
2016-09-01
Two procedures for the measurement of the extinction cross section (ECS) of one particle using a slightly focused Gaussian beam have been introduced and numerically tested. While the first one relies on previously introduced ideas and has close connection with the optical theorem, the second procedure is new and is mostly related with light measurements where the detector collects much of the energy of the incident beam. Both procedures prove to be valid and somehow complementary up to particle sizes of the order of the beam waist, thus enlarging the capability of simple measurement set-ups based on Gaussian beams for the estimation of the ECS of one particle.
High-energy flat-top beams for laser launching using a Gaussian mirror.
Fujiwara, Hiroki; Brown, Kathryn E; Dlott, Dana D
2010-07-01
Converting a Gaussian to a flat-top beam is useful for many applications including laser-launched thin-foil flyer plates. A flat-top beam is needed to maintain a constant launch velocity across the flyer; otherwise, the flyer can disintegrate in flight. Here we discuss and demonstrate the use of a variable reflectivity mirror (VRM) with a Gaussian reflectivity profile with an additional hard aperture and compare it to a refractive beam shaper. An ideal VRM would generate a flat-top beam with 37% efficiency. Readily available high-power Gaussian or super-Gaussian mirrors create an approximate flat-top profile, but there is a trade-off between flatness and efficiency. We show that a super-Gaussian mirror can, in principle, convert an input Gaussian beam with 30% efficiency to a flat-top beam with 3% (maximum-to-minimum) variation. With a Gaussian mirror and a high-energy pulsed Nd:YAG laser having relatively poor beam quality, we generate flat-top beams with 25% conversion efficiency having 6% variation (standard deviation sigma=4.2%). The beams are used to launch 400 microm diameter, 25 microm thick Al flyer plates, whose flight was monitored by a high-speed displacement interferometer. The plates flew across a 300 microm gap at 1.3 km/s. The distribution of arrival times at the witness plate was 5 ns, as determined by the rise time of the impact emission. Compared to a total flight time of 260 ns, the velocity spread of different parts of the flyer plate was 2%.
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
NASA Technical Reports Server (NTRS)
Steely, Sidney L.
1993-01-01
The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.
Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium
NASA Astrophysics Data System (ADS)
Chen, Bo; Chen, Chidao; Peng, Xi; Peng, Yulian; Zhou, Meiling; Deng, Dongmei; Guo, Hong
2016-05-01
Nonlinear optical phenomena are of great practical interest in optics. The evolution of ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium is investigated using the nonlinear Schrödinger equation. Numerical simulations indicate that the distribution factor b can influence the formation of the ring Airy Gaussian beams. Results show that the beams can be oscillating, and the light filament can be achieved under appropriate laser input power. On the other hand, the evolution of the ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium can be implemented, and the numerical simulations of the holographic generation of the ring Airy Gaussian vortex beams propagated in the medium demonstrate that the vortex can be preserved along the propagation. The Poynting vector shows that the energy flow of the ring Airy Gaussian beams flows in the opposite direction on both sides of the focus plane; however, for beams with a spiral phase, the flow direction remains the same; the energy flow can rotate in opposite directions on both sides of the focal plane.
Propagation and self-healing ability of a Bessel-Gaussian beam modulated by Bessel gratings
NASA Astrophysics Data System (ADS)
Qiao, Chunhong; Feng, Xiaoxing; Chu, Xiuxiang
2016-04-01
A new type of Bessel-like beam which can be generated by using Bessel gratings to modulate the amplitude and phase of a Bessel beam is proposed. In analogy to study a Bessel beam in free space, the intensity evolution and self-healing property of the Bessel-like beam have been studied. Meanwhile, based on the Fresnel diffraction integral, the propagation of the Bessel-like beam in free space has also been investigated. Results show that the Bessel-like beam and the Bessel-Gaussian-like beams have some special and interesting properties.
Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.
Zhai, Chao; Tan, Liying; Yu, Siyuan; Ma, Jing
2015-06-15
Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.
Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan
2016-06-27
We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power. PMID:27410594
Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams.
Naik, Dinesh N; Pradeep Chakravarthy, T; Viswanathan, Nirmal K
2016-04-20
We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.
Stable propagation of non-Gaussian beams in a multiple-pass cell.
Takasaki, T; Suda, A; Sato, K; Nagasaka, K; Tashiro, H
1997-05-20
To apply annular output beams emitted from an unstable resonator to a multiple-pass cell (MPC) for Raman conversion, we studied the mode-matching condition of non-Gaussian beams to a MPC using beam propagation analysis based on Laguerre-Gaussian functions. During transits of the MPC, the radial profile of an annular beam changes between annular and Airy patterns. Although such behavior indicates that it is impossible to achieve complete mode matching of an annular beam, we found a quasi-mode-matching condition under which the variation of beam size was minimized. The above theoretical analysis was verified experimentally using a CO(2) laser beam prepared for a para-hydrogen Raman laser. PMID:18253356
Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams.
Naik, Dinesh N; Pradeep Chakravarthy, T; Viswanathan, Nirmal K
2016-04-20
We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section. PMID:27140138
Second-harmonic generation excited by a rotating Laguerre-Gaussian beam
Petrov, Dmitri
2010-09-15
Experimental data demonstrate that unlike linear optical processes, an optical Laguerre-Gaussian beam of frequency {omega}, with topological charge m, rotating with angular frequency {Omega}<<{omega}, may not be considered as a monochromatic beam with the shifted frequency {omega}+m{Omega} (Doppler angular shift) for the second-harmonic generation nonlinear process.
Contribution of longitudinal electric field of a gaussian beam to second harmonic generation
NASA Astrophysics Data System (ADS)
Mishra, S. R.; Rustagi, K. C.
1990-01-01
A laser beam with a nonuniform transverse intensity profile necessarily has a longitudinal component of the electric field. We show that a detectable second harmonic can be generated due to coupling of this longitudinal component with the transverse field of a gaussian beam in a configuration in which second harmonic generation is forbidden for plane wave interaction.
Device and method for creating Gaussian aberration-corrected electron beams
McMorran, Benjamin; Linck, Martin
2016-01-19
Electron beam phase gratings have phase profiles that produce a diffracted beam having a Gaussian or other selected intensity profile. Phase profiles can also be selected to correct or compensate electron lens aberrations. Typically, a low diffraction order produces a suitable phase profile, and other orders are discarded.
Zavalin, Andre; Yang, Junhai; Haase, Andreas; Holle, Armin; Caprioli, Richard
2014-06-01
We have investigated the use of a Gaussian beam laser for MALDI Imaging Mass Spectrometry to provide a precisely defined laser spot of 5 μm diameter on target using a commercial MALDI TOF instrument originally designed to produce a 20 μm diameter laser beam spot at its smallest setting. A Gaussian beam laser was installed in the instrument in combination with an aspheric focusing lens. This ion source produced sharp ion images at 5 μm spatial resolution with signals of high intensity as shown for images from thin tissue sections of mouse brain.
NASA Astrophysics Data System (ADS)
Zavalin, Andre; Yang, Junhai; Haase, Andreas; Holle, Armin; Caprioli, Richard
2014-06-01
We have investigated the use of a Gaussian beam laser for MALDI Imaging Mass Spectrometry to provide a precisely defined laser spot of 5 μm diameter on target using a commercial MALDI TOF instrument originally designed to produce a 20 μm diameter laser beam spot at its smallest setting. A Gaussian beam laser was installed in the instrument in combination with an aspheric focusing lens. This ion source produced sharp ion images at 5 μm spatial resolution with signals of high intensity as shown for images from thin tissue sections of mouse brain.
Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram
NASA Astrophysics Data System (ADS)
Lu, Yang; Jiang, Bo; Lü, Shuchao; Liu, Yongqi; Li, Shasha; Cao, Zheng; Qi, Xinyuan
2016-03-01
We generate various kinds of arrays of Gaussian vortex, Bessel and Airy beams, respectively, with digital phase holograms (DPH) based on the fractional-Talbot effect by using the phase-only spatial light modulator (SLM). The linear and nonlinear transmissions of these beam arrays in strontium barium niobate (SBN) crystal are investigated numerically and experimentally. Compared with Gaussian vortex arrays, Bessel and Airy beam arrays can keep their patterns unchanged in over 20 mm, realizing non-diffracting transmission. The Fourier spectra (far-field diffraction patterns) of the lattices are also studied. The experimental results are in good agreement with the numerical simulations.
Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam
NASA Astrophysics Data System (ADS)
F, Boufalah; L, Dalil-Essakali; H, Nebdi; A, Belafhal
2016-06-01
The propagation characteristics of the Pearcey–Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.
Distributed static linear Gaussian models using consensus.
Belanovic, Pavle; Valcarcel Macua, Sergio; Zazo, Santiago
2012-10-01
Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance trade-off.
Fraunhofer diffraction of Laguerre-Gaussian laser beam by helical axicon
NASA Astrophysics Data System (ADS)
Topuzoski, S.
2014-11-01
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with “0” radial mode number and “l” azimuthal mode number (LG0l) by helical axicon. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the back focal plane of a convergent lens are derived in a form of product of a Gauss-doughnut function and a sum of hypergeometric Kummer functions. Also, the diffracted LG beam by axicon only, as well as by spiral phase plate only, and the diffracted Gaussian beam by helical axicon, are described mathematically in the back focal plane of a convergent lens. Different possibilities for obtaining output vortex beam with reduced or increased topological charge compared to that of the incident beam, or for obtaining chargeless beam are analyzed.
Interaction of Airy-Gaussian beams in saturable media
NASA Astrophysics Data System (ADS)
Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei
2016-08-01
Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.
Interaction of Airy–Gaussian beams in saturable media
NASA Astrophysics Data System (ADS)
Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei
2016-08-01
Based on the nonlinear Schrödinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.
Irradiance scintillation for Gaussian-beam wave propagating through weak non-Kolmogorov turbulence.
Cui, Linyan; Xue, Bindang; Cao, Lei; Zheng, Shiling; Xue, Wenfang; Bai, Xiangzhi; Cao, Xiaoguang; Zhou, Fugen
2011-08-29
Kolmogorov turbulence theory based models cannot be directly applied in non-Kolmogorov turbulence case, which has been reported recently by increasing experimental evidence and theoretical investigation. In this study, based on the generalized von Karman spectral model, the theoretical expression of the irradiance scintillation index is derived for Gaussian-beam wave propagating through weak non-Kolmogorov turbulence with horizontal path. In the derivation, the expression is divided into two parts for physical analysis purpose and mathematical analysis convenience. This expression considers the influences of finite turbulence inner and outer scales and has a general spectral power law value in the range 3 to 4 instead of standard power law value of 11/3 (for Kolmogorov turbulence). Numerical simulations are conducted to investigate the influences.
Cheng, Mingjian; Guo, Lixin; Zhang, Yixin
2015-12-14
Analytic expression of the receiver-aperture-averaged scintillation index (SI) was derived for Gaussian-beam waves propagating through non-Kolmogorov maritime atmospheric environment by establishing a generalized maritime atmospheric spectrum model. The error performance of an intensity-modulated and direct-detection (IM/DD) free-space optical (FSO) system was investigated using the derived SI and log-normal distribution. The combined effects of non-Kolmogorov power-law exponent, turbulence inner scale, structure parameter, propagation distance, receiver aperture, and wavelength were also evaluated. Results show that inner scale and power-law exponent obviously affect SI. Large wavelength and receiver aperture can mitigate the effects of turbulence. The proposed model can be evaluated ship-to-ship/shore FSO system performance.
NASA Astrophysics Data System (ADS)
Gardner, Judd Steven
1999-10-01
Optical proximity sensing is often used in industry and the commercial realm to provide a system with information it may use in some decision making process. The applications for optical proximity sensing have changed and expanded over the years, and has presented a continually increased demand for higher accuracy. In order to satisfy this demand, new optical techniques have been established which have provided more precise proximity data than ever before, e.g. Atomic Force Microscopy and Photothermal Detection. To accommodate the increase in sensing precision, the precision of the mathematical models used to predict the behavior of the optical scheme must also increase. The particular interest pursued in this dissertation involves the detection of the change in the position of a beam due to some phenomena, e.g. Photothermal Deflection or Atomic Force Microscopy. The deflection of the beam in these cases may be on the order of microradians, and too small to detect with ordinary means. To remedy this, a reflecting cylinder is strategically positioned to reflect the incident deflected beam and, by the cylinder geometry, the reflected beam from the cylinder shows an increased deflection angle compared to the incident beam. If the optical scheme has been designed successfully, the resulting deflection of the reflected beam will be large enough to be detected by a sensor. In order to predict the optical behavior of an incident deflected beam reflected from a cylinder, three mathematical methods, Geometrical Optics, Physical Optics, and an Exact Formulation rigorously based on Maxwell's equations are employed. From these methods, a Geometrical Optics solution, two Physical Optics solutions, and an Exact solution are obtained and compared to demonstrate the accuracy of these mathematical models to predict the electric field behavior of a beam reflected from a cylinder. In all cases a Gaussian, well focused beam is used. The near, transitional, and far zones are considered
Chaitanya, N Apurv; Jabir, M V; Banerji, J; Samanta, G K
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625
NASA Astrophysics Data System (ADS)
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-09-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma
Misra, Shikha; Mishra, S. K.
2008-09-15
In this communication the authors have investigated the focusing of a ring ripple on a Gaussian electromagnetic beam propagating in a plasma, considering each of the three kinds of basic nonlinearities, namely, ponderomotive, collisional, and relativistic. In this analysis, the electric field profile of the propagating beam is assumed to be composed of the radial electric field distribution of the Gaussian beam as well as that of the ring ripple; a paraxial like approach has been adopted to analyze the characteristics of the propagation. Thus, one considers a unique dielectric function for the beam propagation and a radial field sensitive diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple. Further, the variation of the phase associated with the beam on account of the r independent terms in the eikonal has also been accounted for.
S., Juan Manuel Franco; Cywiak, Moises; Cywiak, David; Mourad, Idir
2015-06-24
A homodyne profiler is used for recording the intensity distribution of focused non-truncated Gaussian beams. The spatial distributions are obtained at planes in the vicinity of the back-focal plane of a focusing lens placed at different distances from a He–Ne laser beam with a Gaussian intensity profile. Comparisons of the experimental data with those obtained from the analytical equations for an ideal focusing lens allow us to propose formulae to fine-tune the quadratic term in the Fresnel Gaussian shape invariant at each interface of the propagated field. Furthermore, we give analytical expressions to calculate adequately the propagation of the field through an optical system.
Kuo, Hung-Fei; Frederick
2014-04-01
Optical scatterometry has attracted extensive interest in extracting the geometric shape information of nanolithography patterns because of the trend of shrinking device size and complicated stack structure. RCWA is the numerical algorithm implemented in the current scatterometry tool to calculate the diffraction efficiency. However, the known weakness for the RCWA method is the analysis of metallic gratings illuminated by the TM wave. This research applies the FDTD method using the Gaussian beam excitation source to analyze the diffraction efficiency of HKMG gratings for the use in the optical scatterometry and verifies the numerical diffraction efficiency discrepancy between the Gaussian beam and plane wave excitation methods. The numerical study is carried out with the line/space nanolithography patterns on the HKMG process stacks at 45 nm node technology. The nanolithography patterns are modeled as 1-D surface relief gratings. The 0th order diffraction efficiency is analyzed as a function of CDs, SWAs, incident angles and pitches of the gratings. The study presents the impact of the polarizations of the incident waves on the diffraction efficiency. In addition, this research investigates the phase of the 0th diffraction order as a function of the SWAs and illustrates the corresponding SWA parameter effect on the phase distribution. This research suggests the minimum beam radius to converge the numerical diffraction efficiency using Gaussian beam excitation to it using the plan wave.
Acoustic radiation force on a double-layer microsphere by a Gaussian focused beam
NASA Astrophysics Data System (ADS)
Wu, Rongrong; Cheng, Kaixuan; Liu, Xiaozhou; Liu, Jiehui; Mao, Yiwei; Gong, Xiufen
2014-10-01
A new model for calculating the radiation force on double-layer microsphere is proposed based on the ray acoustics approach. The axial acoustic radiation force resulting from a focused Gaussian beam incident on spherical shells immersed in water is examined theoretically in relation to its thickness and the contents of its double-layer. The attenuation both in the water and inside the sphere is considered in this method, which cannot be ignored while the high frequency ultrasonic is used. Results of numerical calculations are presented for fat and low density polyethylene materials, with the hollow region filled with animal oil, water, or air. These results show how the acoustic impedance and the sound velocity of both layers, together with the thickness of the shell, affect the acoustic radiation force.
Acoustic radiation force on a double-layer microsphere by a Gaussian focused beam
Wu, Rongrong; Cheng, Kaixuan; Liu, Jiehui; Mao, Yiwei; Gong, Xiufen; Liu, Xiaozhou
2014-10-14
A new model for calculating the radiation force on double-layer microsphere is proposed based on the ray acoustics approach. The axial acoustic radiation force resulting from a focused Gaussian beam incident on spherical shells immersed in water is examined theoretically in relation to its thickness and the contents of its double-layer. The attenuation both in the water and inside the sphere is considered in this method, which cannot be ignored while the high frequency ultrasonic is used. Results of numerical calculations are presented for fat and low density polyethylene materials, with the hollow region filled with animal oil, water, or air. These results show how the acoustic impedance and the sound velocity of both layers, together with the thickness of the shell, affect the acoustic radiation force.
Characterization of saturable absorbers using an open-aperture Gaussian-beam Z scan
Gu Bing; Fan Yaxian; Wang Jin; Chen Jing; Ding Jianping; Wang Huitian; Guo Bin
2006-06-15
We present a theoretical investigation on the open-aperture Gaussian-beam Z-scan technique for two dominant saturable absorption models, by using the Adomian decomposition method. Analytic expressions of the Z-scan traces are deduced for a cw laser and a pulsed laser, respectively; in particular, for performable simulations, the optimal sum upper limit is found. We give an experimental demonstration, in which a side-chain azobenzene polymer poly [6-[1-(4-(4-nitrophenylazo)phenyl) piperazine] hexyl methacrylate] (Pda) film behaves as a test sample. The results manifest that our theory is reasonable and the Pda film is a good saturable absorber at the wavelength of 532 nm.
NASA Astrophysics Data System (ADS)
Liu, Jianfeng; Gong, Jinhui; Liu, Kan; Zhang, Xinyu; Xie, Changsheng
2011-11-01
A special software is constructed effectively for reconstructing the fine phase distribution of the diffracted Gaussian laser beams in the terahertz frequency range, according to common diffraction theory. The fine surface microrelief patterns of the elements, which originate from the simple patterns in photomask and further etched onto the surface of {100}- oriented silicon wafer by a low cost and rapid method, are created by the software above according to the phase distribution designed. Being different with the traditional silicon diffractive lenses fabricated by multiple level processes, the elements produced by the method introduced by us can transfer common Gaussian beams into desired images through created fine patterns over the surface of the elements. Two typical type of diffractive elements, which are used to transform common Gaussian laser beams in terahertz frequency into highly focused spot or so-called common focus, and the desired figure of the "umber one", are designed and fabricated. For testing the element, the LASER SIEIR 50 of Coherent Company is used to generate common Gaussian laser beams (the diameter of the beams is 10mm), and the PYROCAM THERE of Spiricon Company is also used to display the images acquired. Experimental results show that the elements can be used to form needed light fields and expected images, respectively.
Focusing of Gaussian beam passed under small angle to optical axis of uniaxial crystal
NASA Astrophysics Data System (ADS)
Ivanov, M. O.; Shostka, N. V.
2016-07-01
We showed both experimentally and analytically, the effect of focusing of a Gaussian beam propagated under small angle ϕ with respect to the optical axis of a uniaxial crystal, on the generation of a bottle beam. At ϕ = 0° two foci that correspond to ordinary and extraordinary parts of a beam form a closed 3D structure of a bottle beam. At this point, the beam, in the foci points, has radially and azimuthally aligned polarizations. Increasing the value of ϕ leads to dramatic changes in the intensity and polarization structure of a bottle beam. Starting from the value of ϕ = ±2° the closed 3D symmetric structure of a bottle beam breaks down. At ϕ = ±5° both beams are focused at the same transverse plane, while its polarization evolves to x- and y-linear. With a further increase in angle ϕ two foci ‘switch’ their spatial positions and move further away.
Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes.
Mahon, Ronan J; Murphy, J Anthony
2013-02-01
The Laguerre-Gaussian (LG) beam expansion is described as a numerical and physical model of paraxial ultrashort pulse diffraction in the time domain. An overview of the dynamics of higher-order ultrashort planar LG modes is given through numerical simulations, and the finite width of these beams is shown to induce a dispersive-like axial broadening of the fields, which creates related variations in the on-axis amplitude of such pulses. The propagation of a pulsed plane wave scattered at an aperture is then illustrated as a finite weighted sum of individual planar LG pulses, which allows for intuitive illustration of the convergence of this expansion technique. By applying such an expansion to diffraction at a hard aperture, the planar pulsed LG beams are described as the paraxial analogs of the Bessel boundary waves typically observed in such situations, with both exhibiting superluminal group velocities along the optical axis. Numerical results of pulse diffraction at an aperture highlight the suitability of the LG expansion method for efficient and practical simulation of ultrashort fields in the paraxial regime.
Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams
Lloyd, David T.; O’Keeffe, Kevin; Anderson, Patrick N.; Hooker, Simon M.
2016-01-01
High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial coherence induced by both variation of the intensity-dependent dipole phase as well as finite spatial coherence of the driving radiation. These findings are used to suggest ways in which the coherence of harmonic beams could be increased further, which would have direct benefits to imaging with high-harmonic radiation. PMID:27465654
2-D Gaussian beam imaging of multicomponent seismic data in anisotropic media
NASA Astrophysics Data System (ADS)
Protasov, M. I.
2015-12-01
An approach for true-amplitude seismic beam imaging of multicomponent seismic data in 2-D anisotropic elastic media is presented and discussed. Here, the recovered true-amplitude function is a scattering potential. This approach is a migration procedure based on the weighted summation of pre-stack data. The true-amplitude weights are computed by applying Gaussian beams (GBs). We shoot a pair of properly chosen GBs with a fixed dip and opening angles from the current imaging point towards an acquisition system. This pair of beams is used to compute a true-amplitude selective image of a rapid velocity variation. The total true-amplitude image is constructed by superimposing selective images computed for a range of available dip angles. The global regularity of the GBs allows one to disregard whether a ray field is regular or irregular. P- and S-wave GBs can be used to handle raw multicomponent data without separating the waves. The use of anisotropic GBs allows one to take into account the anisotropy of the background model.
Transverse superresolution technique involving rectified Laguerre-Gaussian LG(p)⁰ beams.
Cagniot, Emmanuel; Fromager, Michael; Godin, Thomas; Passilly, Nicolas; Aït-Ameur, Kamel
2011-08-01
A promising technique has been proposed recently [Opt. Commun. 284, 1331 (2011), Opt. Commun. 284, 4107 (2011)] for breaking the diffraction limit of light. This technique consists of transforming a symmetrical Laguerre-Gaussian LG(p)⁰ beam into a near-Gaussian beam at the focal plane of a thin converging lens thanks to a binary diffractive optical element (DOE) having a transmittance alternatively equal to -1 or +1, transversely. The effect of the DOE is to convert the alternately out-of-phase rings of the LG(p)⁰ beam into a unified phase front. The benefits of the rectified beam at the lens focal plane are a short Rayleigh range, which is very useful for many laser applications, and a focal volume much smaller than that obtained with a Gaussian beam. In this paper, we demonstrate numerically that the central lobe's radius of the rectified beam at the lens focal plane depends exclusively on the dimensionless radial intensity vanishing factor of the incident beam. Consequently, this value can be easily predicted.
NASA Astrophysics Data System (ADS)
Xu, Lu; Yu, Lianghong; Liang, Xiaoyan
2016-04-01
We present for the first time a scheme to amplify a Laguerre-Gaussian vortex beam based on non-collinear optical parametric chirped pulse amplification (OPCPA). In addition, a three-dimensional numerical model of non-collinear optical parametric amplification was deduced in the frequency domain, in which the effects of non-collinear configuration, temporal and spatial walk-off, group-velocity dispersion and diffraction were also taken into account, to trace the dynamics of the Laguerre-Gaussian vortex beam and investigate its critical parameters in the non-collinear OPCPA process. Based on the numerical simulation results, the scheme shows promise for implementation in a relativistic twisted laser pulse system, which will diversify the light-matter interaction field.
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2016-10-01
Based on the angular spectrum decomposition method (ASDM), a nonparaxial solution for the Hermite-Gaussian (HG m ) light-sheet beam of any order m is derived. The beam-shape coefficients (BSCs) are expressed in a compact form and computed using the standard Simpson’s rule for numerical integration. Subsequently, the analysis is extended to evaluate the longitudinal and transverse radiation forces as well as the spin torque on an absorptive dielectric cylindrical particle in 2D without any restriction to a specific range of frequencies. The dynamics of the cylindrical particle are also examined based on Newton’s second law of motion. The numerical results show that a Rayleigh or Mie cylindrical particle can be trapped, pulled or propelled in the optical field depending on its initial position in the cross-sectional plane of the HG m light-sheet. Moreover, negative or positive axial spin torques can arise depending on the choice of the non-dimensional size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the location of the absorptive cylinder in the beam. This means that the HG m light-sheet beam can induce clockwise or anti-clockwise rotations depending on its shift from the center of the cylinder. In addition, individual vortex behavior can arise in the cross-sectional plane of wave propagation. The present analysis presents an analytical model to predict the optical radiation forces and torque induced by a HG m light-sheet beam on an absorptive cylinder for applications in optical light-sheet tweezers, optical micro-machines, particle manipulation and opto-fluidics to name a few areas of research.
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
Sharma, Prerana
2015-07-31
This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.
Tang, Haibo; Chen, Lixiang; She, Weilong
2010-11-22
We present in this paper a wave coupling theory of linear electro-optic (EO) effect for quasi-phase matched (QPM) of focused Gaussian beam in an optical superlattice (OSL). The numerical results indicate that, due to the EO effect of an appropriate applied electric field, the output beam will form spatially inhomogeneous polarization, changing continuously in transverse section of beam; the confocal parameter has a significant impact on the output polarization of Gaussian beam and determines the half-wave voltage.
Terahertz generation by mixing of two super-Gaussian laser beams in collisional plasma
NASA Astrophysics Data System (ADS)
Singh, Divya; Malik, Hitendra K.
2014-08-01
Considering a realistic situation, where electron-neutral collisions persist in plasma, analytical calculations are carried out for the Terahertz (THz) radiation generation by beating of two Super-Gaussian (SG) lasers of index p. The competency of these lasers over Gaussian lasers is discussed in detail with respect to the effects of collision and beam width on the THz field amplitude and efficiency of the mechanism. A critical transverse distance of the peak of the THz field is defined that shows a dependence on the index of SG lasers. Although electron-neutral collisions and larger beam width lead to the drastic reduction in the THz field when the SG lasers are used in the plasma, the efficiency of the mechanism remains much larger than the case of Gaussian lasers. Moreover, the higher index SG lasers produce stronger and focused THz radiation.
Terahertz generation by mixing of two super-Gaussian laser beams in collisional plasma
Singh, Divya; Malik, Hitendra K. E-mail: hkmalik@physics.iitd.ac.in
2014-08-15
Considering a realistic situation, where electron-neutral collisions persist in plasma, analytical calculations are carried out for the Terahertz (THz) radiation generation by beating of two Super-Gaussian (SG) lasers of index p. The competency of these lasers over Gaussian lasers is discussed in detail with respect to the effects of collision and beam width on the THz field amplitude and efficiency of the mechanism. A critical transverse distance of the peak of the THz field is defined that shows a dependence on the index of SG lasers. Although electron-neutral collisions and larger beam width lead to the drastic reduction in the THz field when the SG lasers are used in the plasma, the efficiency of the mechanism remains much larger than the case of Gaussian lasers. Moreover, the higher index SG lasers produce stronger and focused THz radiation.
Saturation of fluorescence in flames with a Gaussian laser beam
NASA Technical Reports Server (NTRS)
Daily, J. W.
1978-01-01
The method of saturated fluorescence for measuring species concentrations in flames is usually performed with laser beams that do not provide a constant intensity distribution across the focal volume. Because of the intensity distribution across the beam, the fluorescence signal does not depend on laser power or intensity in the same manner as for uniform illumination. This leads to anomolous apparent saturation intensities. In the following, the effect is considered for atomic fluorescence. Relations for the fluorescence signal under two common excitation geometries are derived and uncertainty relations used to consider the benefits of high laser intensity.
Power deposited by a Gaussian beam on a decentered circular aperture
NASA Astrophysics Data System (ADS)
Barbeau, Nicolas R.
1995-10-01
An expression for the energy or power deposited by a Gaussian beam on a decentered circular aperture is derived. It represents a generalization of the classic laser-beam truncation problem, with applications in the areas of laser scanning, detection theory, lidar, free-space communications, and so on. In addition, it can be used to quantify the effect of alignment errors on laser systems.
Direct measurement of an electric field in femtosecond Bessel-Gaussian beams.
Gilbertson, Steve; Feng, Ximao; Khan, Sabih; Chini, Michael; Wang, He; Mashiko, Hiroki; Chang, Zenghu
2009-08-15
We demonstrated the mapping of the spatial oscillation of electric fields in the transverse plane of a femtosecond Bessel-Gaussian laser beam from the first principle of classical electrodynamics. An attosecond burst of electrons for probing the electric force was placed in the Bessel beam through photoemission with single isolated 276 as extreme ultraviolet pulses. The direction reversal of the electric field in adjacent Bessel rings was directly confirmed by observing the momentum shift of the probe electrons.
Focal shift for a gaussian beam by an aperture written in terms of matrix optics
NASA Astrophysics Data System (ADS)
Lu, Xuanhui; Wang, Shaomin; Ronchi, Laura
1992-05-01
The focal shift in a gaussian beam focussed by an optical system with an aperture is generalized by applying Collin's diffraction integral. By this implementation, the field distribution on axis is given. The method may be useful to determine the focal shift of a thin lens and of an optical focusing system as well.
Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam
Stallard, B.W.; Makowski, M.A.; Byers, J.A.
1992-05-19
An optical converter for efficient conversion of millimeter wavelength whispering-gallery gyrotron output into a linearly polarized, free-space Gaussian-like beam is described. The converter uses a mode-converting taper and three mirror optics. The first mirror has an azimuthal tilt to eliminate the k[sub [phi
On the reconstruction of parameters of quasi-Gaussian pump beams during transient SBS
Dementjev, Aleksandr S; Kosenko, E K; Murauskas, E; Girdauskas, V
2006-08-31
The radii and radii of curvature of Stokes stimulated Brillouin scattering (SBS) beams are measured by the method of moments for smooth nearly Gaussian focused pump beams with the propagation ratio M{sup 2}{sub {sigma}p{<=}}1.2. It is shown that in the case of sufficiently deeply focused pump radiation, the propagation ratio M{sup 2}{sub {sigma}S} of Stokes beams near the threshold of the transient SBS is smaller than M{sup 2}{sub {sigma}p} and approaches it with increasing the pump pulse energy. It is also found that the radii of Stokes beams at the output from a nonlinear medium are smaller than the radii of pump beams, while the radii of wave-front curvature are close (in modulus) to the radii of wave-front curvature for pump beams. (laser beams)
A comparative study of Gaussian geostatistical models and Gaussian Markov random field models1
Song, Hae-Ryoung; Fuentes, Montserrat; Ghosh, Sujit
2008-01-01
Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GM-RFs) are two distinct approaches commonly used in spatial models for modeling point referenced and areal data, respectively. In this paper, the relations between GGMs and GMRFs are explored based on approximations of GMRFs by GGMs, and approximations of GGMs by GMRFs. Two new metrics of approximation are proposed: (i) the Kullback-Leibler discrepancy of spectral densities and (ii) the chi-squared distance between spectral densities. The distances between the spectral density functions of GGMs and GMRFs measured by these metrics are minimized to obtain the approximations of GGMs and GMRFs. The proposed methodologies are validated through several empirical studies. We compare the performance of our approach to other methods based on covariance functions, in terms of the average mean squared prediction error and also the computational time. A spatial analysis of a dataset on PM2.5 collected in California is presented to illustrate the proposed method. PMID:19337581
NASA Astrophysics Data System (ADS)
Yeliseyev, Oleg A.
2013-07-01
This paper investigates the dispersion of a three-dimensional Gaussian wave beam on a two-dimensional periodic array of short-circuited waveguides with a beveled (nonrectangular) grid in the autocollimation mode. The correlation of reflection rates in terms of the power and the length of the short-circuited waveguides has been estimated for specular and non-specular beams. The relationship between the directional pattern of the reflected beam in the far field and the array and incident beam parameters has been investigated. Three-dimensional directional patterns have been designed in terms of the power of specular and non-specular beams in the far field. Energy characteristics and three-dimensional directional patterns have been obtained for the non-specular beam in the far field. A new algorithm for analyzing three-dimensional problems of scattering of linearly polarized wave beams on two-dimensional periodic structures is proposed. This algorithm allows the investigation of wave beams with arbitrary field distributions over the cross-section. The case of oblique incidence of a linearly polarized Gaussian wave beam on a two-dimensional periodic structure is considered. A reflective array with short rectangular waveguides is chosen as the structure. The beam pattern transformation of the scattered beam in the far field is investigated. The effects of narrowing of the beam pattern and distortion of the reflected beam pattern are detected. A physical explanation of these effects is offered. The results are presented in the form of two-dimensional and three-dimensional patterns of the scattered field of the beam in the far field.
Scintillation index and bit error rate of hollow Gaussian beams in atmospheric turbulence
NASA Astrophysics Data System (ADS)
Qiao, Na; Zhang, Bin; Pan, Pingping; Dan, Youquan
2011-06-01
Based on the Huygens-Fresnel principle and Rytov method, the on-axis scintillation index is derived for hollow Gaussian beams (HGBs) in weak turbulence. The relationship between bit error rate (BER) and scintillation index is found by only considering the effect of atmosphere turbulence based on the probability distribution of intensity fluctuation, and the expression of the BER is obtained. Furthermore, the scintillation and the BER properties of HGBs in turbulence are discussed in detail. The results show that the scintillation index and BER of HGBs depend on the propagation length, the structure constant of the refractive index fluctuations of turbulence, the wavelength, the beam order and the waist width of the fundamental Gaussian beam. The scintillation index, increasing with the propagation length in turbulence, for the HGB with higher beam order increases more slowly. The BER of the HGBs increases rapidly against the propagation length in turbulence. For propagating the same distance, the BER of the fundamental Gaussian beam is the greatest, and that of the HGB with higher order is smaller.
Gaussian beams for a linearized cold plasma confined in a torus
NASA Astrophysics Data System (ADS)
Cardinali, A.; Dobrokhotov, S. Yu.; Klevin, A.; Tirozzi, B.
2016-04-01
We consider a system of linear pde describing a cold plasma in a toroidal region in three-dimensional space. This system simulates the passage of a laser beam through the TOKAMAK, it consists of 9 equations for the electric field and the velocities of electrons and ions in a given magnetic field. Asymptotic solutions describing high-frequency Gaussian beams are constructed using the theory of Maslov complex germ in a fairly effective form. The solutions of the system are localized in the neighborhood of the beam passing through the toroidal domain (the camera). The equations for a ray take into account the density of particles in the camera and don't ``feel'' the presence of the magnetic field because of the high frequency of the Gaussian beam; the dependence on the magnetic field is contained in the amplitude of the electric field. Before the TOKAMAK camera the amplitude of the Gaussian beam is the same as in free space, but after the camera the amplitude vector rotates under the influence of the magnetic field. The formula for the angle of rotation is given explicitly. An analytical-numerical algorithm based on the asymptotic solutions is used to analyze the parameters of the magnetic field in the TOKAMAK.
Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization.
Sumaya-Martinez, J; Mata-Mendez, O; Chavez-Rivas, F
2003-05-01
A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions. PMID:12747430
Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media
NASA Astrophysics Data System (ADS)
Chen, Chidao; Peng, Xi; Chen, Bo; Peng, Yulian; Zhou, Meiling; Yang, Xiangbo; Deng, Dongmei
2016-05-01
We investigate the propagation of an Airy-Gaussian vortex (AiGV) beam in free space and Kerr media. It is interesting to see that the beam will perform self-healing and main lobe focusing both in free space and Kerr media when the vortex locates at the center of the plane. By controlling the number of the topological charge, the beam distribution factor χ 0 and the position of the vortex, we can control the intensity distribution of the AiGV beam in the out plane both in free space and Kerr media. It is found that when the vortex is close to the center of the plane, it has a strong effect on the intensity distribution of the beam. When the beam propagates in the number of the topological charge, the partial collapse will take place even with low initial input power. We find that the main lobe focusing contributes to this partial collapse.
Generating a Bessel-Gaussian beam for the application in optical engineering
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-01-01
Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology. PMID:26690264
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
NASA Astrophysics Data System (ADS)
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Enhanced thermal self-focusing of a Gaussian laser beam in a collisionless plasma
Gupta, Devki Nandan; Suk, Hyyong
2011-12-15
Theory given by Wang-Zhou [Phys. Plasmas 18, 043101 (2011)] for the thermal self-focusing of a Gaussian laser beam in a collisionless plasma is revisited by including the effect of a localized upward plasma-density ramp. As the equilibrium electron density is an increasing function of the distance of propagation of the laser beam, the diffraction length decreases rapidly as the beam penetrates deeper into the plasma and the diffraction effect becomes reduced; thus, the laser becomes more focused. A significant enhancement in laser thermal self-focusing in a collisionless plasma is consequently observed if a localized plasma density ramp is introduced.
Spin-controlled orbital motion in tightly focused high-order Laguerre-Gaussian beams.
Cao, Yongyin; Zhu, Tongtong; Lv, Haiyi; Ding, Weiqiang
2016-02-22
Spin angular momentum can contribute to both optical force and torque exerted on spheres. Orbit rate of spheres located in tightly focused LG beams with the same azimuthal mode index l is spin-controlled due to spin-orbit coupling. Laguerre-Gaussian beams with high-order azimuthal mode are used here to study the orbit rate of dielectric spheres. Orbit rates of spheres with varying sizes and refravtive indices are investigated as well as optical forces acting on spheres in LG beams with different azimuthal modes. These results would be much helpful to investigation on optical rotation and transfer of spin and orbital angular momentum. PMID:26906996
Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam
Stallard, Barry W.; Makowski, Michael A.; Byers, Jack A.
1992-01-01
An optical converter for efficient conversion of millimeter wavelength whispering-gallery gyrotron output into a linearly polarized, free-space Gaussian-like beam. The converter uses a mode-converting taper and three mirror optics. The first mirror has an azimuthal tilt to eliminate the k.sub..phi. component of the propagation vector of the gyrotron output beam. The second mirror has a twist reflector to linearly polarize the beam. The third mirror has a constant phase surface so the converter output is in phase.
Zhou, Guoquan; Cai, Yangjian; Chu, Xiuxiang
2012-04-23
The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams.
Gaussian mixture models as flux prediction method for central receivers
NASA Astrophysics Data System (ADS)
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
NASA Astrophysics Data System (ADS)
Li, Ye; Zhang, Yixin; Wang, Donglin; Shan, Lei; Xia, Mingchao; Zhao, Yuanhang
2016-05-01
The effects of strong turbulence on the orbital angular momentum (OAM) states of infrared and non-diffraction beam propagation in a terrestrial atmosphere are investigated. A new probability density model for OAM states of Bessel-Gaussian-Schell beam in the paraxial and strong turbulent channel is modeled based on the modified Rytov approximation. We find that the normalization energy weight of signal OAM modes at each OAM level is approximate equivalence in strong turbulence regime, one can constitute multiple mode channels by choosing OAM modes with large energy level difference between modes to reduce mode interference, and one can utilize BGS beam with OAM modes increasing the channel capacity of optical communications.
Strong terahertz generation by optical rectification of a super-Gaussian laser beam
NASA Astrophysics Data System (ADS)
Kumar, Subodh; Kishor Singh, Ram; Sharma, R. P.
2016-06-01
Terahertz (THz) generation by optical rectification of a laser beam having spatially super-Gaussian and temporally Gaussian intensity profile is investigated when it is propagating in a pre-formed rippled density plasma. The quasi-static ponderomotive force which is generated due to the variation in intensity of laser pulse leads to a nonlinear current density in the direction transverse to the direction of propagation which drives a radiation. The frequency of this radiation falls in the THz range if the pulse duration of the laser is chosen suitably. The density ripple provides the phase matching. The yield of generated THz has been compared when the phase matching is exact and when there is slight mismatch of phases. The variation in the intensity of the generated THz with the index of super-Gaussian pulse has also been studied.
Investigation of Anderson localization in disordered heterostructures irradiated by a Gaussian beam
NASA Astrophysics Data System (ADS)
Ardakani, Abbas Ghasempour
2016-02-01
The propagation of a Gaussian beam through a one-dimensional disordered media is studied. By employing the transfer matrix method, the localization length as a function of frequency is calculated for different values of transverse coordinate r. It is demonstrated that the localization length significantly depends on r in different frequency ranges. This result is in contrast to those reported for a plane wave incident on disordered structures in which the localization length is transversely constant. For some frequency regions, the peak of localization length is red-shifted and becomes smaller with increasing the transverse coordinate. At some frequencies, the system is in the localized state for particular values of r, while at other r values the system is in the extend regime at the same frequencies. It is observed that the quality of localization at each frequency depends on r. To quantify the localization behavior of the whole Gaussian beam, a modified localization length is defined in terms of the input and output powers of the Gaussian beam where the dependence of Anderson localization on the transverse coordinate is considered. It is suggested that this modified localization length is used in experiments performed for study of wave propagation in one-dimensional random media under illumination of laser beams.
Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma
Jafari Milani, M. R.; Niknam, A. R.; Farahbod, A. H.
2014-06-15
The propagation characteristics of a Gaussian laser beam through warm collisional plasma are investigated by considering the ponderomotive force nonlinearity and the complex eikonal function. By introducing the dielectric permittivity of warm unmagnetized plasma and using the WKB and paraxial ray approximations, the coupled differential equations defining the variations of laser beam parameters are obtained and solved numerically. Effects of laser and plasma parameters such as the collision frequency, the initial laser intensity and its spot size on the beam width parameter and the axis laser intensity distribution are analyzed. It is shown that, self-focusing of the laser beam takes place faster by increasing the collision frequency and initial laser spot size and then after some distance propagation the laser beam abruptly loses its initial diameter and vastly diverges. Furthermore, the modified electron density distribution is obtained and the collision frequency effect on this distribution is studied.
Self-Focusing/Defocusing of Chirped Gaussian Laser Beam in Collisional Plasma with Linear Absorption
NASA Astrophysics Data System (ADS)
Wani, Manzoor Ahmad; Kant, Niti
2016-09-01
This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma. Supported by a financial grant from CSIR, New Delhi, India, under Project No. 03(1277)/13/EMR-II
Design and performance of a refractive optical system that converts a Gaussian to a flattop beam.
Hoffnagle, J A; Jefferson, C M
2000-10-20
A system of two aspheric lenses is described, which efficiently converts a collimated Gaussian beam to a flattop beam. Departing from earlier designs, both aspheric surfaces were convex, simplifying their fabrication; the output beam was designed with a continuous roll-off, allowing control of the far-field diffraction pattern; and diffraction from the entrance and exit apertures was held to a negligible level. The design principles are discussed in detail, and the performance of the as-built optics is compared quantitatively with the theoretical design. Approximately 78% of the incident power is enclosed in a region with 5% rms power variation. The 8-mm-diameter beam propagates approximately 0.5 m without significant change in the intensity profile; when the beam is expanded to 32 mm in diameter, this range increases to several meters.
Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis
2013-02-01
Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.
Negative refraction and backward wave in pseudochiral mediums: illustrations of Gaussian beams.
Chern, Ruey-Lin; Chang, Po-Han
2013-02-11
We investigate the phenomena of negative refraction and backward wave in pseudochiral mediums, with illustrations of Gaussian beams. Due to symmetry breaking intrinsic in pseudochiral mediums, there exist two elliptically polarized eigenwaves with different wave vectors. As the chirality parameter increases from zero, the two waves begin to split from each other. For a wave incident from vacuum onto a pseudochiral medium, negative refraction may occur for the right-handed wave, whereas backward wave may appear for the left-handed wave. These features are illustrated with Gaussian beams based on Fourier integral formulations for the incident, reflected, and transmitted waves. Negative refraction and backward wave are manifest, respectively, on the energy flow in space and wavefront movement in time.
Phase-only shaping algorithm for Gaussian-apodized Bessel beams.
Durfee, Charles G; Gemmer, John; Moloney, Jerome V
2013-07-01
Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly. PMID:23842364
Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis
2013-02-01
Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented. PMID:23385926
Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan
2016-04-01
The radial average-power distribution and normalized average power of orbital-angular-momentum (OAM) modes in a vortex Gaussian beam after passing through weak-to-strong atmospheric turbulence are theoretically formulated. Based on numerical calculations, the role of the intrinsic mode index, initial beam radius and turbulence strength in OAM-mode variations of a propagated vortex Gaussian beam is explored, and the validity of the pure-phase-perturbation approximation employed in existing theoretical studies is examined. Comparison between turbulence-induced OAM-mode scrambling of vortex Gaussian beams and that of either Laguerre-Gaussian (LG) beams or pure vortex beams has been made. Analysis shows that the normalized average power of OAM modes changes with increasing receiver-aperture size until it approaches a nearly stable value. For a receiver-aperture size of practical interest, OAM-mode scrambling is severer with a larger mode index or smaller initial beam radius besides stronger turbulence. Under moderate-to-strong turbulence condition, for two symmetrically-neighboring extrinsic OAM modes, the normalized average power of the one with an index closer to zero may be greater than that of the other one. The validity of the pure-phase-perturbation approximation is determined by the intrinsic mode index, initial beam radius and turbulence strength. It makes sense to jointly control the amplitude and phase of a fundamental Gaussian beam for producing an OAM-carrying beam.
Zhang, Xiaofeng; Song, Zhiguang; Chen, Dongmei; Zhang, Guangbin; Cao, Hui
2015-04-01
This paper focuses on studying the interaction between an acoustical Gaussian beam and cylindrical particles. Based on the finite series method, the Gaussian beam is expanded as cylindrical functions and the beam coefficient of a Gaussian beam is obtained. An expression for the acoustic radiation force function that is the radiation force per unit energy density and unit cross-sectional surface area for a cylinder in a Gaussian beam is presented. Numerical results for the radiation force function of a Gaussian beam are presented for rigid cylinders, liquid cylinders, elastic cylinders, and viscoelastic cylinders to illustrate the theory. The radiation force function versus the dimensionless frequency ka (where k is the wave number and a is the radius of the cylinder) are discussed for different beam waists. The simulation results show the differences from those of a plane wave when the beam waist w0≤5λ (where λ is the wave length). The beam waist has no effects on the radiation force function when ka<1, while the beam waist has greater effects when ka>1. The radiation force function reaches the plane wave limit when w0>5λ. The acoustic radiation force function is also determined by the parameters of the particles.
Gaussian Beam Scattering by a Spheroidal Particle with an Embedded Conducting Sphere
NASA Astrophysics Data System (ADS)
Yan, Bing; Zhang, Huayong; Liu, Chenhua
2011-01-01
A method is provided for calculating the scattering of Gaussian beam incident obliquely on a spheroidal particle with a conducting spherical inclusion within the framework of the generalized Lorenz-Mie theory (GLMT). By virtue of a transformation between the spheroidal and spherical vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.
Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center
NASA Astrophysics Data System (ADS)
Yan, Bing; Zhang, Huayong; Liu, Chenhua
2011-08-01
An analytic solution to electromagnetic scattering by a spheroidal particle having a spherical inclusion at the center, for oblique incidence of a Gaussian beam, is obtained within the framework of the generalized Lorenz-Mie theory (GLMT). By virtue of a transformation between the spheroidal and spherical vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are evaluated.
Scattering of Gaussian Beam by a Conducting Spheroidal Particle with Confocal Dielectric Coating
NASA Astrophysics Data System (ADS)
Sun, Xianming; Wang, Haihua; Zhang, Huayong
2010-09-01
An analytic solution to the scattering by a coated spheroidal particle, for arbitrary incidence of a Gaussian beam, is constructed by expanding the incident and scattered electromagnetic fields in terms of spheroidal vector wave functions. The unknown expansion coefficients are determined by a system of linear equations derived from the appropriate boundary conditions. Numerical results of the normalized differential scattering cross section of the conducting and coated spheroidal particle are evaluated, and the scattering characteristics are discussed concisely.
Wu, Xuecheng; Wu, Yingchun; Zhou, Binwu; Wang, Zhihua; Gao, Xiang; Gréhan, Gérard; Cen, Kefa
2013-07-20
We propose an asymmetric wavelet method to reconstruct a particle from a hologram illuminated by an elliptical, astigmatic Gaussian beam. The particle can be reconstructed by a convolution of the asymmetric wavelet and hologram. The reconstructed images have the same size and resolution as the recorded hologram; therefore, the reconstructed 3D field is convenient for automatic particle locating and sizing. The asymmetric wavelet method is validated by both simulated holograms of spherical particles and experimental holograms of opaque, nonspherical coal particles.
Gaussian beams for surface waves in laterally slowly-varying media
NASA Technical Reports Server (NTRS)
Yomogida, K.
1985-01-01
Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. The elastodynamic equations of motion in ray-centered coordinates are derived, and a laterally slowly-varying approximation for elastodynamic equations is obtained. Parabolic equations for Love and Rayleigh waves are studied and solved, and the properties of Gaussian beams of seismic surface waves are examined.
NASA Astrophysics Data System (ADS)
Li, Xinzhong; Tai, Yuping; Nie, Zhaogang; Wang, Hui; Li, Hehe; Wang, Jingge; Tang, Jie; Wang, Yishan
2015-12-01
We investigate the Fraunhofer diffraction of a Laguerre-Gaussian (LG) beam incident on a dynamic superposed dual-triangular aperture. The evolution of the diffraction pattern from this aperture is analyzed experimentally and theoretically. A special aperture, called the hex-star triangular aperture, demonstrates interesting diffraction patterns. Further, the diffraction properties of integer, half-integer, and fractional orders of topological charges at the Fraunhofer zone are studied by using the hex-star triangular aperture. This study can provide additional information to enhance the understanding of the diffraction properties of the LG beam transmitted through a complex aperture.
Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams
Alexandrescu, Adrian; Cojoc, Dan; Fabrizio, Enzo Di
2006-06-23
We derive the interaction Hamiltonian between a diatomic molecule and a Laguerre-Gaussian beam under the assumption of a small spread of the center of mass wave function of the molecule in comparison with the beam waist. Considering the dynamical variables of the center of mass, vibrational, rotational, and electronic motion, we show that, within the electronic dipole approximation, the orbital angular momentum of the field couples with the rotational and electronic motion. The changes in the transition probabilities and selection rules induced by the field orbital angular momentum and the applicability of the derived interaction mechanisms for polyatomic molecules are discussed.
Gaussian beam scattering from a dielectric cylinder, including the evanescent region.
Pawliuk, Peter; Yedlin, Matthew
2009-12-01
The scattering of a two-dimensional Gaussian beam from a homogeneous dielectric cylinder is analyzed using a plane-wave spectrum. Special attention is given to the computation of the evanescent field of the beam and its effect in the scattering. A comparison is made between the evanescent field in Cartesian coordinates and in cylindrical coordinates as a sum of cylindrical waves. The field given by the cylindrical wave equation is found to converge spatially as we include more Bessel modes. The evanescent field incident on the dielectric cylinder is found to cause radiating waves to form and propagate outward.
Kaur, Sukhdeep; Sharma, A. K.; Salih, Hyder A.
2009-04-15
Second harmonic generation of a right circularly polarized Gaussian electromagnetic beam in a magnetized plasma is investigated. The beam causes Ohmic heating of electrons and subsequent redistribution of the plasma, leading to self-defocusing. The radial density gradient, in conjunction with the oscillatory electron velocity, produces density oscillation at the wave frequency. The density oscillation beats with the oscillatory velocity to produce second harmonic current density, giving rise to resonant second harmonic radiation when the wave frequency is one-third of electron cyclotron frequency. The second harmonic field has azimuthal dependence as exp(i{theta}). The self-defocusing causes a reduction in the efficiency of harmonic generation.
Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium.
Zhao, Ruihuang; Deng, Fu; Yu, Weihao; Huang, Jiayao; Deng, Dongmei
2016-06-01
Propagation of Airy-Gaussian vortex (AiGV) beams through the gradient-index medium is investigated analytically and numerically with the transfer matrix method. Deriving the analytic expression of the AiGV beams based on the Huygens diffraction integral formula, we obtain the propagate path, intensity and phase distributions, and the Poynting vector of the first- and second-order AiGV beams, which propagate through the paraxial ABCD system. The ballistic trajectory is no longer conventional parabolic but trigonometric shapes in the gradient-index medium. Especially, the AiGV beams represent the singular behavior at the propagation path and the light intensity distribution. The phase distribution and the Poynting vector exhibit in reverse when the AiGV beams through the singularity. As the order increases, the main lobe of the AiGV beams is gradually overlapped by the vortex core. Further, the sidelobe weakens when the AiGV beams propagate nearly to the singularity. Additionally, the figure of the Poynting vector of the AiGV beams proves the direction of energy flow corresponding to the intensity distribution. The vortex of the second-order AiGV beams is larger, and the propagation velocity is faster than that of the first order. PMID:27409428
Effects of non-Kolmogorov turbulence on the spiral spectrum of Hypergeometric-Gaussian laser beams.
Zhu, Yun; Zhang, Licheng; Hu, Zhengda; Zhang, Yixin
2015-04-01
We study the effects of non-Kolmogorov turbulence on the orbital angular momentum (OAM) of Hypergeometric-Gaussian (HyGG) beams in a paraxial atmospheric link. The received power and crosstalk power of OAM states of the HyGG beams are established. It is found that the hollowness parameter of the HyGG beams plays an important role in the received power and crosstalk power. The larger values of hollowness parameter give rise to the higher received power and lower crosstalk power. The results also show that the smaller OAM quantum number and longer wavelength of the launch beam may lead to the higher received power and lower crosstalk power.
Scintillation reduction for combined Gaussian-vortex beam propagating through turbulent atmosphere
Berman, Gennady P; Gorshkov, V. N.; Torous, S. V.
2010-12-14
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams (PCBs), including the optical vortices, propagating in turbulent atmospheres, The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. A method for significantly reducing the SI, by averaging the signal at the detector over a set of PCBs, is described, This novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the SI is effectively suppressed without any high-frequency modulators.
Wang Ying; Yuan Chengxun; Gao Ruilin; Zhou Zhongxiang
2012-10-15
Theoretical investigations of a Gaussian laser beam propagating in relativistic plasmas have been performed with the WKB method and complex eikonal function. We consider the relativistic nonlinearity induced by intense laser beam, and present the relativistically generalized forms of the plasma frequency and electron collision frequency in plasmas. The coupled differential equations describing the propagation variations of laser beam are derived and numerically solved. The obtained simulation results present the similar variation tendency with experiments. By changing the plasma density, we theoretically analyze the feasibility of using a plasmas slab of a fixed thickness to compress the laser beam-width and acquire the focused laser intensity. The present work complements the relativistic correction of the electron collision frequency with reasonable derivations, promotes the theoretical approaching to experiments and provides effective instructions to the practical laser-plasma interactions.
Self-focusing and defocusing of Gaussian laser beams in plasmas with linear temperature ramp
Zhou Zhongxiang; Wang Ying; Yuan Chengxun; Du Yanwei
2011-07-15
The propagation characteristics of the Gaussian laser beam in plasmas in the presence of a linear electron temperature ramp have been investigated by taking the electron temperature as an individual variable. The ponderomotive force and collision have been considered as the mechanisms of nonlinearity. The second order differential equation of the dimensionless beam-width parameter has been acquired and solved with several initial electron temperatures and plus-minus temperature ramp parameters. The propagation regimes of laser beam are found to be sensitive with the selection of electron temperature. The linear temperature ramp breaks the stationary propagating mode and enhances the self-focusing or defocusing propagation properties. Results indicate the feasibility of extended propagation of focused laser beam in plasmas by modifying the electron temperature.
NASA Astrophysics Data System (ADS)
Habibi, M.; Ghamari, F.
2014-06-01
Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)].
NASA Astrophysics Data System (ADS)
Stilgoe, Alexander B.; Nieminen, Timo A.; Rubinsztein-Dunlop, Halina
2015-12-01
Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre-, Hermite- and Ince-Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light-matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter.
The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
NASA Astrophysics Data System (ADS)
Ferrando, A.; García-March, M. A.
2016-06-01
We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre-Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.
Moving target detection algorithm based on Gaussian mixture model
NASA Astrophysics Data System (ADS)
Wang, Zhihua; Kai, Du; Zhang, Xiandong
2013-07-01
In real-time video surveillance system, background noise and disturbance for the detection of moving objects will have a significant impact. The traditional Gaussian mixture model;GMM&;has strong adaptive various complex background ability, but slow convergence speed and vulnerable to illumination change influence. the paper proposes an improved moving target detection algorithm based on Gaussian mixture model which increase the convergence rate of foreground to the background model transformation and introducing the concept of the changing factors, through the three frame differential method solved light mutation problem. The results show that this algorithm can improve the accuracy of the moving object detection, and has good stability and real-time.
Two-Gaussian excitations model for the glass transition
NASA Astrophysics Data System (ADS)
Matyushov, Dmitry V.; Angell, C. A.
2005-07-01
We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between Tg and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.
Non-Gaussianities from the Standard Model Higgs
Simone, Andrea De; Perrier, Hideki; Riotto, Antonio E-mail: hideki.perrier@unige.ch
2013-01-01
We have recently proposed that the Standard Model Higgs might be responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In this paper we study the level of non-Gaussianity in the cosmological perturbations which are inevitably generated due to the non-linearities of the Standard Model Higgs potential. In particular, for the current central value of the top mass, we find that a future detection of non-Gaussianity would exclude the detection of tensor modes by the PLANCK satellite.
Philip, Geo M; Viswanathan, Nirmal K
2010-11-01
We report here the generation of a chain of three-dimensional (3-D) optical bottle beams by focusing a π-phase shifted multi-ring hollow Gaussian beam (HGB) using a lens with spherical aberration. The rings of the HGB of suitable radial (k(r)) and axial (k(z)) wave vectors are generated using a double-negative axicon chemically etched in the optical fiber tips. Moving the lens position with respect to the fiber tip results in variation of the semi-angle of the cones of wave vectors of the HGBs and their diameter, using which we demonstrate tunability in the size and the periodicity of the 3-D optical bottle beams over a wide range, from micrometers to millimeters. The propagation characteristics of the beams resulting from focusing of single- and multi-ring HGBs and resulting in a quasi-non-diffracting beam and a chain of 3-D optical bottle beams, respectively, are simulated using only the input beam parameters and are found to agree well with experimental results.
Scattering of an anisotropic sphere by an arbitrarily incident Hermite-Gaussian beam
NASA Astrophysics Data System (ADS)
Qu, Tan; Wu, Zhensen; Shang, Qingchao; Li, Zhengjun; Bai, Lu; Li, Haiying
2016-02-01
An analytic theory for the scattering of an off-axis Hermite-Gaussian (HG) beam obliquely incident on an anisotropic sphere is developed. Based on the complex-source-point method and coordinate rotation theory, a general expansion expression for an arbitrarily incident HG beam in terms of Spherical Vector Wave Functions (SVWFs) is derived, and its convergence is numerically discussed. By introducing the Fourier transformation, the internal field expressions of the anisotropic sphere are represented. With the continuous tangential boundary conditions applied, the unknown scattering coefficients are solved. The theory and code are verified from the comparisons between the degenerated cases using our theory and those in the references. Two eigenmodes inside the uniaxial anisotropic sphere are characterized. The influences of beam mode, oblique incident angles, permittivity and permeability tensors, and sphere radius on the scattered field are analyzed numerically. The scattering intensity distributions on uniaxial anisotropic sphere in xoz and yoz plane are enantiomorphous for on-axis oblique illumination.
Zhu, Kaicheng; Li, Shaoxin; Tang, Ying; Yu, Yan; Tang, Huiqin
2012-03-01
Based on the integral representation of Bessel function and the extended Huygens-Fresnel principle, an integral expression of the Wigner distribution function (WDF) for partially coherent Bessel-Gaussian beams (PBGBs) propagating through turbulent atmosphere has been obtained. Also, the analytical formulas of the M2-factor for PBGB propagation in such a medium have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations. The performed numerical results reveal that the M2-factor of a PBGB in turbulent atmosphere depends on the beam parameters of the initial input beam, the structure constants of the turbulent atmosphere, and the propagation distance. These results may be useful in long-distance optical communications in free space or in turbulent atmosphere.
Optical trapping by Laguerre-Gaussian beams: Far-field matching, equilibria, and dynamics
NASA Astrophysics Data System (ADS)
Kiselev, Alexei D.; Plutenko, Dmytro O.
2016-07-01
By using the method of far-field matching we obtain the far-field expressions for the optical (radiation) force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle and study the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. Numerical analysis is performed for both nonvortex and optical-vortex LG beams. For the purely azimuthal LG beams, the dynamics is found to be locally nonconservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). We also discuss effects related to the Mie resonances (maxima of the internal field Mie coefficients) that under certain conditions manifest themselves as the points changing the trapping properties of the particles.
Conservation relation of nonclassicality and entanglement for Gaussian states in a beam splitter
NASA Astrophysics Data System (ADS)
Ge, Wenchao; Tasgin, Mehmet Emre; Zubairy, M. Suhail
2015-11-01
We study the relation between single-mode nonclassicality and two-mode entanglement in a beam splitter. We show that single-mode nonclassicality (the entanglement potential) of incident light cannot be transformed into two-mode entanglement completely after a single beam splitter. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as an increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam splitters.
Wu, Yuqian; Zhang, Yixin; Zhu, Yun
2016-08-01
We studied Gaussian beams with three different partially coherent models, including the Gaussian-Schell model (GSM), Laguerre-Gaussian Schell model (LGSM), and Bessel-Gaussian Schell model (BGSM), propagating through oceanic turbulence. The expressions of average intensity, beam spreading, and beam wander for GSM, LGSM, and BGSM beams in the paraxial channel are derived. We make a contrast for the three models in numerical simulations and find that the GSM beam has smaller spreading than the others, and the LGSM beam needs longer propagation distance to transform into a well-like profile of average intensity than the BGSM beam in the same conditions. The salinity fluctuation has a greater contribution to the wander of LGSM and BGSM beams than that of the temperature fluctuation. Our results can be helpful in the design of an optical wireless communication link operating in oceanic environment. PMID:27505642
Wu, Yuqian; Zhang, Yixin; Zhu, Yun
2016-08-01
We studied Gaussian beams with three different partially coherent models, including the Gaussian-Schell model (GSM), Laguerre-Gaussian Schell model (LGSM), and Bessel-Gaussian Schell model (BGSM), propagating through oceanic turbulence. The expressions of average intensity, beam spreading, and beam wander for GSM, LGSM, and BGSM beams in the paraxial channel are derived. We make a contrast for the three models in numerical simulations and find that the GSM beam has smaller spreading than the others, and the LGSM beam needs longer propagation distance to transform into a well-like profile of average intensity than the BGSM beam in the same conditions. The salinity fluctuation has a greater contribution to the wander of LGSM and BGSM beams than that of the temperature fluctuation. Our results can be helpful in the design of an optical wireless communication link operating in oceanic environment.
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
NASA Astrophysics Data System (ADS)
Leung, Shingyu; Qian, Jianliang
2010-11-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Flores, J. Mauricio; Cywiak, Moises; Servin, Manuel; Juarez P, Lorenzo
2008-09-20
Recently, an interferometric profilometer based on the heterodyning of three Gaussian beams has been reported. This microscope interferometer, called a three Gaussian beam interferometer, has been used to profile high quality optical surfaces that exhibit constant reflectivity with high vertical resolution and lateral resolution near {lambda}. We report the use of this interferometer to measure the profiles of two commercially available optical surfaces for data storage, namely, the compact disk (CD-R) and the digital versatile disk (DVD-R). We include experimental results from a one-dimensional radial scan of these devices without data marks. The measurements are taken by placing the devices with the polycarbonate surface facing the probe beam of the interferometer. This microscope interferometer is unique when compared with other optical measuring instruments because it uses narrowband detection, filters out undesirable noisy signals, and because the amplitude of the output voltage signal is basically proportional to the local vertical height of the surface under test, thus detecting with high sensitivity. We show that the resulting profiles, measured with this interferometer across the polycarbonate layer, provide valuable information about the track profiles, making this interferometer a suitable tool for quality control of surface storage devices.
Bayesian Gaussian Copula Factor Models for Mixed Data
Murray, Jared S.; Dunson, David B.; Carin, Lawrence; Lucas, Joseph E.
2013-01-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.1 PMID:23990691
Bayesian Gaussian Copula Factor Models for Mixed Data.
Murray, Jared S; Dunson, David B; Carin, Lawrence; Lucas, Joseph E
2013-06-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.
Araujo, Marcos A. de; Silva, Rubens; Lima, Emerson de; Pereira, Daniel P.; Oliveira, Paulo C. de
2009-01-10
We revisited the well known Khosrofian and Garetz inversion algorithm [Appl. Opt.22, 3406-3410 (1983)APOPAI0003-6935] that was developed to analyze data obtained by the application of the traveling knife-edge technique. We have analyzed the approximated fitting function that was used for adjusting their experimental data and have found that it is not optimized to work with a full range of the experimentally-measured data. We have numerically calculated a new set of coefficients, which makes the approximated function suitable for a full experimental range, considerably improving the accuracy of the measurement of a radius of a focused Gaussian laser beam.
The influence of oceanic turbulence on the spectral properties of chirped Gaussian pulsed beam
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, Yaochuan; Wang, Guiqiu; Yin, Hongming; Wang, Jinren
2016-08-01
Based on the extended Huygens-Fresnel principle, the spectral behaviors of a chirped Gaussian pulsed beam propagating in oceanic turbulence are illustrated. The influence of the parameters of oceanic turbulence (the rate of dissipation of turbulent kinetic energy per unit mass of fluid, rate of dissipation of mean-square temperature, relative strength of temperature and salinity fluctuations), relative position parameter and propagation distance on the spectra shift is analysed and given by numerical examples. The research results have the potential application in underwater wireless laser communication and remote sensing.
Vectorial structure of helical hollow Gaussian beams in the far field
NASA Astrophysics Data System (ADS)
Tang, Huiqin; Li, Xuguang; Zhou, Guoquan; Zhu, Kaicheng
2009-02-01
The analytical vectorial structure of helical hollow Gaussian beam (HHGB) is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HHGB in the far-field, which is composed of TE term with the electric field transverse to the propagation axis, and TM term with the magnetic field transverse to the propagation axis, are demonstrated. The physics pictures of HHGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HHGB propagation.
NASA Astrophysics Data System (ADS)
Arkhipov, Ievgen I.; Peřina, Jan
2016-09-01
A method for revealing the covariance matrix of an unknown two-mode Gaussian state is given based on the interference with a reference twin beam whose covariance matrix is known. In the method, first- and second-order cross-correlation intensity moments are determined varying the overall phase of the reference twin beam.
Transversal symmetry breaking and axial spreading modification for gaussian optical beams
NASA Astrophysics Data System (ADS)
Araújo, Manoel P.; De Leo, Stefano; Lima, Marina
2016-03-01
For a long time, it was believed there was no reason to include the geometrical phase in studying the propagation of gaussian optical beams through dielectric blocks. This can be justified by the fact that the first-order term in the Taylor expansion of this phase is responsible for the lateral shift of the optical beam which is also predicted by ray optics. From this point of view, the geometrical phase can be seen as a purely auxiliary concept. In this paper, we show how the second-order term in the Taylor expansion accounts for the symmetry breaking of the transversal spatial distribution and acts as an axial spreading modifier. These new effects clearly show the importance of the geometrical phase in describing the correct behavior of light. To test our theoretical predictions, we briefly discuss a possible experimental implementation.
Angular spectrum and localized model of Davis-type beam.
Lock, James A
2013-03-01
The angular spectrum of the Davis fifth-order linearly polarized, dual, and symmetrized fields of a focused Gaussian laser beam is obtained. Since the original Davis fields are not an exact solution of the vector wave equation and Maxwell's equations, a beam remodeling procedure within the angular spectrum is described that produces an exact solution. The spherical multipole beam shape coefficients of the remodeled beam are then obtained, and it is shown that in the weak focusing limit they simplify to the localized model Gaussian beam shape coefficients for both on-axis and off-axis beams. The angular spectrum method is then applied to a transversely confined electromagnetic beam with arbitrary profile in the focal plane, and to a general zero-order Bessel beam.
Designing Multi-target Compound Libraries with Gaussian Process Models.
Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert
2016-05-01
We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design.
Designing Multi-target Compound Libraries with Gaussian Process Models.
Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert
2016-05-01
We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design. PMID:27492085
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating
Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings.
Janicijevic, Ljiljana; Topuzoski, Suzana
2008-11-01
Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.
Robust image reconstruction enhancement based on Gaussian mixture model estimation
NASA Astrophysics Data System (ADS)
Zhao, Fan; Zhao, Jian; Han, Xizhen; Wang, He; Liu, Bochao
2016-03-01
The low quality of an image is often characterized by low contrast and blurred edge details. Gradients have a direct relationship with image edge details. More specifically, the larger the gradients, the clearer the image details become. Robust image reconstruction enhancement based on Gaussian mixture model estimation is proposed here. First, image is transformed to its gradient domain, obtaining the gradient histogram. Second, the gradient histogram is estimated and extended using a Gaussian mixture model, and the predetermined function is constructed. Then, using histogram specification technology, the gradient field is enhanced with the constraint of the predetermined function. Finally, a matrix sine transform-based method is applied to reconstruct the enhanced image from the enhanced gradient field. Experimental results show that the proposed algorithm can effectively enhance different types of images such as medical image, aerial image, and visible image, providing high-quality image information for high-level processing.
Classifying gamma-ray bursts with Gaussian Mixture Model
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Bin; Yang, En-Bo; Choi, Chul-Sung; Chang, Heon-Young
2016-11-01
Using Gaussian Mixture Model (GMM) and expectation-maximization algorithm, we perform an analysis of time duration (T90) for Compton Gamma Ray Observatory (CGRO)/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts (GRBs). The T90 distributions of 298 redshift-known Swift/BAT GRBs have also been studied in both observer and rest frames. Bayesian information criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the CGRO/BATSE and Fermi/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the Swift/BAT bursts in the rest frame, which is consistent with some previous results. However, Swift GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of Swift/BAT.
Model for non-Gaussian intraday stock returns
NASA Astrophysics Data System (ADS)
Gerig, Austin; Vicente, Javier; Fuentes, Miguel A.
2009-12-01
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.
Mean-field fluid behavior of the Gaussian core model
NASA Astrophysics Data System (ADS)
Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
Stochastic model updating utilizing Bayesian approach and Gaussian process model
NASA Astrophysics Data System (ADS)
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
Generalized Penner model and the Gaussian beta ensemble
NASA Astrophysics Data System (ADS)
Chair, Noureddine
2014-01-01
In this paper, a new expression for the partition function of the generalized Penner model given by Goulden, Harer and Jackson is derived. The Penner and the orthogonal Penner partition functions are special cases of this formula. The parametrized Euler characteristic ξgs(γ) deduced from our expression of the partition function is shown to exhibit a contribution from the orbifold Euler characteristic of the moduli space of Riemann surfaces of genus g, with s punctures, for all parameters γ and g odd. The other contributions for g even are linear combinations of the Bernoulli polynomials at rational arguments. It turns out that the free energy coefficients of the generalized Penner model in the continuum limit, are identical to those coefficients in the large N expansion of the Gaussian β-ensemble. Moreover, the duality enjoyed by the generalized Penner model, is also the duality symmetry of the Gaussian β-ensemble. Finally, a shift in the 't Hooft coupling constant required by the refined topological string, would leave the Gaussian β-ensemble duality intact. This duality is identified with the remarkable duality of the c=1 string at radius R=β.
Utilizing Gaussian Markov random field properties of Bayesian animal models.
Steinsland, Ingelin; Jensen, Henrik
2010-09-01
In this article, we demonstrate how Gaussian Markov random field properties give large computational benefits and new opportunities for the Bayesian animal model. We make inference by computing the posteriors for important quantitative genetic variables. For the single-trait animal model, a nonsampling-based approximation is presented. For the multitrait model, we set up a robust and fast Markov chain Monte Carlo algorithm. The proposed methodology was used to analyze quantitative genetic properties of morphological traits of a wild house sparrow population. Results for single- and multitrait models were compared.
Patil, S. D.; Takale, M. V.
2014-06-15
Habibi and Ghamari have presented a Comment on our paper [Phys. Plasmas 20, 072703 (2013)] by examining quantum dielectric response in thermal quantum plasma. They have modeled the relativistic self-focusing of Gaussian laser beam in cold and warm quantum plasmas and reported that self-focusing length does not change in both situations. In this response, we have reached the following important conclusions about the comment itself.
NASA Astrophysics Data System (ADS)
Genovese, Mariangela; Napoli, Ettore; Petra, Nicola
2014-04-01
Background identification is a fundamental task in many video processing systems. The Gaussian Mixture Model is a background identification algorithm that models the pixel luminance with a mixture of K Gaussian distributions. The number of Gaussian distributions determines the accuracy of the background model and the computational complexity of the algorithm. This paper compares two hardware implementations of the Gaussian Mixture Model that use three and five Gaussians per pixel. A trade off analysis is carried out by evaluating the quality of the processed video sequences and the hardware performances. The circuits are implemented on FPGA by exploiting state of the art, hardware oriented, formulation of the Gaussian Mixture Model equations and by using truncated binary multipliers. The results suggest that the circuit that uses three Gaussian distributions provides video with good accuracy while requiring significant less resources than the option that uses five Gaussian distributions per pixel.
Tan, Liying; Zhai, Chao; Yu, Siyuan; Ma, Jing; Lu, Gaoyuan
2015-05-01
In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.
Nanda, Vikas; Kant, Niti
2014-07-15
The effect of plasma density ramp on self-focusing of cosh-Gaussian laser beam considering ponderomotive nonlinearity is analyzed using WKB and paraxial approximation. It is noticed that cosh-Gaussian laser beam focused earlier than Gaussian beam. The focusing and de-focusing nature of the cosh-Gaussian laser beam with decentered parameter, intensity parameter, magnetic field, and relative density parameter has been studied and strong self-focusing is reported. It is investigated that decentered parameter “b” plays a significant role for the self-focusing of the laser beam as for b=2.12, strong self-focusing is seen. Further, it is observed that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For b=2.12, with the increase in the value of magnetic field self-focusing effect, in case of extraordinary mode, becomes very strong under plasma density ramp. Present study may be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers. Moreover, plasma density ramp plays a vital role to enhance the self-focusing effect.
Two particle tracking and detection in a single Gaussian beam optical trap.
Praveen, P; Yogesha; Iyengar, Shruthi S; Bhattacharya, Sarbari; Ananthamurthy, Sharath
2016-01-20
We have studied in detail the situation wherein two microbeads are trapped axially in a single-beam Gaussian intensity profile optical trap. We find that the corner frequency extracted from a power spectral density analysis of intensity fluctuations recorded on a quadrant photodetector (QPD) is dependent on the detection scheme. Using forward- and backscattering detection schemes with single and two laser wavelengths along with computer simulations, we conclude that fluctuations detected in backscattering bear true position information of the bead encountered first in the beam propagation direction. Forward scattering, on the other hand, carries position information of both beads with substantial contribution from the bead encountered first along the beam propagation direction. Mie scattering analysis further reveals that the interference term from the scattering of the two beads contributes significantly to the signal, precluding the ability to resolve the positions of the individual beads in forward scattering. In QPD-based detection schemes, detection through backscattering, thereby, is imperative to track the true displacements of axially trapped microbeads for possible studies on light-mediated interbead interactions.
Two particle tracking and detection in a single Gaussian beam optical trap.
Praveen, P; Yogesha; Iyengar, Shruthi S; Bhattacharya, Sarbari; Ananthamurthy, Sharath
2016-01-20
We have studied in detail the situation wherein two microbeads are trapped axially in a single-beam Gaussian intensity profile optical trap. We find that the corner frequency extracted from a power spectral density analysis of intensity fluctuations recorded on a quadrant photodetector (QPD) is dependent on the detection scheme. Using forward- and backscattering detection schemes with single and two laser wavelengths along with computer simulations, we conclude that fluctuations detected in backscattering bear true position information of the bead encountered first in the beam propagation direction. Forward scattering, on the other hand, carries position information of both beads with substantial contribution from the bead encountered first along the beam propagation direction. Mie scattering analysis further reveals that the interference term from the scattering of the two beads contributes significantly to the signal, precluding the ability to resolve the positions of the individual beads in forward scattering. In QPD-based detection schemes, detection through backscattering, thereby, is imperative to track the true displacements of axially trapped microbeads for possible studies on light-mediated interbead interactions. PMID:26835934
Study of Gaussian and Bessel beam propagation using a new analytic approach
NASA Astrophysics Data System (ADS)
Dartora, C. A.; Nobrega, K. Z.
2012-03-01
The main feature of Bessel beams realized in practice is their ability to resist diffractive effects over distances exceeding the usual diffraction length. The theory and experimental demonstration of such waves can be traced back to the seminal work of Durnin and co-workers already in 1987. Despite that fact, to the best of our knowledge, the study of propagation of apertured Bessel beams found no solution in closed analytic form and it often leads to the numerical evaluation of diffraction integrals, which can be very awkward. In the context of paraxial optics, wave propagation in lossless media is described by an equation similar to the non-relativistic Schrödinger equation of quantum mechanics, but replacing the time t in quantum mechanics by the longitudinal coordinate z. Thus, the same mathematical methods can be employed in both cases. Using Bessel functions of the first kind as basis functions in a Hilbert space, here we present a new approach where it is possible to expand the optical wave field in a series, allowing to obtain analytic expressions for the propagation of any given initial field distribution. To demonstrate the robustness of the method two cases were taken into account: Gaussian and zeroth-order Bessel beam propagation.
Wu, Xuecheng; Wu, Yingchun; Yang, Jing; Wang, Zhihua; Zhou, Binwu; Gréhan, Gérard; Cen, Kefa
2013-05-20
Application of the modified convolution method to reconstruct digital inline holography of particle illuminated by an elliptical Gaussian beam is investigated. Based on the analysis on the formation of particle hologram using the Collins formula, the convolution method is modified to compensate the astigmatism by adding two scaling factors. Both simulated and experimental holograms of transparent droplets and opaque particles are used to test the algorithm, and the reconstructed images are compared with that using FRFT reconstruction. Results show that the modified convolution method can accurately reconstruct the particle image. This method has an advantage that the reconstructed images in different depth positions have the same size and resolution with the hologram. This work shows that digital inline holography has great potential in particle diagnostics in curvature containers.
Robust Point Set Registration Using Gaussian Mixture Models.
Jian, Bing; Vemuri, Baba C
2011-08-01
In this paper, we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers. The key idea of this registration framework is to represent the input point sets using Gaussian mixture models. Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We show that the popular iterative closest point (ICP) method [1] and several existing point set registration methods [2], [3], [4], [5], [6], [7] in the field are closely related and can be reinterpreted meaningfully in our general framework. Our instantiation of this general framework is based on the the L2 distance between two Gaussian mixtures, which has the closed-form expression and in turn leads to a computationally efficient registration algorithm. The resulting registration algorithm exhibits inherent statistical robustness, has an intuitive interpretation, and is simple to implement. We also provide theoretical and experimental comparisons with other robust methods for point set registration. PMID:21173443
Eckstein, Hans-Christoph; Zeitner, Uwe Detlef
2009-09-28
Unstable resonators show an intense discrimination of undesired higher order modes but a high beam quality cannot be obtained with conventional resonators composed of spherical mirrors. In the present paper we demonstrate the possibility to tailor the fundamental mode by inserting diffractive elements into the resonator to generate a desirable output beam profile even for unstable resonators. We show a concept to design such surface structured elements for customizing the amplitude shape of the outcoupled beam. Further we demonstrate the first experimental realization of an unstable diffractive resonator with a Gaussian shaped amplitude profile of the laser beam for a vertical external cavity surface emitting laser (VECSEL). PMID:19907524
Parameter Optimization for the Gaussian Model of Folded Proteins
NASA Astrophysics Data System (ADS)
Erman, Burak; Erkip, Albert
2000-03-01
Recently, we proposed an analytical model of protein folding (B. Erman, K. A. Dill, J. Chem. Phys, 112, 000, 2000) and showed that this model successfully approximates the known minimum energy configurations of two dimensional HP chains. All attractions (covalent and non-covalent) as well as repulsions were treated as if the monomer units interacted with each other through linear spring forces. Since the governing potential of the linear springs are derived from a Gaussian potential, the model is called the ''Gaussian Model''. The predicted conformations from the model for the hexamer and various 9mer sequences all lie on the square lattice, although the model does not contain information about the lattice structure. Results of predictions for chains with 20 or more monomers also agreed well with corresponding known minimum energy lattice structures. However, these predicted conformations did not lie exactly on the square lattice. In the present work, we treat the specific problem of optimizing the potentials (the strengths of the spring constants) so that the predictions are in better agreement with the known minimum energy structures.
NASA Astrophysics Data System (ADS)
Ibrahim, Hany L. S.; Wriedt, Thomas; Khaled, Elsayed Esam M.
2016-04-01
Scattering of an arbitrarily focused electromagnetic Gaussian beam by a chain cluster consisting of axisymmetric particles is presented. The illustrated technique in this paper combines the plane-waves spectrum method and the cluster T-matrix calculation technique. This combination provides a powerful mathematical and numerical tool to solve such types of scattering problems. Computed results are shown for different particles shapes in the cluster and for different beam focusing.
BEAMS3D Neutral Beam Injection Model
Lazerson, Samuel
2014-04-14
With the advent of applied 3D fi elds in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous velocity reduction, and pitch angle scattering are modeled with the ADAS atomic physics database [1]. Benchmark calculations are presented to validate the collisionless particle orbits, neutral beam injection model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.
Measure of the diffraction efficiency of a holographic grating created by two Gaussian beams.
Leclere, P; Renotte, Y; Lion, Y
1992-08-10
We present a methodology for analyzing the characteristics of a photosensitive material for holography. When two Gaussian beams of equal intensities are exactly superimposed on the recording material, the modulation of the interference pattern is equal to unity. When they are no longer exactly superimposed, this modulation varies from one to zero depending on the analyzed point. On the other hand, the modulation is constant in a direction that is perpendicular to the incident plane. Therefore it is possible to consider a complete analysis (point by point) of only one holographic grating to measure the diffraction efficiency eta at a given modulation versus exposure or for varying modulation (or beam ratio K) for a given exposure. We present the results that are obtained with an experimental setup that was devised for that purpose. From these measurements it was possible to extract various parameters such as refractive-index modulation of the photosensitive support. The tested recording materials consist of film of dichromated gelatin and films of dichromate polyvinyl alcohol. PMID:20725484
Automatic approaching method for atomic force microscope using a Gaussian laser beam.
Han, Cheolsu; Lee, Haiwon; Chung, Chung Choo
2009-07-01
In this paper, a criterion for a fast automatic approach method in conventional atomic force microscope is introduced. There are currently two approach methods: automatic and semiautomatic methods. However, neither of them provides a high approach speed to enable the avoidance of possible damage to tips or samples. Industrial atomic force microscope requires a high approach speed and good repeatability for inspecting a large volume. Recently, a rapid automatic engagement method was reported to improve the approach speed. However, there was no information on how to determine the safe distance. This lack of information increases the chance for damage to occur in calibrating optimal approach speed. In this paper, we show that the proposed criterion can be used for decision making in determining mode transitions from fast motion to slow motion. The criterion is calculated based on the average intensity of a Gaussian laser beam. The tip-sample distance where the average intensity becomes the maximum value is used for the criterion. We explain the effects of the beam spot size and the window size on the average intensity. From experimental results with an optical head used in a commercial atomic force microscope, we observed that the mean and standard deviation (of the distance at which intensity is the maximum for the 25 experiments) are 194.0 and 15.0 microm, respectively, for a rectangular cantilever (or 224.8 and 12.6 microm for a triangular cantilever). Numerical simulation and experimental results are in good agreement.
Generic inference of inflation models by local non-Gaussianity
NASA Astrophysics Data System (ADS)
Dorn, Sebastian; Ramirez, Erandy; Kunze, Kerstin E.; Hofmann, Stefan; Enßlin, Torsten A.
2014-05-01
The presence of multiple fields during inflation might seed a detectable amount of non-Gaussianity in the curvature perturbations, which in turn becomes observable in present data sets like the cosmic microwave background (CMB) or the large scale structure (LSS). Within this proceeding we present a fully analytic method to infer inflationary parameters from observations by exploiting higher-order statistics of the curvature perturbations. To keep this analyticity, and thereby to dispense with numerically expensive sampling techniques, a saddle-point approximation is introduced whose precision has been validated for a numerical toy example. Applied to real data, this approach might enable to discriminate among the still viable models of inflation.
Analyzing hyperspectral images into multiple subspaces using Gaussian mixture models
NASA Astrophysics Data System (ADS)
Spence, Clay D.
2016-05-01
I argue that the spectra in a hyperspectral datacube will usually lie in several low-dimensional subspaces, and that these subspaces are more easily estimated from the data than the endmembers. I present an algorithm for finding the subspaces. The algorithm fits the data with a Gaussian mixture model, in which the means and covariance matrices are parameterized in terms of the subspaces. The locations of materials can be inferred from the fit of library spectra to the subspaces. The algorithm can be modified to perform material detection. This has better performance than standard algorithms such as ACE, and runs in real time.
a Gaussian Process Based Multi-Person Interaction Model
NASA Astrophysics Data System (ADS)
Klinger, T.; Rottensteiner, F.; Heipke, C.
2016-06-01
Online multi-person tracking in image sequences is commonly guided by recursive filters, whose predictive models define the expected positions of future states. When a predictive model deviates too much from the true motion of a pedestrian, which is often the case in crowded scenes due to unpredicted accelerations, the data association is prone to fail. In this paper we propose a novel predictive model on the basis of Gaussian Process Regression. The model takes into account the motion of every tracked pedestrian in the scene and the prediction is executed with respect to the velocities of all interrelated persons. As shown by the experiments, the model is capable of yielding more plausible predictions even in the presence of mutual occlusions or missing measurements. The approach is evaluated on a publicly available benchmark and outperforms other state-of-the-art trackers.
Learning Gaussian mixture models with entropy-based criteria.
Penalver Benavent, Antonio; Escolano Ruiz, Francisco; Saez, Juan Manuel
2009-11-01
In this paper, we address the problem of estimating the parameters of Gaussian mixture models. Although the expectation-maximization (EM) algorithm yields the maximum-likelihood (ML) solution, its sensitivity to the selection of the starting parameters is well-known and it may converge to the boundary of the parameter space. Furthermore, the resulting mixture depends on the number of selected components, but the optimal number of kernels may be unknown beforehand. We introduce the use of the entropy of the probability density function (pdf) associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels. We propose two methods to approximate the entropy of each kernel and a modification of the classical EM algorithm in order to find the optimum number of components of the mixture. Moreover, we use two stopping criteria: a novel global mixture entropy-based criterion called Gaussianity deficiency (GD) and a minimum description length (MDL) principle-based one. Our algorithm, called entropy-based EM (EBEM), starts with a unique kernel and performs only splitting by selecting the worst kernel attending to GD. We have successfully tested it in probability density estimation, pattern classification, and color image segmentation. Experimental results improve the ones of other state-of-the-art model order selection methods. PMID:19770090
Phase diagram of the Gaussian-core model.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-05-01
We trace with high numerical accuracy the phase diagram of the Gaussian-core model, a classical system of point particles interacting via a Gaussian-shaped, purely repulsive potential. This model, which provides a reliable qualitative description of the thermal behavior of interpenetrable globular polymers, is known to exhibit a polymorphic fcc-bcc transition at low densities and reentrant melting at high densities. Extensive Monte Carlo simulations, carried out in conjunction with accurate calculations of the solid free energies, lead to a thermodynamic scenario that is partially modified with respect to previous knowledge. In particular, we find that: (i) the fluid-bcc-fcc triple-point temperature is about one third of the maximum freezing temperature; (ii) upon isothermal compression, the model exhibits a fluid-bcc-fcc-bcc-fluid sequence of phases in a narrow range of temperatures just above the triple point. We discuss these results in relation to the behavior of star-polymer solutions and of other softly repulsive systems. PMID:16089510
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity. PMID:26366908
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity.
NASA Technical Reports Server (NTRS)
Burkholder, Robert J.; Pathak, Prabhakar H.
1991-01-01
Gaussian beam (GB) representation methods are used to analyze the electromagnetic coupling into and the scattering by a large nonuniform cavity. The aperture field in the cavity is decomposed into beams using the Gabor expansion, and shooting techniques are then employed. The method is illustrated only for the two-dimensional (2-D) case. The GBs are tracked axially using the rules of beam optics which ignore any beam distortion upon reflection at the walls. The effects of beam distortion are not significant for relatively slowly varying waveguide cavities. The field scattered into the exterior by the termination within the cavity is found using a reciprocity integral formulation which requires a knowledge of the beam fields near the termination. Numerical results based on this GB approach are presented and compared with results based on an independent reference solution.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
NASA Astrophysics Data System (ADS)
Patil, S. D.; Takale, M. V.
2013-08-01
We have studied the steady state self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime for upward increasing plasma ramp density profile. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual Wentzel-Kramers-Brillouin and paraxial approximations. The variation of beam width parameter with respect to dimensionless distance of propagation is presented graphically by varying the parameters of density profile, intensity parameter, and electronic temperature. It shows that the above stated parameters play an important role in propagation characteristics and give reasonably interesting results.
Zhang, Yixin; Cheng, Mingjian; Zhu, Yun; Gao, Jie; Dan, Weiyi; Hu, Zhengda; Zhao, Fengsheng
2014-09-01
We analyze the effects of turbulence on the detection probability spectrum and the mode weight of the orbital angular momentum (OAM) for Whittaker-Gaussian (WG) laser beams in weak non-Kolmogorov turbulence channels. Our numerical results show that WG beam is a better light source for mitigating the effects of turbulence with several adjustable parameters. The real parameters of WG beams γ and W0, which have significant effects on the mode weight, have no influence on the detection probability spectrum. Larger signal OAM quantum number, shorter wavelength, smaller beamwidth and coherence length will lead to the lower detection probability of the signal OAM mode.
NASA Technical Reports Server (NTRS)
Lock, James A.
1993-01-01
I review the theory of the scattering of a Gaussian laser beam by a dielectric spherical particle and give the details for constructing a computer program to implement the theory. Computational results indicate that if the width of the laser beam is much less than the diameter of the particle and if the axis of the beam is incident near the edge of the particle, the fifth-, sixth-, and ninth-order rainbows should be evident in the far-field scattered intensity. I performed an experiment that yielded tentative evidence for the presence of the sixth- order rainbow.
NASA Astrophysics Data System (ADS)
Shelton, John D.
1995-10-01
Expressions for the variance and the power spectral density of turbulence-induced log-amplitude fluctuations are derived for Gaussian-beam waves in the regime of weak scattering. This formulation includes effects that are due to turbulence strength variations along the propagation path, offset of the observation point from the beam axis, and sensitivity to focus and beam diameter. Comparison of theoretical results with observed scintillation during experiments with a laser-illuminated satellite reveals good agreement. Copyright (c) 1995 Optical Society of America
Patil, S. D.; Takale, M. V.
2013-08-15
We have studied the steady state self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime for upward increasing plasma ramp density profile. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual Wentzel–Kramers–Brillouin and paraxial approximations. The variation of beam width parameter with respect to dimensionless distance of propagation is presented graphically by varying the parameters of density profile, intensity parameter, and electronic temperature. It shows that the above stated parameters play an important role in propagation characteristics and give reasonably interesting results.
Visual saliency detection based on modeling the spatial Gaussianity
NASA Astrophysics Data System (ADS)
Ju, Hongbin
2015-04-01
In this paper, a novel salient object detection method based on modeling the spatial anomalies is presented. The proposed framework is inspired by the biological mechanism that human eyes are sensitive to the unusual and anomalous objects among complex background. It is supposed that a natural image can be seen as a combination of some similar or dissimilar basic patches, and there is a direct relationship between its saliency and anomaly. Some patches share high degree of similarity and have a vast number of quantity. They usually make up the background of an image. On the other hand, some patches present strong rarity and specificity. We name these patches "anomalies". Generally, anomalous patch is a reflection of the edge or some special colors and textures in an image, and these pattern cannot be well "explained" by their surroundings. Human eyes show great interests in these anomalous patterns, and will automatically pick out the anomalous parts of an image as the salient regions. To better evaluate the anomaly degree of the basic patches and exploit their nonlinear statistical characteristics, a multivariate Gaussian distribution saliency evaluation model is proposed. In this way, objects with anomalous patterns usually appear as the outliers in the Gaussian distribution, and we identify these anomalous objects as salient ones. Experiments are conducted on the well-known MSRA saliency detection dataset. Compared with other recent developed visual saliency detection methods, our method suggests significant advantages.
Beyond Gaussians: a study of single spot modeling for scanning proton dose calculation
Li, Yupeng; Zhu, Ronald X.; Sahoo, Narayan; Anand, Aman; Zhang, Xiaodong
2013-01-01
Active spot scanning proton therapy is becoming increasingly adopted by proton therapy centers worldwide. Unlike passive-scattering proton therapy, active spot scanning proton therapy, especially intensity-modulated proton therapy, requires proper modeling of each scanning spot to ensure accurate computation of the total dose distribution contributed from a large number of spots. During commissioning of the spot scanning gantry at the Proton Therapy Center in Houston, it was observed that the long-range scattering protons in a medium may have been inadequately modeled for high-energy beams by a commercial treatment planning system, which could lead to incorrect prediction of field-size effects on dose output. In the present study, we developed a pencil-beam algorithm for scanning-proton dose calculation by focusing on properly modeling individual scanning spots. All modeling parameters required by the pencil-beam algorithm can be generated based solely on a few sets of measured data. We demonstrated that low-dose halos in single-spot profiles in the medium could be adequately modeled with the addition of a modified Cauchy-Lorentz distribution function to a double-Gaussian function. The field-size effects were accurately computed at all depths and field sizes for all energies, and good dose accuracy was also achieved for patient dose verification. The implementation of the proposed pencil beam algorithm also enabled us to study the importance of different modeling components and parameters at various beam energies. The results of this study may be helpful in improving dose calculation accuracy and simplifying beam commissioning and treatment planning processes for spot scanning proton therapy. PMID:22297324
Fuzzy local Gaussian mixture model for brain MR image segmentation.
Ji, Zexuan; Xia, Yong; Sun, Quansen; Chen, Qiang; Xia, Deshen; Feng, David Dagan
2012-05-01
Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxel's neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.
Mineralogy of HED Meteorites Using the Modified Gaussian Model
NASA Astrophysics Data System (ADS)
Canas, Lina; Duffard, René; Seixas, Teresa
2008-06-01
The correlation between specific meteorites and asteroids is a long-standing problem. The best-known correlation seems to be the HED-Vesta, although several problems still remain to be solved. We report the spectral reflectance analysis (0.4-2.5 μm) of a set of HED meteorites, taken from the RELAB database and three V-type asteroids, taken from MIT-UH-IRTF Joint Campaign for NEO Reconnaissance. We used the Modified Gaussian Model to fit the spectra to a series of overlapping, modified Gaussian absorptions. The fitted individual bands are validated against established laboratory calibrations. With spectral resolution extending to the near-infrared, we are able to resolve the presence of both high-calcium pyroxene (HCP) and low-calcium pyroxene (LCP) and, thus, use the HCP/(HCP + LCP) ratios to remotely trace igneous processing on the parent asteroids. A search of this mineral provides a useful probe of differentiation. The high HCP/(HCP + LCP) ratios found require extensive differentiation of these asteroids and/or their primordial parent body. The degree of melting obtained for the eucrites, using the former ratio, is comparable with that obtained for all V-type asteroids here analyzed, suggesting a comparable geologic history.
A Gaussian graphical model approach to climate networks
NASA Astrophysics Data System (ADS)
Zerenner, Tanja; Friederichs, Petra; Lehnertz, Klaus; Hense, Andreas
2014-06-01
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
A Gaussian graphical model approach to climate networks
Zerenner, Tanja; Friederichs, Petra; Hense, Andreas; Lehnertz, Klaus
2014-06-15
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
Direct Simulation of Multiple Scattering by Discrete Random Media Illuminated by Gaussian Beams
NASA Technical Reports Server (NTRS)
Mackowski, Daniel W.; Mishchenko, Michael I.
2011-01-01
The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.
NASA Astrophysics Data System (ADS)
Marshall, Jeffrey S.; Wu, Junru
2015-10-01
A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer to as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force.
NASA Astrophysics Data System (ADS)
Cui, Linyan
2016-07-01
Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3-4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.
Marshall, Jeffrey S.; Wu, Junru
2015-10-15
A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer to as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force.
Gaussian-Charge Polarizable and Nonpolarizable Models for CO2.
Jiang, Hao; Moultos, Othonas A; Economou, Ioannis G; Panagiotopoulos, Athanassios Z
2016-02-11
A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor-liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important. PMID:26788614
Gaussian Process for Activity Modeling and Anomaly Detection
NASA Astrophysics Data System (ADS)
Liao, W.; Rosenhahn, B.; Yang, M. Ying
2015-08-01
Complex activity modeling and identification of anomaly is one of the most interesting and desired capabilities for automated video behavior analysis. A number of different approaches have been proposed in the past to tackle this problem. There are two main challenges for activity modeling and anomaly detection: 1) most existing approaches require sufficient data and supervision for learning; 2) the most interesting abnormal activities arise rarely and are ambiguous among typical activities, i.e. hard to be precisely defined. In this paper, we propose a novel approach to model complex activities and detect anomalies by using non-parametric Gaussian Process (GP) models in a crowded and complicated traffic scene. In comparison with parametric models such as HMM, GP models are nonparametric and have their advantages. Our GP models exploit implicit spatial-temporal dependence among local activity patterns. The learned GP regression models give a probabilistic prediction of regional activities at next time interval based on observations at present. An anomaly will be detected by comparing the actual observations with the prediction at real time. We verify the effectiveness and robustness of the proposed model on the QMUL Junction Dataset. Furthermore, we provide a publicly available manually labeled ground truth of this data set.
Efficient speaker verification using Gaussian mixture model component clustering.
De Leon, Phillip L.; McClanahan, Richard D.
2012-04-01
In speaker verification (SV) systems that employ a support vector machine (SVM) classifier to make decisions on a supervector derived from Gaussian mixture model (GMM) component mean vectors, a significant portion of the computational load is involved in the calculation of the a posteriori probability of the feature vectors of the speaker under test with respect to the individual component densities of the universal background model (UBM). Further, the calculation of the sufficient statistics for the weight, mean, and covariance parameters derived from these same feature vectors also contribute a substantial amount of processing load to the SV system. In this paper, we propose a method that utilizes clusters of GMM-UBM mixture component densities in order to reduce the computational load required. In the adaptation step we score the feature vectors against the clusters and calculate the a posteriori probabilities and update the statistics exclusively for mixture components belonging to appropriate clusters. Each cluster is a grouping of multivariate normal distributions and is modeled by a single multivariate distribution. As such, the set of multivariate normal distributions representing the different clusters also form a GMM. This GMM is referred to as a hash GMM which can be considered to a lower resolution representation of the GMM-UBM. The mapping that associates the components of the hash GMM with components of the original GMM-UBM is referred to as a shortlist. This research investigates various methods of clustering the components of the GMM-UBM and forming hash GMMs. Of five different methods that are presented one method, Gaussian mixture reduction as proposed by Runnall's, easily outperformed the other methods. This method of Gaussian reduction iteratively reduces the size of a GMM by successively merging pairs of component densities. Pairs are selected for merger by using a Kullback-Leibler based metric. Using Runnal's method of reduction, we were able
NASA Astrophysics Data System (ADS)
Hertog, Maarten L. A. T. M.; Scheerlinck, Nico; Nicolaï, Bart M.
2009-01-01
When modelling the behaviour of horticultural products, demonstrating large sources of biological variation, we often run into the issue of non-Gaussian distributed model parameters. This work presents an algorithm to reproduce such correlated non-Gaussian model parameters for use with Monte Carlo simulations. The algorithm works around the problem of non-Gaussian distributions by transforming the observed non-Gaussian probability distributions using a proposed SKN-distribution function before applying the covariance decomposition algorithm to generate Gaussian random co-varying parameter sets. The proposed SKN-distribution function is based on the standard Gaussian distribution function and can exhibit different degrees of both skewness and kurtosis. This technique is demonstrated using a case study on modelling the ripening of tomato fruit evaluating the propagation of biological variation with time.
NASA Astrophysics Data System (ADS)
Zhao, Yuanhang; Zhang, Yixin; Hu, Zhengda; Li, Ye; Wang, Donglin
2016-07-01
Polarization and spatial coherence of quantization Gaussian Schell-beams propagating through the anisotropic non-Kolmogorov turbulence of marine-atmosphere channel are studied based on the quantized Huygens-Fresnel principle and the degree of quantum polarization. The spatial coherence length and the polarization degree of linearly polarization quantization Gaussian Schell-beams are developed. The effects of outer scale on the lateral coherence length are not obvious as same as the effects of wavelength on the degree of polarization. The degree of polarization decreases as the source transverse coherent width, anisotropic factor, the number of received photons, spectral index, the inner scale of turbulent eddies and source transverse radius decrease or generalized refractive-index structure parameter increases. The refractive-index structure parameter, spectral index and inner scale have also effect on the changes of lateral coherence length. Those results can be used to improve the performance of a polarization-encoded quantum communication system.
Mourka, A.; Mazilu, M.; Wright, E. M.; Dholakia, K.
2013-01-01
The modal characterization of various families of beams is a topic of current interest. We recently reported a new method for the simultaneous determination of both the azimuthal and radial mode indices for light fields possessing orbital angular momentum. The method is based upon probing the far-field diffraction pattern from a random aperture and using the recorded data as a ‘training set'. We then transform the observed data into uncorrelated variables using the principal component analysis (PCA) algorithm. Here, we show the generic nature of this approach for the simultaneous determination of the modal parameters of Hermite-Gaussian and Bessel beams. This reinforces the widespread applicability of this method for applications including information processing, spectroscopy and manipulation. Additionally, preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode. Thus, this approach represents a powerful method for characterizing the optical multi-dimensional Hilbert space. PMID:23478330
Thermodynamical Limit for Correlated Gaussian Random Energy Models
NASA Astrophysics Data System (ADS)
Contucci, P.; Esposti, M. Degli; Giardinà, C.; Graffi, S.
Let {EΣ(N)}ΣΣN be a family of |ΣN|=2N centered unit Gaussian random variables defined by the covariance matrix CN of elements cN(Σ,τ):=Av(EΣ(N)Eτ(N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N1+N2, and all pairs (Σ,τ)ΣN×ΣN:
Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis
Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun
2014-01-01
As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687
Gaussian and Lognormal Models of Hurricane Gust Factors
NASA Technical Reports Server (NTRS)
Merceret, Frank
2009-01-01
A document describes a tool that predicts the likelihood of land-falling tropical storms and hurricanes exceeding specified peak speeds, given the mean wind speed at various heights of up to 500 feet (150 meters) above ground level. Empirical models to calculate mean and standard deviation of the gust factor as a function of height and mean wind speed were developed in Excel based on data from previous hurricanes. Separate models were developed for Gaussian and offset lognormal distributions for the gust factor. Rather than forecasting a single, specific peak wind speed, this tool provides a probability of exceeding a specified value. This probability is provided as a function of height, allowing it to be applied at a height appropriate for tall structures. The user inputs the mean wind speed, height, and operational threshold. The tool produces the probability from each model that the given threshold will be exceeded. This application does have its limits. They were tested only in tropical storm conditions associated with the periphery of hurricanes. Winds of similar speed produced by non-tropical system may have different turbulence dynamics and stability, which may change those winds statistical characteristics. These models were developed along the Central Florida seacoast, and their results may not accurately extrapolate to inland areas, or even to coastal sites that are different from those used to build the models. Although this tool cannot be generalized for use in different environments, its methodology could be applied to those locations to develop a similar tool tuned to local conditions.
Spiked Dirichlet Process Priors for Gaussian Process Models
Savitsky, Terrance; Vannucci, Marina
2013-01-01
We expand a framework for Bayesian variable selection for Gaussian process (GP) models by employing spiked Dirichlet process (DP) prior constructions over set partitions containing covariates. Our approach results in a nonparametric treatment of the distribution of the covariance parameters of the GP covariance matrix that in turn induces a clustering of the covariates. We evaluate two prior constructions: the first one employs a mixture of a point-mass and a continuous distribution as the centering distribution for the DP prior, therefore, clustering all covariates. The second one employs a mixture of a spike and a DP prior with a continuous distribution as the centering distribution, which induces clustering of the selected covariates only. DP models borrow information across covariates through model-based clustering. Our simulation results, in particular, show a reduction in posterior sampling variability and, in turn, enhanced prediction performances. In our model formulations, we accomplish posterior inference by employing novel combinations and extensions of existing algorithms for inference with DP prior models and compare performances under the two prior constructions. PMID:23950763
Huang, Yongping; Wang, Fanhou; Gao, Zenghui; Zhang, Bin
2015-01-26
Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian (PCESHG) vortex beams through non-Kolmogorov atmospheric turbulence, including the spectral degree of polarization and evolution behavior of coherent vortices and average intensity are investigated in detail by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of non-Kolmogorov turbulence. It is shown that the motion, creation and annihilation of the coherent vortices of PCESHG vortex beams in non-Kolmogorov turbulence may appear with the increasing propagation distance, and the distance for the conservation of the topological charge depends on the turbulence parameters and beam parameters. In additions, the evolution behavior of coherent vortices, average intensity and spectral degree of polarization vary significantly for different values of the generalized exponent parameter and the generalized refractive-index structure parameter of non-Kolmogorov turbulence, and the beam parameters as well as the propagation distance. PMID:25835869
Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption
NASA Astrophysics Data System (ADS)
Niti, Kant; Manzoor, Ahmad Wani
2015-07-01
Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter, and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel-Kramers-Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density, decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly. Supported by a Financial Grant from CSIR, New Delhi, India, under Project No. 03(1277)/13/EMR-II
Huang, Yongping; Wang, Fanhou; Gao, Zenghui; Zhang, Bin
2015-01-26
Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian (PCESHG) vortex beams through non-Kolmogorov atmospheric turbulence, including the spectral degree of polarization and evolution behavior of coherent vortices and average intensity are investigated in detail by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of non-Kolmogorov turbulence. It is shown that the motion, creation and annihilation of the coherent vortices of PCESHG vortex beams in non-Kolmogorov turbulence may appear with the increasing propagation distance, and the distance for the conservation of the topological charge depends on the turbulence parameters and beam parameters. In additions, the evolution behavior of coherent vortices, average intensity and spectral degree of polarization vary significantly for different values of the generalized exponent parameter and the generalized refractive-index structure parameter of non-Kolmogorov turbulence, and the beam parameters as well as the propagation distance.
Compressive sensing by learning a Gaussian mixture model from measurements.
Yang, Jianbo; Liao, Xuejun; Yuan, Xin; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2015-01-01
Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.
Habibi, M.; Ghamari, F.
2014-06-15
Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)].
Guo, Dagang; Lin, Rongming; Wang, Weijun
2005-08-01
A generalized study has been carried out on the modeling of a Fabry-Perot microcavity for sensing applications. Different analytical models on transmission characteristics of a Fabry-Perot microcavity are established by using plane-wave-based techniques, such as the Macleod characteristic matrix technique, the transfer matrix technique, and Smith's technique. A novel Gaussian-optics-based model for a Fabry-Perot microcavity illuminated by a laser beam is then developed and validated. The influence of laser beam waist on microcavity optical response is investigated, and the required minimal beam waist size is explored to ensure a useful optical response for sensing applications that can be accurately predicted by plane-wave optics. Also, the perturbations of microcavity performance induced by different types of microcavity mirror imperfections are discussed, based on the novel optical model. The prototype of the proposed Fabry-Perot microcavity for sensing applications has been successfully fabricated and characterized.
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Wang, Qiu; Hu, Zhengda
2016-11-01
For Gaussian beams with three different partially coherent models, including Gaussian-Schell model (GSM), Laguerre-Gaussian Schell-model (LGSM) and Bessel-Gaussian Schell-model (BGSM) beams propagating through a biological turbulent tissue, the expression of the spatial coherence radius of a spherical wave propagating in a turbulent biological tissue, and the average intensity and beam spreading for GSM, LGSM and BGSM beams are derived based on the fractal model of power spectrum of refractive-index variations in biological tissue. Effects of partially coherent model and parameters of biological turbulence on such beams are studied in numerical simulations. Our results reveal that the spreading of GSM beams is smaller than LGSM and BGSM beams on the same conditions, and the beam with larger source coherence width has smaller beam spreading than that with smaller coherence width. The results are useful for any applications involved light beam propagation through tissues, especially the cases where the average intensity and spreading properties of the light should be taken into account to evaluate the system performance and investigations in the structures of biological tissue.
BEAMS3D Neutral Beam Injection Model
NASA Astrophysics Data System (ADS)
McMillan, Matthew; Lazerson, Samuel A.
2014-09-01
With the advent of applied 3D fields in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous slowing down, and pitch angle scattering are modeled with the ADAS atomic physics database. Elementary benchmark calculations are presented to verify the collisionless particle orbits, NBI model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields. Notice: this manuscript has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
Gaussian model of explosive percolation in three and higher dimensions
NASA Astrophysics Data System (ADS)
Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.
2011-10-01
The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.035701 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple cubic lattice, in the thermodynamic limit we report a finite jump of the order parameter J=0.415±0.005. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension dA=2.5±0.2. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with a finite number of clusters at the threshold.
NASA Technical Reports Server (NTRS)
Burkholder, R. J.; Pathak, P. H.
1988-01-01
The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.
Bayesian modeling of JET Li-BES for edge electron density profiles using Gaussian processes
NASA Astrophysics Data System (ADS)
Kwak, Sehyun; Svensson, Jakob; Brix, Mathias; Ghim, Young-Chul; JET Contributors Collaboration
2015-11-01
A Bayesian model for the JET lithium beam emission spectroscopy (Li-BES) system has been developed to infer edge electron density profiles. The 26 spatial channels measure emission profiles with ~15 ms temporal resolution and ~1 cm spatial resolution. The lithium I (2p-2s) line radiation in an emission spectrum is calculated using a multi-state model, which expresses collisions between the neutral lithium beam atoms and the plasma particles as a set of differential equations. The emission spectrum is described in the model including photon and electronic noise, spectral line shapes, interference filter curves, and relative calibrations. This spectral modeling gets rid of the need of separate background measurements for calculating the intensity of the line radiation. Gaussian processes are applied to model both emission spectrum and edge electron density profile, and the electron temperature to calculate all the rate coefficients is obtained from the JET high resolution Thomson scattering (HRTS) system. The posterior distributions of the edge electron density profile are explored via the numerical technique and the Markov chain Monte Carlo (MCMC) samplings. See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing; Cheng, Qi; Zhang, Dan
2016-06-10
The analytical formulas for the orbital angular momentum (OAM) mode probability density, signal OAM mode detection probability, and spiral spectrum of partially coherent Laguerre-Gaussian (LG) beams with optical vortices propagation in weak horizontal oceanic turbulent channels were developed, based on the Rytov approximation theory. The effect of oceanic turbulence and beam source parameters on the propagation behavior of the optical vortices carried by partially coherent LG beams was investigated in detail. Our results indicated that optical turbulence in an ocean environment produced a much stronger effect on the optical vortex than that in an atmosphere environment; the effective range of the signal OAM mode of LG beams with a smaller ratio of the mode crosstalk was limited to only several tens of meters in turbulent ocean. The existence of oceanic turbulence evidently induced OAM mode crosstalk and spiral spectrum spread. The effects of oceanic turbulence on the OAM mode detection probability increased with the increase of radial and azimuthal mode orders, oceanic turbulent equivalent temperature structure parameter, and temperature-salinity balance parameter. The spatial partial coherence of the beam source would enhance the effect of turbulent aberrations on the signal OAM mode detection probability, and fully coherent vortex beams provided better performance than partially coherent ones. Increasing wavelength of the vortex beams would help improve the performance of this quantum optical communication system. These results might be of interest for the potential application of optical vortices in practical underwater quantum optical communication among divers, submarines, and sensors in the ocean environment. PMID:27409021
Khaled, E E; Hill, S C; Barber, P W
1994-01-20
The electric energy in a lossless or lossy spherical particle that is illuminated with a plane wave or a Gaussian beam is investigated. The analysis uses a combination of the plane-wave spectrum technique and the T-matrix method. Expressions for the electric energy in any mode as well as the total electric energy inside the particle are given. The amount of energy coupling into the particle for different beam illuminations is also investigated. The high-Q (low-order) resonant modes can dominate the electric energy inside a spherical particle many linewidths away from the resonance location, particularly if the beam is focused at the droplet edge or outside the droplet. If the sphere is lossy, low-order modes can still dominate the electric energy if the beam is focused far enough outside the sphere. As the absorption coefficient of the particle increases, the energy in a high-Q mode decreases much faster at the resonance frequency than it does at near or off-resonance frequencies. The effects of the absorption on the dominance of the internal fields by a high-Q mode decreases as the beam is shifted farther away from the particle. As the beam is shifted farther away from the particle the fraction of the incident energy coupled into the sphere at resonance first increases and then decreases. Although the coupled energy decreases as the beam is shifted farther from the sphere, most of that energy is in the lowest-order mode.
Doerner, Edgardo; Caprile, Paola
2016-01-01
The shape of the radiation source of a linac has a direct impact on the delivered dose distributions, especially in the case of small radiation fields. Traditionally, a single Gaussian source model is used to describe the electron beam hitting the target, although different studies have shown that the shape of the electron source can be better described by a mixed distribution consisting of two Gaussian components. Therefore, this study presents the implementation of a double Gaussian source model into the BEAMnrc Monte Carlo code. The impact of the double Gaussian source model for a 6 MV beam is assessed through the comparison of different dosimetric parameters calculated using a single Gaussian source, previously com-missioned, the new double Gaussian source model and measurements, performed with a diode detector in a water phantom. It was found that the new source can be easily implemented into the BEAMnrc code and that it improves the agreement between measurements and simulations for small radiation fields. The impact of the change in source shape becomes less important as the field size increases and for increasing distance of the collimators to the source, as expected. In particular, for radiation fields delivered using stereotactic collimators located at a distance of 59 cm from the source, it was found that the effect of the double Gaussian source on the calculated dose distributions is negligible, even for radiation fields smaller than 5 mm in diameter. Accurate determination of the shape of the radiation source allows us to improve the Monte Carlo modeling of the linac, especially for treatment modalities such as IMRT, were the radiation beams used could be very narrow, becoming more sensitive to the shape of the source. PMID:27685141
Storytelling Voice Conversion: Evaluation Experiment Using Gaussian Mixture Models
NASA Astrophysics Data System (ADS)
Přibil, Jiří; Přibilová, Anna; Ďuračková, Daniela
2015-07-01
In the development of the voice conversion and personification of the text-to-speech (TTS) systems, it is very necessary to have feedback information about the users' opinion on the resulting synthetic speech quality. Therefore, the main aim of the experiments described in this paper was to find out whether the classifier based on Gaussian mixture models (GMM) could be applied for evaluation of different storytelling voices created by transformation of the sentences generated by the Czech and Slovak TTS system. We suppose that it is possible to combine this GMM-based statistical evaluation with the classical one in the form of listening tests or it can replace them. The results obtained in this way were in good correlation with the results of the conventional listening test, so they confirm practical usability of the developed GMM classifier. With the help of the performed analysis, the optimal setting of the initial parameters and the structure of the input feature set for recognition of the storytelling voices was finally determined.
Node-Based Learning of Multiple Gaussian Graphical Models
Mohan, Karthik; London, Palma; Fazel, Maryam; Witten, Daniela; Lee, Su-In
2014-01-01
We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory networks on the basis of gene expression data containing heterogeneous samples, such as different disease states, multiple species, or different developmental stages. We assume that most aspects of the conditional dependence networks are shared, but that there are some structured differences between them. Rather than assuming that similarities and differences between networks are driven by individual edges, we take a node-based approach, which in many cases provides a more intuitive interpretation of the network differences. We consider estimation under two distinct assumptions: (1) differences between the K networks are due to individual nodes that are perturbed across conditions, or (2) similarities among the K networks are due to the presence of common hub nodes that are shared across all K networks. Using a row-column overlap norm penalty function, we formulate two convex optimization problems that correspond to these two assumptions. We solve these problems using an alternating direction method of multipliers algorithm, and we derive a set of necessary and sufficient conditions that allows us to decompose the problem into independent subproblems so that our algorithm can be scaled to high-dimensional settings. Our proposal is illustrated on synthetic data, a webpage data set, and a brain cancer gene expression data set. PMID:25309137
Chen, Gui-Yang; Song, Feng; Wang, Hui-Tian
2013-10-01
The focal electric fields for a 4π high numerical aperture (NA) focusing system with both the doughnut and higher-order Laguerre-Gaussian (LG) radially polarized (RP) beams are investigated in the case of NA=1, and the full width at half-maximum values of the focal spots are calculated. Compared with the single-lens high NA focusing configuration, a sharper spot, whose size is reduced efficiently in the transverse as well as the axial direction, can be formed. Such size reduction is attributed to not only the destruction interference of the longitudinal component caused by the π phase shift between any two adjacent rings of the incident higher-order LG RP beam coming from one particular direction but also the perfect destruction interference of the radial component formed by the two counter-propagating incident beams. PMID:24081093
Lee, It Ee; Ghassemlooy, Zabih; Ng, Wai Pang; Khalighi, Mohammad-Ali; Liaw, Shien-Kuei
2016-01-01
Joint effects of aperture averaging and beam width on the performance of free-space optical communication links, under the impairments of atmospheric loss, turbulence, and pointing errors (PEs), are investigated from an information theory perspective. The propagation of a spatially partially coherent Gaussian-beam wave through a random turbulent medium is characterized, taking into account the diverging and focusing properties of the optical beam as well as the scintillation and beam wander effects. Results show that a noticeable improvement in the average channel capacity can be achieved with an enlarged receiver aperture in the moderate-to-strong turbulence regime, even without knowledge of the channel state information. In particular, it is observed that the optimum beam width can be reduced to improve the channel capacity, albeit the presence of scintillation and PEs, given that either one or both of these adverse effects are least dominant. We show that, under strong turbulence conditions, the beam width increases linearly with the Rytov variance for a relatively smaller PE loss but changes exponentially with steeper increments for higher PE losses. Our findings conclude that the optimal beam width is dependent on the combined effects of turbulence and PEs, and this parameter should be adjusted according to the varying atmospheric channel conditions. Therefore, we demonstrate that the maximum channel capacity is best achieved through the introduction of a larger receiver aperture and a beam-width optimization technique.
Gupta, Naveen Singh, Arvinder; Singh, Navpreet
2015-11-15
This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.
Beam modeling and verification of a photon beam multisource model
Ahnesjoe, Anders; Weber, Lars; Murman, Anders; Saxner, Mikael; Thorslund, Ingvar; Traneus, Erik
2005-06-15
Dose calculations for treatment planning of photon beam radiotherapy require a model of the beam to drive the dose calculation models. The beam shaping process involves scattering and filtering that yield radiation components which vary with collimator settings. The necessity to model these components has motivated the development of multisource beam models. We describe and evaluate clinical photon beam modeling based on multisource models, including lateral beam quality variations. The evaluation is based on user data for a pencil kernel algorithm and a point kernel algorithm (collapsed cone) used in the clinical treatment planning systems Helax-TMS and Nucletron-Oncentra. The pencil kernel implementations treat the beam spectrum as lateral invariant while the collapsed cone involves off axis softening of the spectrum. Both algorithms include modeling of head scatter components. The parameters of the beam model are derived from measured beam data in a semiautomatic process called RDH (radiation data handling) that, in sequential steps, minimizes the deviations in calculated dose versus the measured data. The RDH procedure is reviewed and the results of processing data from a large number of treatment units are analyzed for the two dose calculation algorithms. The results for both algorithms are similar, with slightly better results for the collapsed cone implementations. For open beams, 87% of the machines have maximum errors less than 2.5%. For wedged beams the errors were found to increase with increasing wedge angle. Internal, motorized wedges did yield slightly larger errors than external wedges. These results reflect the increased complexity, both experimentally and computationally, when wedges are used compared to open beams.
NASA Astrophysics Data System (ADS)
Li, Xiangzhen; Han, Xiang'e.
2009-10-01
Within the framework of geometrical optics, we obtain the on-axis Gaussian beam scattering of nonuniform glass microbeads. The phase shift due to the optical path is deduced and the scattering angles of the p ray are given. On the basis of this work, the scattering intensity distribution is calculated and compared with that obtained by the generalized Lorenz-Mie theory. As indicated by the comparison, the surface wave effect of this gradient index (GRIN) microbead is smaller than that of a homogeneous microbead. The calculation time of the geometrical-optics approximation (GOA) is much less than that of generalized Lorenz-Mie theory (GLMT).
Sokolov, V I; Marusin, N V; Molchanova, S I; Savelyev, A G; Khaydukov, E V; Panchenko, V Ya
2014-11-30
The problem of reflection of a TE-polarised Gaussian light beam from a layered structure under conditions of resonance excitation of waveguide modes using a total internal reflection prism is considered. Using the spectral approach we have derived the analytic expressions for the mode propagation lengths, widths and depths of m-lines (sharp and narrow dips in the angular dependence of the specular reflection coefficient), depending on the structure parameters. It is shown that in the case of weak coupling, when the propagation lengths l{sub m} of the waveguide modes are mainly determined by the extinction coefficient in the film, the depth of m-lines grows with the mode number m. In the case of strong coupling, when l{sub m} is determined mainly by the radiation of modes into the prism, the depth of m-lines decreases with increasing m. The change in the TE-polarised Gaussian beam shape after its reflection from the layered structure is studied, which is determined by the energy transfer from the incident beam into waveguide modes that propagate along the structure by the distance l{sub m}, are radiated in the direction of specular reflection and interfere with a part of the beam reflected from the working face of the prism. It is shown that this interference can lead to the field intensity oscillations near m-lines. The analysis of different methods for determining the parameters of thin-film structures is presented, including the measurement of mode angles θ{sub m} and the reflected beam shape. The methods are based on simultaneous excitation of a few waveguide modes in the film with a strongly focused monochromatic Gaussian beam, the waist width of which is much smaller than the propagation length of the modes. As an example of using these methods, the refractive index and the thickness of silicon monoxide film on silica substrate at the wavelength 633 nm are determined. (fibre and integrated-optical structures)
Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation
NASA Technical Reports Server (NTRS)
Steinwolf, Alexander; Rizzi, Stephen A.
2003-01-01
The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.
Application of Gaussian Process Modeling to Analysis of Functional Unreliability
R. Youngblood
2014-06-01
This paper applies Gaussian Process (GP) modeling to analysis of the functional unreliability of a “passive system.” GPs have been used widely in many ways [1]. The present application uses a GP for emulation of a system simulation code. Such an emulator can be applied in several distinct ways, discussed below. All applications illustrated in this paper have precedents in the literature; the present paper is an application of GP technology to a problem that was originally analyzed [2] using neural networks (NN), and later [3, 4] by a method called “Alternating Conditional Expectations” (ACE). This exercise enables a multifaceted comparison of both the processes and the results. Given knowledge of the range of possible values of key system variables, one could, in principle, quantify functional unreliability by sampling from their joint probability distribution, and performing a system simulation for each sample to determine whether the function succeeded for that particular setting of the variables. Using previously available system simulation codes, such an approach is generally impractical for a plant-scale problem. It has long been recognized, however, that a well-trained code emulator or surrogate could be used in a sampling process to quantify certain performance metrics, even for plant-scale problems. “Response surfaces” were used for this many years ago. But response surfaces are at their best for smoothly varying functions; in regions of parameter space where key system performance metrics may behave in complex ways, or even exhibit discontinuities, response surfaces are not the best available tool. This consideration was one of several that drove the work in [2]. In the present paper, (1) the original quantification of functional unreliability using NN [2], and later ACE [3], is reprised using GP; (2) additional information provided by the GP about uncertainty in the limit surface, generally unavailable in other representations, is discussed
Absorption Band Modeling in Reflectance Spectra: Availability of the Modified Gaussian Model
NASA Astrophysics Data System (ADS)
Sunshine, J. M.; Pieters, C. M.; Pratt, S. F.; McNaron-Brown, K. S.
1999-03-01
The modified Gaussian model, a physically based description of absorption bands in spectra, has been updated to provide compatibility with most computer systems. These new versions, written in MATLAB and IDL, are available at the RELAB Website (www.planetary.brown.edu).
A non-gaussian model of continuous atmospheric turbulence for use in aircraft design
NASA Technical Reports Server (NTRS)
Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.
1976-01-01
A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.
Self-focusing of a Hermite-cosh Gaussian laser beam in a magnetoplasma with ramp density profile
Nanda, Vikas; Kant, Niti; Wani, Manzoor Ahmad
2013-11-15
The early and strong self-focusing of a Hermite-cosh-Gaussian laser beam in magnetoplasma in the presence of density ramp has been observed. Focusing and de-focusing nature of the Hermite-cosh-Gaussian laser beam with decentered parameter and magnetic field has been studied, and strong self-focusing is reported. It is investigated that decentered parameter 'b' plays a significant role for the self-focusing of the laser beam and is very sensitive as in case of extraordinary mode. For mode indices, m = 0, 1, 2, and b = 4.00, 3.14, and 2.05, strong self-focusing is observed. Similarly in case of ordinary mode, for m = 0, 1, 2 and b = 4.00, 3.14, 2.049, respectively, strong self-focusing is reported. Further, it is seen that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For mode indices m = 0, 1, and 2, diffraction term becomes more dominant over nonlinear term for decentered parameter b=0. For selective higher values of decentered parameter in case of mode indices m=0, 1, and 2, self-focusing effect becomes strong for extraordinary mode. Also increase in the value of magnetic field enhances the self-focusing ability of the laser beam, which is very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers.
Properties of an Axial Optical Vortex Generated with the Use of a Gaussian Beam and Two Ramps.
Khoroshun, A N; Chernykh, A V; Tsimbaluk, A N; Kirichenko, J A; Yezhov, P V; Kuzmenko, A V; Kim, J T
2016-02-01
The behavior of an axial optical vortex (OV), which is generated with the use of a Gaussian beam and two ramps implemented by a phase-only spatial light modulator (SLM), is studied as a function of the parameters of two ramps. The analytic solution of a wave equation is obtained in the Fresnel approximation for the diffraction of a Gaussian beam on the two-ramp structure. Nonlinear dependences of the ellipticity gamma of the intensity distribution in the OV core, as well as the angle (phi between the x-axis and the major ellipse axis of the vortex core, on the ramp phase gradient K, are analyzed. The values of given parameters obtained in optical and numerical experiments are in good agreement. It is shown that, as the gradients of the phases of two ramps vary in the limits of 3pi rad/cm, the ellipticity and the slope angle of the major axis ellipse are changed, respectively, by 0.3 and 56 degrees. This gives possibility to efficiently control the parameters of OVs. PMID:27433739
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2015-11-01
Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θi, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ɛ.
Mitri, F. G.
2015-11-14
Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.
Simulation and analysis of grinding wheel based on Gaussian mixture model
NASA Astrophysics Data System (ADS)
Chi, Yulun; Li, Haolin
2012-12-01
This article presents an application of numerical simulation technique for the generation and analysis of the grinding wheel surface topographies. The ZETA 20 imaging and metrology microscope is employed to measure the surface topographies. The Gaussian mixture model (GMM) is used to transform the measured non-Gaussian field to Gaussian fields, and the simulated topographies are generated. Some numerical examples are used to illustrate the viability of the method. It shows that the simulated grinding wheel topographies are similar with the measured and can be effective used to study the abrasive grains and grinding mechanism.
Spectral renormalization group for the Gaussian model and ψ4 theory on nonspatial networks
NASA Astrophysics Data System (ADS)
Tuncer, Aslı; Erzan, Ayşe
2015-08-01
We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, d ˜. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At d ˜=2 , the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a ψ4 perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2
Poly-Gaussian model of randomly rough surface in rarefied gas flow
Aksenova, Olga A.; Khalidov, Iskander A.
2014-12-09
Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be applied in numerical DSMC methods as well as in analytical investigations.
Non-Gaussianity and large-scale structure in a two-field inflationary model
Tseliakhovich, Dmitriy; Hirata, Christopher
2010-08-15
Single-field inflationary models predict nearly Gaussian initial conditions, and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large-scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter f-tilde{sub NL} and the ratio {xi} of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and Sloan Digital Sky Survey data.
A gaussian model for simulated geomagnetic field reversals
NASA Astrophysics Data System (ADS)
Wicht, Johannes; Meduri, Domenico G.
2016-10-01
Field reversals are the most spectacular events in the geomagnetic history but remain little understood. Here we explore the dipole behaviour in particularly long numerical dynamo simulations to reveal statistically significant conditions required for reversals and excursions to happen. We find that changes in the axial dipole moment behaviour are crucial while the equatorial dipole moment plays a negligible role. For small Rayleigh numbers, the axial dipole always remains strong and stable and obeys a clearly Gaussian probability distribution. Only when the Rayleigh number is increased sufficiently the axial dipole can reverse and its distribution becomes decisively non-Gaussian. Increased likelihoods around zero indicate a pronounced lingering in a new low dipole moment state. Reversals and excursions can only happen when axial dipole fluctuations are large enough to drive the system from the high dipole moment state assumed during stable polarity epochs into the low dipole moment state. Since it is just a matter of chance which polarity is amplified during dipole recovery, reversals and grand excursions, i.e. excursions during which the dipole assumes reverse polarity, are equally likely. While the overall reversal behaviour seems Earth-like, a closer comparison to palaeomagnetic findings suggests that the simulated events last too long and that grand excursions are too rare. For a particularly large Ekman number we find a second but less Earth-like type of reversals where the total field decays and recovers after a certain time.
Hamby, D M
2002-01-01
Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.
NASA Astrophysics Data System (ADS)
Bhowmik, Anal; Mondal, Pradip Kumar; Majumder, Sonjoy; Deb, Bimalendu
2016-06-01
The exchange of orbital angular momentum (OAM) between paraxial optical vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In this paper, we develop a theory for the microscopic interaction between matter and an optical vortex beyond paraxial approximation. We show how superposition of vortex states of BEC can be created with a focused optical vortex. Since the polarization or spin angular momentum (SAM) of the optical field is coupled with OAM of the field, in this case, these angular momenta can be transferred to the internal electronic and external center-of-mass motion of atoms provided both the motions are coupled. We propose a scheme for producing the superposition of matter-wave vortices using Gaussian and a focused Laguerre-Gaussian beam. We study how two-photon Rabi frequencies of stimulated Raman transitions vary with focusing angles for different combinations of OAM and SAM of optical states. We demonstrate the formation of vortex-antivortex structure and discuss interference of three vortex states in a BEC.
NASA Astrophysics Data System (ADS)
Cheng, Ke; Jiao, Liyang; Zhong, Xianqiong
2016-05-01
Based on the vector angular spectrum representation and stationary phase method, the analytical far-field vectorial expressions of radial noncanonical vortex Airy beam arrays (NVAiBAs) and radial noncanonical vortex Gaussian beam arrays (NVGBAs) are derived, and used to investigate their far-field vectorial properties, e.g. center optical vortices and energy fluxes of these corresponding beams, where the effect of noncanonical strength, topological charge, initial phase index and the number of beamlet on far-field vectorial properties of these corresponding beams is emphasized, respectively. The results show that the topological charge of center optical vortices in the far field is equal to initial phase index for the case of the radial NVAiBAs, whereas for radial NVGBAs the topological charge not only lies on initial phase index, but also is closely related to the odevity and sign of optical vortices embedded in beamlet, where mathematical analysis is made to explain the topological charge of center optical vortices, and the limitation of the number of beamlet to the topological charge of center optical vortices is also discussed. In addition, energy fluxes of radial NVAiBAs and NVGBAs exhibit different space orientations by controlling noncancial strength and present larger dark zones by increasing topological charge of beamlet, respectively. Finally, the relationship between the center optical vortices and energy fluxes of radial NVAiBAs and NVGBAs in even or odd N beamlets is also revealed, respectively.
Kumar, Subodh; Singh, Ram Kishor Sharma, R. P.
2015-10-15
Terahertz (THz) generation by beating of two co-axial Gaussian laser beams, propagating in ripple density plasma, has been studied when both ponderomotive and relativistic nonlinearities are operative. When the two lasers co-propagate in rippled density plasma, electrons acquire a nonlinear velocity at beat frequency in the direction transverse to the direction of propagation. This nonlinear oscillatory velocity couples with the density ripple to generate a nonlinear current, which in turn generates THz radiation at the difference frequency. The necessary phase matching condition is provided by the density ripple. Relativistic ponderomotive focusing of the two lasers and its effects on yield of the generated THz amplitude have been discussed. Numerical results show that conversion efficiency of the order of 10{sup −3} can be achieved in the terahertz radiation generation with relativistic ponderomotive focusing.
Chaudhari, M I; Pratt, L R; Paulaitis, M E
2015-07-23
Parallel-tempering MD results for a CH3(CH2-O-CH2)mCH3 chain in water are exploited as a database for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in null water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple k → ∞ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting and scaling the discrete-Gaussian model helps to identify the low-k to high-k transition near k ≈ 2π/0.6 nm when an empirically matched number of Gaussian links is about one-third of the total number of effective atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the r space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distribution of Rg(2) is compared with the classic predictions for both the Gaussian model and freely jointed chains. ⟨Rg(2)(j)⟩, the contribution of the jth chain segment to ⟨Rg(2)⟩, depends on the contour index about as expected for Gaussian chains despite significant quantitative discrepancies that express the swelling of these chains in water. Monomers central to the chain contour occupy the center of the chain globule. The density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due to the close proximity of central elements to the globule center. However, that density structuring washes out for longer chains where many chain elements additively contribute to the density profiles. Gaussian chain models thus become more satisfactory for the density profiles for longer chains. PMID:25121580
Intensity influence on Gaussian beam laser based measurements using quadrant photodiodes.
Panduputra, Yohannes; Ng, Tuck Wah; Neild, Adrian; Robinson, Michael
2010-07-01
In many measurement applications using quadrant photodiodes, the signal is normally obtained from integrated devices incorporating current-to-voltage amplifiers that provide the necessary difference outputs with amplification. Quadrant photodiodes permit two-axis laser beam size and beam deflection determination. We show here that photodiode saturation, nonlinear characteristics of amplifying circuits, and voltage clipping features meant to prevent the output of a circuit from exceeding a predetermined voltage level to distort applied waveforms, play a significant role in measurement at low and high intensity levels, respectively. These two factors conspire to underestimate laser beam size measurement. A best-fit computation of the size versus power trend was found to permit satisfactory estimation of the beam size as well as the optimal laser power to be used. The intensity of light was also found to strongly affect the sensitivity of beam deflection measurements, in which a correction based on best-fit computation was deficient. In this case, calibration steps would be needed when light levels changed. PMID:20648132
NASA Astrophysics Data System (ADS)
Han, L.; Han, Y. P.; Wang, J. J.; Gouesbet, G.
2013-09-01
Within the framework of the generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by an on-axis Gaussian beam is formulated analytically, with more attention paid to the investigation of internal and near-surface fields. Numerical results concerning the spatial distributions of internal and near-surface fields are presented. This study may be useful to provide some physical insights to the understanding of focused beam scattering by nonspherical particles.
Plachenov, A B; Radin, A M
2011-01-31
Stability conditions for a ring resonator with an odd number of mirrors and a nonplanar axial contour are studied analytically. New explicit expressions are derived to describe the transverse field distribution of the Gaussian mode with general astigmatism produced in this resonator. Field characteristics for a resonator with the specified parameters are calculated. (laser beams)
Brain MRI segmentation and lesion detection using generalized Gaussian and Rician modeling
NASA Astrophysics Data System (ADS)
Wu, Xuqiang; Bricq, Stéphanie; Collet, Christophe
2011-03-01
In this paper we propose a mixed noise modeling so as to segment the brain and to detect lesion. Indeed, accurate segmentation of multimodal (T1, T2 and Flair) brain MR images is of great interest for many brain disorders but requires to efficiently manage multivariate correlated noise between available modalities. We addressed this problem in1 by proposing an entirely unsupervised segmentation scheme, taking into account multivariate Gaussian noise, imaging artifacts,intrinsic tissue variation and partial volume effects in a Bayesian framework. Nevertheless, tissue classification remains a challenging task especially when one addresses the lesion detection during segmentation process2 as we did. In order to improve brain segmentation into White and Gray Matter (resp. WM and GM) and cerebro-spinal fluid (CSF), we propose to fit a Rician (RC) density distribution for CSF whereas Generalized Gaussian (GG) models are used to fit the likelihood between model and data corresponding to WM and GM. In this way, we present in this paper promising results showing that in a multimodal segmentation-detection scheme, this model fits better with the data and increases lesion detection rate. One of the main challenges consists in being able to take into account various pdf (Gaussian and non- Gaussian) for correlated noise between modalities and to show that lesion-detection is then clearly improved, probably because non-Gaussian noise better fits to the physic of MRI image acquisition.
Teodoro, Tiago Quevedo; Haiduke, Roberto Luiz Andrade
2013-10-15
Accurate relativistic adapted Gaussian basis sets (RAGBSs) for 87 Fr up to 118 Uuo atoms without variational prolapse were developed here with the use of a polynomial version of the Generator Coordinate Dirac-Fock method. Two finite nuclear models have been used, the Gaussian and uniform sphere models. The largest RAGBS error, with respect to numerical Dirac-Fock results, is 15.4 miliHartree for Ununoctium with a basis set size of 33s30p19d14f functions. PMID:23913741
Chambers, Alex; Rajantie, Arttu
2008-02-01
If light scalar fields are present at the end of inflation, their nonequilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using nonlinear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models.
Chambers, Alex; Rajantie, Arttu
2008-02-01
If light scalar fields are present at the end of inflation, their nonequilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using nonlinear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models. PMID:18352255
NASA Astrophysics Data System (ADS)
Szalkowski, Gregory; Majeski, Richard; Schmitt, John
2014-10-01
The lithium tokamak experiment (LTX) is a low aspect ratio tokamak with a steel clad copper shell that can be heated to 300-400 °C and coated with lithium. The lithium coating has been shown to decrease impurities in the plasma and decrease the recycling coefficient, improving plasma performance. The coating is applied to the walls by heating the shells, then using an electron beam to evaporate a pool of lithium located at the bottom of the shell. The beam is steered using the magnetic field generated by the field coils. This method allows for rapid evaporation of the lithium, producing a 50-100 nm coating in approximately 5 minutes. The current electron beam system can only coat half of the shell surface. A new electron beam system has been installed on LTX to coat the remaining shell surface. A model of this electron gun has been created using the AMaze program series (Field Precision LCC). The model will be used to find the magnetic fields needed to steer the electron beam produced by the gun to the lithium pool. The model will also show the electropotential produced both at the electron gun head and in the vessel. The model may also be used to find the dispersion of the beam and therefore the effective power density of the beam as it impacts the lithium pool. Supported by US DOE Contracts DE-AC02-09CH11466 and DE-AC52-07NA27344 and in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internship.
Modelling non-Gaussianity of background and observational errors by the Maximum Entropy method
NASA Astrophysics Data System (ADS)
Pires, Carlos; Talagrand, Olivier; Bocquet, Marc
2010-05-01
The Best Linear Unbiased Estimator (BLUE) has widely been used in atmospheric-oceanic data assimilation. However, when data errors have non-Gaussian pdfs, the BLUE differs from the absolute Minimum Variance Unbiased Estimator (MVUE), minimizing the mean square analysis error. The non-Gaussianity of errors can be due to the statistical skewness and positiveness of some physical observables (e.g. moisture, chemical species) or due to the nonlinearity of the data assimilation models and observation operators acting on Gaussian errors. Non-Gaussianity of assimilated data errors can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations (observation minus background). Following this rationale, we compute measures of innovation non-Gaussianity, namely its skewness and kurtosis, relating it to: a) the non-Gaussianity of the individual error themselves, b) the correlation between nonlinear functions of errors, and c) the heteroscedasticity of errors within diagnostic samples. Those relationships impose bounds for skewness and kurtosis of errors which are critically dependent on the error variances, thus leading to a necessary tuning of error variances in order to accomplish consistency with innovations. We evaluate the sub-optimality of the BLUE as compared to the MVUE, in terms of excess of error variance, under the presence of non-Gaussian errors. The error pdfs are obtained by the maximum entropy method constrained by error moments up to fourth order, from which the Bayesian probability density function and the MVUE are computed. The impact is higher for skewed extreme innovations and grows in average with the skewness of data errors, especially if those skewnesses have the same sign. Application has been performed to the quality-accepted ECMWF innovations of brightness temperatures of a set of High Resolution Infrared Sounder channels. In this context, the MVUE has led in some extreme cases to a potential reduction of 20-60% error
MacKenzie, Donald; Spears, Taylor
2014-06-01
Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance. PMID:25051588
Ambrosio, Leonardo A.; Hernández-Figueroa, Hugo E.
2010-01-01
Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised. PMID:21258549
NASA Astrophysics Data System (ADS)
Niknam, A. R.; Banjafar, M. R.; Jahangiri, F.; Barzegar, S.; Massudi, R.
2016-05-01
Terahertz (THz) radiation generation by the interaction of two co-propagating high intensity laser beams with a warm collisional inhomogeneous plasma is analytically investigated. By presenting the dielectric permittivity of plasma and taking into account the ponderomotive force, the nonlinear current at THz frequency is obtained. A secondary resonant enhancement of THz radiation is observed, in addition to that occurs at the plasma frequency, which can be tuned by plasma density and temperature. Moreover, we show that for each beat frequency, there exists an optimum temperature at which THz radiation is maximized. It is also shown that the power and efficiency of THz radiation decrease by increasing the collision frequency.
A beam source model for scanned proton beams
NASA Astrophysics Data System (ADS)
Kimstrand, Peter; Traneus, Erik; Ahnesjö, Anders; Grusell, Erik; Glimelius, Bengt; Tilly, Nina
2007-06-01
A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.
A beam source model for scanned proton beams.
Kimstrand, Peter; Traneus, Erik; Ahnesjö, Anders; Grusell, Erik; Glimelius, Bengt; Tilly, Nina
2007-06-01
A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.
Haiduke, Roberto L A; De Macedo, Luiz G M; Da Silva, Albérico B F
2005-07-15
An accurate relativistic universal Gaussian basis set (RUGBS) from H through No without variational prolapse has been developed by employing the Generator Coordinate Dirac-Fock (GCDF) method. The behavior of our RUGBS was tested with two nuclear models: (1) the finite nucleus of uniform proton-charge distribution, and (2) the finite nucleus with a Gaussian proton-charge distribution. The largest error between our Dirac-Fock-Coulomb total energy values and those calculated numerically is 8.8 mHartree for the No atom.
Haiduke, Roberto L A; De Macedo, Luiz G M; Da Silva, Albérico B F
2005-07-15
An accurate relativistic universal Gaussian basis set (RUGBS) from H through No without variational prolapse has been developed by employing the Generator Coordinate Dirac-Fock (GCDF) method. The behavior of our RUGBS was tested with two nuclear models: (1) the finite nucleus of uniform proton-charge distribution, and (2) the finite nucleus with a Gaussian proton-charge distribution. The largest error between our Dirac-Fock-Coulomb total energy values and those calculated numerically is 8.8 mHartree for the No atom. PMID:15841472
Lehners, Jean-Luc; Steinhardt, Paul J.
2008-03-15
We analyze the non-Gaussian density perturbations generated in ekpyrotic/cyclic models based on heterotic M theory. In this picture, two scalar fields produce nearly scale-invariant entropic perturbations during an ekpyrotic phase that are converted into curvature modes after the ekpyrotic phase is complete and just before the big bang. Both intrinsic nonlinearity in the entropy perturbation and the conversion process contribute to non-Gaussianity. The range of the non-Gaussianity parameter f{sub NL} depends on how gradual the conversion process is and the steepness of the scalar field potential during the ekpyrotic phase. Although a wider range is possible, in principle, natural values of the ekpyrotic parameters combined with a gradual conversion process lead to values of -50 < or approx. f{sub NL} < or approx. +200, typically much greater than slow-roll inflation but within the current observational bounds.
Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise
NASA Astrophysics Data System (ADS)
Kanazawa, Kiyoshi; Sano, Tomohiko G.; Sagawa, Takahiro; Hayakawa, Hisao
2015-03-01
For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.
Modelling and Evaluation of Spectra in Beam Aided Spectroscopy
Hellermann, M. G. von; Delabie, E.; Jaspers, R.; Lotte, P.; Summers, H. P.
2008-10-22
The evaluation of active beam induced spectra requires advanced modelling of both active and passive features. Three types of line shapes are addressed in this paper: Thermal spectra representing Maxwellian distribution functions described by Gaussian-like line shapes, secondly broad-band fast ion spectra with energies well above local ion temperatures, and, finally, the narrow lines shapes of the equi-spaced Motion Stark multiplet (MSE) of excited neutral beam particles travelling through the magnetic field confining the plasma. In each case additional line shape broadening caused by Gaussian-like instrument functions is taken into account. Further broadening effects are induced by collision velocity dependent effective atomic rates where the observed spectral shape is the result of a convolution of emission rate function and velocity distribution function projected into the direction of observation. In the case of Beam Emission Spectroscopy which encompasses the Motional Stark features, line broadening is also caused by the finite angular spread of injected neutrals and secondly by a ripple in the acceleration voltage associated with high energy neutral beams.
Modelling and Evaluation of Spectra in Beam Aided Spectroscopy
NASA Astrophysics Data System (ADS)
von Hellermann, M. G.; Delabie, E.; Jaspers, R.; Lotte, P.; Summers, H. P.
2008-10-01
The evaluation of active beam induced spectra requires advanced modelling of both active and passive features. Three types of line shapes are addressed in this paper: Thermal spectra representing Maxwellian distribution functions described by Gaussian-like line shapes, secondly broad-band fast ion spectra with energies well above local ion temperatures, and, finally, the narrow lines shapes of the equi-spaced Motion Stark multiplet (MSE) of excited neutral beam particles travelling through the magnetic field confining the plasma. In each case additional line shape broadening caused by Gaussian-like instrument functions is taken into account. Further broadening effects are induced by collision velocity dependent effective atomic rates where the observed spectral shape is the result of a convolution of emission rate function and velocity distribution function projected into the direction of observation. In the case of Beam Emission Spectroscopy which encompasses the Motional Stark features, line broadening is also caused by the finite angular spread of injected neutrals and secondly by a ripple in the acceleration voltage associated with high energy neutral beams.
Predictions of a non-Gaussian model for large scale structure
Fan, Z.H.; Bardeen, J.M.
1992-06-26
A modified CDM model for the origin of structure in the universe based on an inflation model with two interacting scalar fields, is analyzed to make predictions for the statistical properties of the density and velocity fields and the microwave background anisotropy. The initial gauge-invariant potential [zeta] which is defined as [zeta] = [delta][rho]/([rho] + p) + 3[var phi], where [var phi] is the curvature perturbation amplitude and p is the pressure, is the sum of a Gaussian field [phi][sub 1], and the square of a Gaussian field [phi][sub 2]. A Harrison-Zel'dovich scale-invariant power spectrum is assumed for [phi][sub 1]; and a log-normal 'peak' power spectrum for [phi][sub 2]. The location and the width of the peak are described by parameters k[sub c] and a. respectively. The model is motivated to some extent by inflation models with two interacting scalar fields, but is mainly interesting as an example of a model whose statistical properties change with scale. On small scales, it is almost identical to a standard scale-invariant Gaussian CDM model. On scales near the location of the peak of the non-Gaussian field, the distributions have long tails in high positive values of the density and velocity fields. Thus, it is easier to get large-scale streaming velocities than the standard CDM model. The quadrupole amplitude of fluctuations of the cosmic microwave background radiation and the rms variation of the temperature field smoothed with a 10[degree] FWHM Gaussian are calculated; a reasonable agreement is found with the new COBE results.
Lee, E.P.
1980-08-08
An analytical model of beam head dynamics is presented, leading to an estimate of the erosion rate due to the combined effects of Ohmic dissipation and scattering. Agreement with the results of a computer simulation and detailed one-dimensional computations is good in all respects except for the scaling of the erosion rate with net current.
Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.
Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H
2016-11-01
Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training. PMID:26701789
Intuitive understanding of non-Gaussianity in ekpyrotic and cyclic models
Lehners, Jean-Luc; Steinhardt, Paul J.
2008-07-15
It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-Gaussianity. In this paper, we present a physically intuitive, semianalytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-Gaussianity parameter f{sub NL} that is determined by the geometric mean of the equation of state w{sub ek} during the ekpyrotic phase and w{sub c} during the phase that curvature perturbations are generated, and whose value is O(100) or more times the intrinsic value predicted by simple slow-roll inflationary models, f{sub NL}{sup intrinsic}=O(0.1). Other contributions to f{sub NL}, which we also estimate, can increase |f{sub NL}| but are unlikely to decrease it significantly, making non-Gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-Gaussianity and scalar spectral index that sharpens the test.
A utilitarian approach to modeling non-Gaussian characteristics of a topographic field
NASA Astrophysics Data System (ADS)
Goff, John A.
1993-11-01
This paper develops a general framework for the analysis of the moments greater than 2 of a topographic field. This framework uses 'iterated' expectation to reduce a statistical moment function to component parts involving the vertical (disjoint) moment of the same order, lower moments, and two-point conditional expectations. In this way it is possible to isolate the unique informational contribution of each moment. Use of this framework necessitates a 'bootstrap' or perturbation method, where lower moments are modeled first and then are used as constraints in the modeling of higher moments. Functional modeling of any moment is thus reducible to characterization of the disjoint moment (e.g., skewness, kurtosis) and the two-point conditional expectation. In this paper, I demonstrate how it is possible to 'design' a statistical model most sensitive to specific non-Gaussian topographic characteristics by solving for the two-point conditional expectation under an invertable mapping between Gaussian and non-Gaussian fields of interest. Mapping of this sort are useful both for the fact that they can be intuitive descriptions of non-Gaussian characteristics and for their utility in generating non-Gaussian synthetic topography. The primary intent of this methodology is to forge a link between physical topography characteristics, the information we want to know, and statistical moments, our tool for quantitatively measuring topographic fields. In addition, mapping models can be used to calculate the skewness and kurtosis (or higher moments) of topographic slopes directly. The applicability of these methods is demonstrated for mapping models which create vertical and lateral asymmetry and peakiness in a topographic field.
Ma, Denglong; Zhang, Zaoxiao
2016-07-01
Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem. PMID:27035273
NASA Astrophysics Data System (ADS)
Krems, Roman; Cui, Jie; Li, Zhiying
2016-05-01
We show how statistical learning techniques based on kriging (Gaussian Process regression) can be used for improving the predictions of classical and/or quantum scattering theory. In particular, we show how Gaussian Process models can be used for: (i) efficient non-parametric fitting of multi-dimensional potential energy surfaces without the need to fit ab initio data with analytical functions; (ii) obtaining scattering observables as functions of individual PES parameters; (iii) using classical trajectories to interpolate quantum results; (iv) extrapolation of scattering observables from one molecule to another; (v) obtaining scattering observables with error bars reflecting the inherent inaccuracy of the underlying potential energy surfaces. We argue that the application of Gaussian Process models to quantum scattering calculations may potentially elevate the theoretical predictions to the same level of certainty as the experimental measurements and can be used to identify the role of individual atoms in determining the outcome of collisions of complex molecules. We will show examples and discuss the applications of Gaussian Process models to improving the predictions of scattering theory relevant for the cold molecules research field. Work supported by NSERC of Canada.
A Non-Gaussian Stock Price Model: Options, Credit and a Multi-Timescale Memory
NASA Astrophysics Data System (ADS)
Borland, L.
We review a recently proposed model of stock prices, based on astatistical feedback model that results in a non-Gaussian distribution of price changes. Applications to option pricing and the pricing of debt is discussed. A generalization to account for feedback effects over multiple timescales is also presented. This model reproduces most of the stylized facts (ie statistical anomalies) observed in real financial markets.
A summary of some beam-beam models
Chao, A.W.
1989-01-01
Two categories of theoretical models for the beam-beam interaction are reviewed: the linear-lens models and the single-resonance models. In a linear-lens model, the beam-beam force is linearized and represented by a localized linear lens. Analyses of incoherent single particle effects can be performed exactly in these models by using matrix techniques. Although the results do not agree with the experimental observations in many respects, the linear-lens models constitute a starting point of our understanding of the beam-beam interaction. In the single-resonance models, one is concerned with the possible incoherent instabilities as the betatron tune of some of the particles is close to a certain rational number. It is assumed in these models that one and only one such rational number dominates the single-particle beam-beam effects. It is found that static single resonances cannot explain many of the experimental results. Some attempts have been made to modify the static single-resonance theory by including some mechanisms for diffusive tune fluctuations or periodic tune modulations. These modified single-resonance models have met only with some limited qualitative success. 21 refs., 13 figs.
Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes
NASA Astrophysics Data System (ADS)
Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin
2014-05-01
We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all
Broadband spatiotemporal Gaussian Schell-model pulse trains.
Dutta, Rahul; Korhonen, Minna; Friberg, Ari T; Genty, Göery; Turunen, Jari
2014-03-01
A new class of partially coherent model sources is introduced on the basis of the second-order coherence theory of nonstationary optical fields. These model sources are spatially fully coherent at each frequency but can have broadband spectra and variable spectral coherence properties, which lead to reduced spatiotemporal coherence in the time domain. The source model is motivated by the spectral coherence properties of supercontinuum pulse trains generated in single-spatial-mode optical fibers. We demonstrate that such broadband light is highly (but not completely) spatially coherent, even though the spectral and temporal coherence properties may vary over a wide range. The model sources introduced here are convenient in assessing the spatiotemporal coherence of broadband pulses in optical systems. PMID:24690663
Munsch, Mathieu; Malik, Nitin S; Dupuy, Emmanuel; Delga, Adrien; Bleuse, Joël; Gérard, Jean-Michel; Claudon, Julien; Gregersen, Niels; Mørk, Jesper
2013-04-26
We introduce the photonic trumpet, a dielectric structure which ensures a nearly perfect coupling between an embedded quantum light source and a Gaussian free-space beam. A photonic trumpet exploits both the broadband spontaneous emission control provided by a single-mode photonic wire and the expansion of this mode within a conical taper. Numerical simulations highlight the performance and robustness of this concept. As a first application in the field of quantum optics, we report the realization of an ultrabright single-photon source. The device, a high aspect ratio GaAs photonic trumpet containing a few InAs quantum dots, demonstrates a first-lens external efficiency of 0.75±0.1 and an external coupling efficiency to a Gaussian beam as high as 0.58±0.08. PMID:23679773
Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry
Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna
2015-01-01
Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717
Large-size Gaussian mode in unstable resonators using Gaussian mirrors.
McCarthy, N; Lavigne, P
1985-11-01
Gaussian modes with large sections have been experimentally produced in Cassegrain resonators using Gaussian reflectivity convex couplers. The far field of the beam, which was coupled through a Gaussian coupler, was found to be free from secondary rings. PMID:19730482
Zhou, Huan-Xiang
2002-01-01
The discrepancy of the pH dependence of the unfolding free energy for staphylococcal nuclease from what is expected from an idealized model for the unfolded state is accounted for by the recently developed Gaussian-chain model. Residual electrostatic effects in the unfolded state are attributed to nonspecific interactions dominated by charges close along the sequence. The dominance of nonspecific local interactions appears to be supported by some experimental evidence. PMID:12496071
NASA Astrophysics Data System (ADS)
Kudashov, V. N.; Plachenov, A. B.; Radin, A. M.
2000-01-01
An analysis is carried out of the ring cavities whose fundamental modes represent Gaussian beams with complex astigmatism. The analysis is made for the case where the block B or C in the cavity ray matrix ABCD of dimension 4×4 is a symmetric nondegenerate matrix. Explicit formulas are obtained, which permits the expression of beam characteristics directly in terms of the cavity ray matrix without the laborious process of finding its eigenvectors. The results obtained in the study can be used for controlling astigmatism in lasers and laser systems, the calculation of polarization of three-dimensional active media in linear and ring optical cavities of complex configuration, etc.
Novel Methods for Surface EMG Analysis and Exploration Based on Multi-Modal Gaussian Mixture Models.
Vögele, Anna Magdalena; Zsoldos, Rebeka R; Krüger, Björn; Licka, Theresia
2016-01-01
This paper introduces a new method for data analysis of animal muscle activation during locomotion. It is based on fitting Gaussian mixture models (GMMs) to surface EMG data (sEMG). This approach enables researchers/users to isolate parts of the overall muscle activation within locomotion EMG data. Furthermore, it provides new opportunities for analysis and exploration of sEMG data by using the resulting Gaussian modes as atomic building blocks for a hierarchical clustering. In our experiments, composite peak models representing the general activation pattern per sensor location (one sensor on the long back muscle, three sensors on the gluteus muscle on each body side) were identified per individual for all 14 horses during walk and trot in the present study. Hereby we show the applicability of the method to identify composite peak models, which describe activation of different muscles throughout cycles of locomotion. PMID:27362752
Novel Methods for Surface EMG Analysis and Exploration Based on Multi-Modal Gaussian Mixture Models
Vögele, Anna Magdalena; Zsoldos, Rebeka R.; Krüger, Björn; Licka, Theresia
2016-01-01
This paper introduces a new method for data analysis of animal muscle activation during locomotion. It is based on fitting Gaussian mixture models (GMMs) to surface EMG data (sEMG). This approach enables researchers/users to isolate parts of the overall muscle activation within locomotion EMG data. Furthermore, it provides new opportunities for analysis and exploration of sEMG data by using the resulting Gaussian modes as atomic building blocks for a hierarchical clustering. In our experiments, composite peak models representing the general activation pattern per sensor location (one sensor on the long back muscle, three sensors on the gluteus muscle on each body side) were identified per individual for all 14 horses during walk and trot in the present study. Hereby we show the applicability of the method to identify composite peak models, which describe activation of different muscles throughout cycles of locomotion. PMID:27362752
Gaussian estimation for discretely observed Cox-Ingersoll-Ross model
NASA Astrophysics Data System (ADS)
Wei, Chao; Shu, Huisheng; Liu, Yurong
2016-07-01
This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. Then, the parameter estimators are obtained by employing the maximum likelihood method and the explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Holder's inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.
Unsupervised Change Detection in SAR Images Using Gaussian Mixture Models
NASA Astrophysics Data System (ADS)
Kiana, E.; Homayouni, S.; Sharifi, M. A.; Farid-Rohani, M.
2015-12-01
In this paper, we propose a method for unsupervised change detection in Remote Sensing Synthetic Aperture Radar (SAR) images. This method is based on the mixture modelling of the histogram of difference image. In this process, the difference image is classified into three classes; negative change class, positive change class and no change class. However the SAR images suffer from speckle noise, the proposed method is able to map the changes without speckle filtering. To evaluate the performance of this method, two dates of SAR data acquired by Uninhabited Aerial Vehicle Synthetic from an agriculture area are used. Change detection results show better efficiency when compared to the state-of-the-art methods.
Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence.
Song, Zhenzhen; Liu, Zhengjun; Zhou, Keya; Sun, Qiongge; Liu, Shutian
2016-01-25
We derive several analytical expressions for the root-mean-square (rms) angular width and the M(2)-factor of the multi-sinc Schell-model (MSSM) beams propagating in non-Kolmogorov turbulence with the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Numerical results show that a MSSM beam with dark-hollow far fields in free space has advantage over the one with flat-topped or multi-rings far fields for reducing the turbulence-induced degradation, which will become more obvious with larger dark-hollow size. Beam quality of MSSM beams can be further improved with longer wavelength and larger beam width, or under the condition of weaker turbulence. We also demonstrate that the non-Kolmogorov turbulence has significantly less effect on the MSSM beams than the Gaussian Schell-model beam.
2.5-D/3-D resistivity modelling in anisotropic media using Gaussian quadrature grids
NASA Astrophysics Data System (ADS)
Zhou, Bing; Greenhalgh, Mark; Greenhalgh, S. A.
2009-01-01
We present a new numerical scheme for 2.5-D/3-D direct current resistivity modelling in heterogeneous, anisotropic media. This method, named the `Gaussian quadrature grid' (GQG) method, cooperatively combines the solution of the Variational Principle of the partial differential equation, Gaussian quadrature abscissae and local cardinal functions so that it has the main advantages of the spectral element method. The formulation shows that the GQG method is a modification of the spectral element method but does not employ the constant elements or require the mesh generator to match the Earth's surface. This makes it much easier to deal with geological models having a 2-D/3-D complex topography than using traditional numerical methods. The GQG technique can achieve a similar convergence rate to the spectral element method. We show it transforms the 2.5-D/3-D resistivity modelling problem into a sparse and symmetric linear equation system that can be solved by an iterative or matrix inversion method. Comparison with analytic solutions for homogeneous isotropic and anisotropic models shows that the error depends on the Gaussian quadrature order (abscissa number) and the subdomain size. The higher the order or the smaller the subdomain size that is employed, the more accurate are the results obtained. Several other synthetic examples, both homogeneous and inhomogeneous, incorporating sloping, undulating and severe topography, are presented and found to yield results comparable to finite element solutions involving a dense mesh.
Mean-field dynamic criticality and geometric transition in the Gaussian core model
NASA Astrophysics Data System (ADS)
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.
Mean-field dynamic criticality and geometric transition in the Gaussian core model.
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model. PMID:27176347
NASA Astrophysics Data System (ADS)
Guo, Yongfeng; Shen, Yajun; Tan, Jianguo
2016-09-01
The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.
Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian
NASA Astrophysics Data System (ADS)
Teneng, Dean
2013-09-01
We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.
Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak
2015-10-15
The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show that the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M; Derocher, Andrew E; Lewis, Mark A; Jonsen, Ian D; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M; Derocher, Andrew E; Lewis, Mark A; Jonsen, Ian D; Mills Flemming, Joanna
2016-05-25
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.
EXACT MINIMAX ESTIMATION OF THE PREDICTIVE DENSITY IN SPARSE GAUSSIAN MODELS1
Mukherjee, Gourab; Johnstone, Iain M.
2015-01-01
We consider estimating the predictive density under Kullback–Leibler loss in an ℓ0 sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density estimates reflects the predictive nature of the problem and optimal strategies need diversification of the future risk. We find that minimax optimal strategies lie outside the Gaussian family but can be constructed with threshold predictive density estimates. Novel minimax techniques involving simultaneous calibration of the sparsity adjustment and the risk diversification mechanisms are used to design optimal predictive density estimates. PMID:26448678
Following a trend with an exponential moving average: Analytical results for a Gaussian model
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.; Serror, Jeremy
2014-01-01
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.
Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks.
Richter, Philipp; Toledano-Ayala, Manuel
2015-01-01
Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996
Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks
Richter, Philipp; Toledano-Ayala, Manuel
2015-01-01
Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996
Schwaab, J; Brons, S; Fieres, J; Parodi, K
2011-12-21
Scanned ion pencil beams carry a low-dose envelope which can extend up to several centimeters from the individual beam central axis. Depending on the energy and species of the beam, this halo consists mainly of secondary particles produced by nuclear interactions in the target or of particles undergoing multiple Coulomb scattering in the beam line components. This halo is often neglected by single Gaussian beam modeling in current treatment planning systems. One possibility of improving the accuracy of treatment planning is to upgrade the used pencil beam models by adding a description of the low-dose envelope. But at the same time it is crucial to keep the calculation time and the complexity for treatment planning in reasonable limits. As a first approach we measured the lateral beam profiles of scanned proton and carbon ion pencil beams at different energies and depths in water and air at the Heidelberg Ion Beam Therapy Center. Then we tried to describe their beam halo by adding a supplementary Gaussian function to the standard single Gauss modeling which is used at the moment by our treatment planning systems. This analysis helped to identify trends in the parameters describing the lateral beam broadening to support its modeling. Finally, it is shown that the accuracy of treatment planning could be improved by the proposed upgrade of the pencil beam model. In particular, the presented experimental data can be either used directly as input for dose calculation or serve for representative comparison with the results of calculation models such as Monte Carlo simulations for the generation of lateral basic data to be input in upgraded beam models of treatment planning systems.
NASA Astrophysics Data System (ADS)
Yu, Junjie; Zhou, Changhe; Wu, Jun; Zhu, Linwei; Jia, Wei; Lu, Yancong; Li, Shubin
2015-01-01
A standing quasi-diffraction-free beam generated by one-order cosine circular Dammann gratings is demonstrated in a single-objective 4Pi focusing system for high-order radially polarized Laguerre-Gaussian incident beams. Numerical results indicate that, similar to a Bessel beam, this standing quasi-diffraction-free beam can also well reconstruct itself after an obstruction, and the self-healing property implies that such beam should be more resistant to scattering. Furthermore, it is shown that, for a focusing system with a water-immersion NA=1.2 objective, the transverse and axial average sizes are about 0.43-0.54λ and 0.36-0.46λ, respectively, for those isotropic focus spots within the whole nondiffracting extent. It suggests that such standing quasi-diffraction-free beam can provide high resolving power along both transverse and axial directions when it is used as the excitation light in fluorescent microscopy. Therefore, this kind of standing quasi-diffraction-free beams should be of high interest in optical biological imaging and also parallel multiplane optical manipulation.
TH-C-BRD-02: Analytical Modeling and Dose Calculation Method for Asymmetric Proton Pencil Beams
Gelover, E; Wang, D; Hill, P; Flynn, R; Hyer, D
2014-06-15
Purpose: A dynamic collimation system (DCS), which consists of two pairs of orthogonal trimmer blades driven by linear motors has been proposed to decrease the lateral penumbra in pencil beam scanning proton therapy. The DCS reduces lateral penumbra by intercepting the proton pencil beam near the lateral boundary of the target in the beam's eye view. The resultant trimmed pencil beams are asymmetric and laterally shifted, and therefore existing pencil beam dose calculation algorithms are not capable of trimmed beam dose calculations. This work develops a method to model and compute dose from trimmed pencil beams when using the DCS. Methods: MCNPX simulations were used to determine the dose distributions expected from various trimmer configurations using the DCS. Using these data, the lateral distribution for individual beamlets was modeled with a 2D asymmetric Gaussian function. The integral depth dose (IDD) of each configuration was also modeled by combining the IDD of an untrimmed pencil beam with a linear correction factor. The convolution of these two terms, along with the Highland approximation to account for lateral growth of the beam along the depth direction, allows a trimmed pencil beam dose distribution to be analytically generated. The algorithm was validated by computing dose for a single energy layer 5×5 cm{sup 2} treatment field, defined by the trimmers, using both the proposed method and MCNPX beamlets. Results: The Gaussian modeled asymmetric lateral profiles along the principal axes match the MCNPX data very well (R{sup 2}≥0.95 at the depth of the Bragg peak). For the 5×5 cm{sup 2} treatment plan created with both the modeled and MCNPX pencil beams, the passing rate of the 3D gamma test was 98% using a standard threshold of 3%/3 mm. Conclusion: An analytical method capable of accurately computing asymmetric pencil beam dose when using the DCS has been developed.
Rezaee, Mostafa Mohammad; Sabaeian, Mohammad; Motazedian, Alireza; Jalil-Abadi, Fatemeh Sedaghat; Khaldi-Nasab, Ali
2015-02-20
In this work, a thorough and detailed solution for the time-dependent heat equation for a cylindrical nonlinear potassium titanyl phosphate (KTP) crystal under a repetitively pulsed pumping source is developed. The convection and radiation boundary conditions, which are usually ignored in the literature, have been taken into account, and their importance on the temperature distribution has been discussed in detail. Moreover, the temperature dependence of thermal conductivity of KTP was considered in the calculations, and its impact is discussed. It is shown that the radiation term has a negligible effect and can be dropped safely, while the temperature dependence of thermal conductivity is more influential, such that ignorance of it brings some errors into the modeling. The time evolution of the temperature while the crystal is pumping with a train of successive Gaussian pulses until reaching equilibrium is shown. To accomplish numerical calculations, we developed a homemade code written with the finite difference time domain method in Intel Fortran (ifort) and ran it with the Linux operating system. PMID:25968183
A Gaussian Mixture Model-Based Continuous Boundary Detection for 3D Sensor Networks
Chen, Jiehui; Salim, Mariam B.; Matsumoto, Mitsuji
2010-01-01
This paper proposes a high precision Gaussian Mixture Model-based novel Boundary Detection 3D (BD3D) scheme with reasonable implementation cost for 3D cases by selecting a minimum number of Boundary sensor Nodes (BNs) in continuous moving objects. It shows apparent advantages in that two classes of boundary and non-boundary sensor nodes can be efficiently classified using the model selection techniques for finite mixture models; furthermore, the set of sensor readings within each sensor node’s spatial neighbors is formulated using a Gaussian Mixture Model; different from DECOMO [1] and COBOM [2], we also formatted a BN Array with an additional own sensor reading to benefit selecting Event BNs (EBNs) and non-EBNs from the observations of BNs. In particular, we propose a Thick Section Model (TSM) to solve the problem of transition between 2D and 3D. It is verified by simulations that the BD3D 2D model outperforms DECOMO and COBOM in terms of average residual energy and the number of BNs selected, while the BD3D 3D model demonstrates sound performance even for sensor networks with low densities especially when the value of the sensor transmission range (r) is larger than the value of Section Thickness (d) in TSM. We have also rigorously proved its correctness for continuous geometric domains and full robustness for sensor networks over 3D terrains. PMID:22163619
NASA Astrophysics Data System (ADS)
Piringer, Martin; Knauder, Werner; Petz, Erwin; Schauberger, Günther
2016-09-01
Direction-dependent separation distances to avoid odour annoyance, calculated with the Gaussian Austrian Odour Dispersion Model AODM and the Lagrangian particle diffusion model LASAT at two sites, are analysed and compared. The relevant short-term peak odour concentrations are calculated with a stability-dependent peak-to-mean algorithm. The same emission and meteorological data, but model-specific atmospheric stability classes are used. The estimate of atmospheric stability is obtained from three-axis ultrasonic anemometers using the standard deviations of the three wind components and the Obukhov stability parameter. The results are demonstrated for the Austrian villages Reidling and Weissbach with very different topographical surroundings and meteorological conditions. Both the differences in the wind and stability regimes as well as the decrease of the peak-to-mean factors with distance lead to deviations in the separation distances between the two sites. The Lagrangian model, due to its model physics, generally calculates larger separation distances. For worst-case calculations necessary with environmental impact assessment studies, the use of a Lagrangian model is therefore to be preferred over that of a Gaussian model. The study and findings relate to the Austrian odour impact criteria.
Non-Gaussian space-variant resolution modelling for list-mode reconstruction
NASA Astrophysics Data System (ADS)
Cloquet, C.; Sureau, F. C.; Defrise, M.; Van Simaeys, G.; Trotta, N.; Goldman, S.
2010-09-01
Partial volume effect is an important source of bias in PET images that can be lowered by accounting for the point spread function (PSF) of the scanner. We measured such a PSF in various points of a clinical PET scanner and modelled it as a product of matrices acting in image space, taking the asymmetrical, shift-varying and non-Gaussian character of the PSF into account (AMP modelling), and we integrated this accurate image space modelling into a conventional list-mode OSEM algorithm (EM-AMP reconstruction). We showed on the one hand that when a sufficiently high number of iterations are considered, the AMP modelling lead to better recovery coefficients at reduced background noise compared to reconstruction where no or only partial resolution modelling is performed, and on the other hand that for a small number of iterations, a Gaussian modelling gave the best recovery coefficients. Moreover, we have demonstrated that a deconvolution based on the AMP system response model leads to the same recovery coefficients as the corresponding EM-AMP reconstruction, but at the expense of an increased background noise.
Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes
Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D.
2016-01-01
This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. PMID:26993062
A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping.
Baptista, Helena; Mendes, Jorge M; MacNab, Ying C; Xavier, Miguel; Caldas-de-Almeida, José
2016-08-01
Conditionally specified Gaussian Markov random field (GMRF) models with adjacency-based neighbourhood weight matrix, commonly known as neighbourhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. In the present paper, we propose a conditionally specified Gaussian random field (GRF) model with a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping. The model, named similarity-based GRF, is motivated for modelling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not vary systematically in space, and the similarity is defined by "similarity" with respect to the associated disease determinant factors. The neighbourhood-based GMRF and the similarity-based GRF are compared and accessed via a simulation study and by two case studies, using new data on alcohol abuse in Portugal collected by the World Mental Health Survey Initiative and the well-known lip cancer data in Scotland. In the presence of disease data with no evidence of positive spatial correlation, the simulation study showed a consistent gain in efficiency from the similarity-based GRF, compared with the adjacency-based GMRF with the determinant risk factors as covariate. This new approach broadens the scope of the existing conditional autocorrelation models.
Content-adaptive pentary steganography using the multivariate generalized Gaussian cover model
NASA Astrophysics Data System (ADS)
Sedighi, Vahid; Fridrich, Jessica; Cogranne, Rémi
2015-03-01
The vast majority of steganographic schemes for digital images stored in the raster format limit the amplitude of embedding changes to the smallest possible value. In this paper, we investigate the possibility to further improve the empirical security by allowing the embedding changes in highly textured areas to have a larger amplitude and thus embedding there a larger payload. Our approach is entirely model driven in the sense that the probabilities with which the cover pixels should be changed by a certain amount are derived from the cover model to minimize the power of an optimal statistical test. The embedding consists of two steps. First, the sender estimates the cover model parameters, the pixel variances, when modeling the pixels as a sequence of independent but not identically distributed generalized Gaussian random variables. Then, the embedding change probabilities for changing each pixel by 1 or 2, which can be transformed to costs for practical embedding using syndrome-trellis codes, are computed by solving a pair of non-linear algebraic equations. Using rich models and selection-channel-aware features, we compare the security of our scheme based on the generalized Gaussian model with pentary versions of two popular embedding algorithms: HILL and S-UNIWARD.
Dorn, Sebastian; Enßlin, Torsten A.; Ramirez, Erandy; Kunze, Kerstin E.
2014-06-01
We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters f{sub NL} and g{sub NL}, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like T- and B-modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.
Canales-Rodríguez, Erick J; Daducci, Alessandro; Sotiropoulos, Stamatios N; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data.
Canales-Rodríguez, Erick J.; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M.; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024
Canales-Rodríguez, Erick J; Daducci, Alessandro; Sotiropoulos, Stamatios N; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024
NASA Astrophysics Data System (ADS)
Mendels, Dan; Tessler, Nir; Organic Materials; Devices Team
2015-03-01
Charge transport in disordered organic systems has been in recent decades mainly discerned from the perspective of a variety of phenomenological models prominent of which those stemming from the Gaussian Disorder Model. But while the use of these models has been prevalent, uncertainty regarding the extent of their validity remains due to the large number of free parameters they consist and their frequent deficiency to consistently account for large sets of experiments while keeping model input parameters and distributions unchanged. In the presented study, we have investigated using Monte Carlo simulations the thermoelectric properties of disordered organic semiconductors under the premise of the Gaussian Disorder Model and its variants. Doing so enabled the provision of additional dimensions for comparison between the aforementioned theoretical frameworks and real systems, beyond those based on extensively studied charge transport properties, and the provision of a frame-of-reference for rising interest in these systems for thermoelectric applications. To illustrate the potential existing in the implementation of combined transport and thermoelectric investigation, strategies will be discussed to experimentally deduce the DOS shape, infer whether a system's activation energy originates from its energetic disorder or a polaron activation energy (while deducing the given polaron activation energy), and discerning whether a system's energetic disorder is spatially correlated or accompanied by off-diagonal disorder.
A blind deconvolution method for attenuative materials based on asymmetrical Gaussian model.
Jin, Haoran; Chen, Jian; Yang, Keji
2016-08-01
During propagation in attenuative materials, ultrasonic waves are distorted by frequency-dependent acoustic attenuation. As a result, reference signals for blind deconvolution in attenuative materials are asymmetrical and should be accurately estimated by considering attenuation. In this study, an asymmetrical Gaussian model is established to estimate the reference signals from these materials, and a blind deconvolution method based on this model is proposed. Based on the symmetrical Gaussian model, the asymmetrical one is formulated by adding an asymmetrical coefficient. Upon establishing the model, the reference signal for blind deconvolution is determined via maximum likelihood estimation, and the blind deconvolution is implemented with an orthogonal matching pursuit algorithm. To verify the feasibility of the established model, spectra of ultrasonic signals from attenuative polyethylene plates with different thicknesses are measured and estimated. The proposed blind deconvolution method is applied to the A-scan signal and B-scan image from attenuative materials. Results demonstrate that the proposed method is capable of separating overlapping echoes and therefore achieves a high temporal resolution. PMID:27586747
Chen, Yunjie; Zhan, Tianming; Zhang, Ji
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Chen, Yunjie; Zhan, Tianming; Zhang, Ji; Wang, Hongyuan
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Option Pricing Formulas Based on a Non-Gaussian Stock Price Model
NASA Astrophysics Data System (ADS)
Borland, Lisa
2002-08-01
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter q. A generalized form of the Black-Scholes (BS) partial differential equation and some closed-form solutions are obtained. The standard BS equation (q=1) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using q=1.5 which well models the empirical distribution of returns, we get a good description of option prices using a single volatility.
Primordial non-Gaussianities in single field inflationary models with non-trivial initial states
Bahrami, Sina; Flanagan, Éanna É. E-mail: eef3@cornell.edu
2014-10-01
We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.
Application of Gaussian moment method to a gene autoregulation model of rational vector field
NASA Astrophysics Data System (ADS)
Kang, Yan-Mei; Chen, Xi
2016-07-01
We take a lambda expression autoregulation model driven by multiplicative and additive noises as example to extend the Gaussian moment method from nonlinear stochastic systems of polynomial vector field to noisy biochemical systems of rational polynomial vector field. As a direct application of the extended method, we also disclose the phenomenon of stochastic resonance. It is found that the transcription rate can inhibit the stochastic resonant effect, but the degradation rate may enhance the phenomenon. These observations should be helpful in understanding the functional role of noise in gene autoregulation.
Fedorov, A K; Anufriev, M N; Zhirnov, A A; Stepanov, K V; Nesterov, E T; Namiot, D E; Karasik, V E; Pnev, A B
2016-03-01
We propose a novel approach to the recognition of particular classes of non-conventional events in signals from phase-sensitive optical time-domain-reflectometry-based sensors. Our algorithmic solution has two main features: filtering aimed at the de-nosing of signals and a Gaussian mixture model to cluster them. We test the proposed algorithm using experimentally measured signals. The results show that two classes of events can be distinguished with the best-case recognition probability close to 0.9 at sufficient numbers of training samples. PMID:27036840
Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data.
Foi, Alessandro; Trimeche, Mejdi; Katkovnik, Vladimir; Egiazarian, Karen
2008-10-01
We present a simple and usable noise model for the raw-data of digital imaging sensors. This signal-dependent noise model, which gives the pointwise standard-deviation of the noise as a function of the expectation of the pixel raw-data output, is composed of a Poissonian part, modeling the photon sensing, and Gaussian part, for the remaining stationary disturbances in the output data. We further explicitly take into account the clipping of the data (over- and under-exposure), faithfully reproducing the nonlinear response of the sensor. We propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image. Experiments with synthetic images and with real raw-data from various sensors prove the practical applicability of the method and the accuracy of the proposed model. PMID:18784024
NASA Astrophysics Data System (ADS)
Shen, Bichuan; Chen, Chi-Hau; Marchisio, Giovanni B.
2012-06-01
In this paper, we aim to study the detection of vehicles from WorldView-2 satellite imagery. For this purpose, accurate modeling of vehicle features and signatures and efficient learning of vehicle hypotheses are critical. We present a joint Gaussian and maximum likelihood based modeling and machine learning approach using SVM and neural network algorithms to describe the local appearance densities and classify vehicles from non-vehicle buildings, objects, and backgrounds. Vehicle hypotheses are fitted by elliptical Gaussians and the bottom-up features are grouped by Gabor orientation filtering based on multi-scale analysis and distance transform. Global contextual information such as road networks and vehicle distributions can be used to enhance the recognition. In consideration of the problem complexity the practical vehicle detection task faces due to dense and overlapping vehicle distributions, partial occlusion and clutters by building, shadows, and trees, we employ a spectral clustering strategy jointly combined with bootstrapped learning to estimate the parameters of centroid, orientation, and extents for local densities. We demonstrate a high detection rate 94.8%,with a missing rate 5.2% and a false alarm rate 5.3% on the WorldView-2 satellite imagery. Experimental results show that our method is quite effective to model and detect vehicles.
Wang, Ting; Ren, Zhao; Ding, Ying; Fang, Zhou; Sun, Zhe; MacDonald, Matthew L; Sweet, Robert A; Wang, Jieru; Chen, Wei
2016-02-01
Biological networks provide additional information for the analysis of human diseases, beyond the traditional analysis that focuses on single variables. Gaussian graphical model (GGM), a probability model that characterizes the conditional dependence structure of a set of random variables by a graph, has wide applications in the analysis of biological networks, such as inferring interaction or comparing differential networks. However, existing approaches are either not statistically rigorous or are inefficient for high-dimensional data that include tens of thousands of variables for making inference. In this study, we propose an efficient algorithm to implement the estimation of GGM and obtain p-value and confidence interval for each edge in the graph, based on a recent proposal by Ren et al., 2015. Through simulation studies, we demonstrate that the algorithm is faster by several orders of magnitude than the current implemented algorithm for Ren et al. without losing any accuracy. Then, we apply our algorithm to two real data sets: transcriptomic data from a study of childhood asthma and proteomic data from a study of Alzheimer's disease. We estimate the global gene or protein interaction networks for the disease and healthy samples. The resulting networks reveal interesting interactions and the differential networks between cases and controls show functional relevance to the diseases. In conclusion, we provide a computationally fast algorithm to implement a statistically sound procedure for constructing Gaussian graphical model and making inference with high-dimensional biological data. The algorithm has been implemented in an R package named "FastGGM".
NASA Astrophysics Data System (ADS)
Ben Alaya, M. A.; Chebana, F.; Ouarda, T. B. M. J.
2016-09-01
Statistical downscaling techniques are required to refine atmosphere-ocean global climate data and provide reliable meteorological information such as a realistic temporal variability and relationships between sites and variables in a changing climate. To this end, the present paper introduces a modular structure combining two statistical tools of increasing interest during the last years: (1) Gaussian copula and (2) quantile regression. The quantile regression tool is employed to specify the entire conditional distribution of downscaled variables and to address the limitations of traditional regression-based approaches whereas the Gaussian copula is performed to describe and preserve the dependence between both variables and sites. A case study based on precipitation and maximum and minimum temperatures from the province of Quebec, Canada, is used to evaluate the performance of the proposed model. Obtained results suggest that this approach is capable of generating series with realistic correlation structures and temporal variability. Furthermore, the proposed model performed better than a classical multisite multivariate statistical downscaling model for most evaluation criteria.
Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model
NASA Astrophysics Data System (ADS)
Liu, B.; Gharamti, M. E.; Hoteit, I.
2016-04-01
An ensemble-based Gaussian mixture (GM) filtering framework is studied in this paper in term of its dependence on the choice of the clustering method to construct the GM. In this approach, a number of particles sampled from the posterior distribution are first integrated forward with the dynamical model for forecasting. A GM representation of the forecast distribution is then constructed from the forecast particles. Once an observation becomes available, the forecast GM is updated according to Bayes' rule. This leads to (i) a Kalman filter-like update of the particles, and (ii) a Particle filter-like update of their weights, generalizing the ensemble Kalman filter update to non-Gaussian distributions. We focus on investigating the impact of the clustering strategy on the behavior of the filter. Three different clustering methods for constructing the prior GM are considered: (i) a standard kernel density estimation, (ii) clustering with a specified mixture component size, and (iii) adaptive clustering (with a variable GM size). Numerical experiments are performed using a two-dimensional reactive contaminant transport model in which the contaminant concentration and the heterogenous hydraulic conductivity fields are estimated within a confined aquifer using solute concentration data. The experimental results suggest that the performance of the GM filter is sensitive to the choice of the GM model. In particular, increasing the size of the GM does not necessarily result in improved performances. In this respect, the best results are obtained with the proposed adaptive clustering scheme.
Wang, Ting; Ren, Zhao; Ding, Ying; Fang, Zhou; Sun, Zhe; MacDonald, Matthew L; Sweet, Robert A; Wang, Jieru; Chen, Wei
2016-02-01
Biological networks provide additional information for the analysis of human diseases, beyond the traditional analysis that focuses on single variables. Gaussian graphical model (GGM), a probability model that characterizes the conditional dependence structure of a set of random variables by a graph, has wide applications in the analysis of biological networks, such as inferring interaction or comparing differential networks. However, existing approaches are either not statistically rigorous or are inefficient for high-dimensional data that include tens of thousands of variables for making inference. In this study, we propose an efficient algorithm to implement the estimation of GGM and obtain p-value and confidence interval for each edge in the graph, based on a recent proposal by Ren et al., 2015. Through simulation studies, we demonstrate that the algorithm is faster by several orders of magnitude than the current implemented algorithm for Ren et al. without losing any accuracy. Then, we apply our algorithm to two real data sets: transcriptomic data from a study of childhood asthma and proteomic data from a study of Alzheimer's disease. We estimate the global gene or protein interaction networks for the disease and healthy samples. The resulting networks reveal interesting interactions and the differential networks between cases and controls show functional relevance to the diseases. In conclusion, we provide a computationally fast algorithm to implement a statistically sound procedure for constructing Gaussian graphical model and making inference with high-dimensional biological data. The algorithm has been implemented in an R package named "FastGGM". PMID:26872036
Chu, Shu-Chun; Chen, Yun-Ting; Tsai, Ko-Fan; Otsuka, Kenju
2012-03-26
This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future. PMID:22453395
NASA Astrophysics Data System (ADS)
Smith, James H.; Crosland, Nigel; Doran, Samuel; Dowling, Robert C.; Hartley, John G.; Hoyle, Philip C.; King, David M. P.; Kutcher, Lawrence; McClelland, Andrew; Turnidge, Martin
2014-03-01
The Vistec VB3001 Gaussian electron-beam lithography system at the College of Nanoscale Science and Engineering (CNSE) in Albany routinely exposes 300 mm wafers to meet the requirements of nano-patterning for metrology and process tool qualification. CNSE and Vistec are partners in a continuous throughput improvement program. The second set of upgrades from this program has recently been implemented on CNSE's VB300 and includes an increase in the maximum exposure clock frequency to 100 MHz and corresponding improvements to the sub-field deflection and beam blanker. To quantify the improvements, we have used an established suite of benchmark patterns2 to compare throughput "before and after". These benchmark patterns show an average throughput improvement factor of 4 times over the timings at the start of the continuous improvement program.
Chu, Shu-Chun; Chen, Yun-Ting; Tsai, Ko-Fan; Otsuka, Kenju
2012-03-26
This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.
Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E
2016-03-01
We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.
Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P. J.; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J.; Ashrafi, Solyman; Molisch, Andreas F.; Tur, Moshe; Willner, Alan E.
2016-01-01
We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively. PMID:26926068
MODELING OF THE NON-GAUSSIAN PDFs OF FIELD VARIATIONS AND INTERMITTENCY IN THE TURBULENT SOLAR WIND
Ragot, B. R.
2013-03-10
The probability distribution functions (PDFs) of magnetic field variations display strong scale-dependent non-Gaussianity in the turbulent solar wind. This is a typical signature of intermittent turbulence. Physical modeling of the turbulent field variations based on the characteristics of the observed turbulence, including the variability of its power level, produces, free of parameter adjustment and over a broad range of inertial scales, accurate fits of the non-Gaussian PDFs. The effects of phase randomization and time resolution of the Fourier power spectra are further tested to determine which of the phase correlation or the spectral variability is responsible for the strong non-Gaussianity of the observed PDFs of field variations. The periods of enhanced power level are found to be responsible for the non-Gaussian tails of the PDFs.
Tan, Liying; Li, Mengnan; Yang, Qingbo; Ma, Jing
2015-03-20
In practice, due to the laser device and the inevitable error of the processing technique, the laser source emitted from the communication terminal is partially coherent, and is represented as a Gaussian Schell model (GSM). The cross-spectral density function based on the Gaussian model in previous research is replaced by the GSM. Thus the fiber-coupling efficiency equation of the GSM laser source through atmospheric turbulence is deduced. The GSM equation presents the effect of the source coherent parameter ζ on the fiber-coupling efficiency, which was not included previously. The effects of the source coherent parameter ζ on the spatial coherent radius and the fiber-coupling efficiency through atmospheric turbulence are numerically simulated and analyzed. The result manifests that the fiber-coupling efficiency invariably degrades with increasing ζ. The work in this paper is aimed to improve the redundancy design of fiber-coupling receiver systems by analyzing the fiber-coupling efficiency with the source coherent parameters.
NASA Astrophysics Data System (ADS)
Xiao, Yiming; Shah, Mohak; Francis, Simon; Arnold, Douglas L.; Arbel, Tal; Collins, D. Louis
Brain tissue segmentation is important in studying markers in human brain Magnetic Resonance Images (MRI) of patients with diseases such as Multiple Sclerosis (MS). Parametric segmentation approaches typically assume unimodal Gaussian distributions on MRI intensities of individual tissue classes, even in applications on multi-spectral images. However, this assumption has not been rigorously verified especially in the context of MS. In this work, we evaluate the local MRI intensities of both healthy and diseased brain tissues of 21 multi-spectral MRIs (63 volumes in total) of MS patients for adherence to this assumption. We show that the tissue intensities are not uniform across the brain and vary across (anatomical) regions of the brain. Consequently, we show that Gaussian mixtures can better model the multi-spectral intensities. We utilize an Expectation Maximization (EM) based approach to learn the models along with a symmetric Jeffreys divergence criterion to study differences in intensity distributions. The effects of these findings are also empirically verified on automatic segmentation of brains with MS.
Cui, Jie; Krems, Roman V.; Li, Zhiying
2015-10-21
We consider a problem of extrapolating the collision properties of a large polyatomic molecule A–H to make predictions of the dynamical properties for another molecule related to A–H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A–X. We assume that the effect of the −H →−X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C{sub 6}H{sub 5}CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C{sub 6}H{sub 6} collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C{sub 6}H{sub 5}CN with He.
NASA Astrophysics Data System (ADS)
Zhao, Fan; Zhao, Jian; Zhao, Wenda; Qu, Feng
2016-05-01
Infrared images are characterized by low signal-to-noise ratio and low contrast. Therefore, the edge details are easily immerged in the background and noise, making it much difficult to achieve infrared image edge detail enhancement and denoising. This article proposes a novel method of Gaussian mixture model-based gradient field reconstruction, which enhances image edge details while suppressing noise. First, by analyzing the gradient histogram of noisy infrared image, Gaussian mixture model is adopted to simulate the distribution of the gradient histogram, and divides the image information into three parts corresponding to faint details, noise and the edges of clear targets, respectively. Then, the piecewise function is constructed based on the characteristics of the image to increase gradients of faint details and suppress gradients of noise. Finally, anisotropic diffusion constraint is added while visualizing enhanced image from the transformed gradient field to further suppress noise. The experimental results show that the method possesses unique advantage of effectively enhancing infrared image edge details and suppressing noise as well, compared with the existing methods. In addition, it can be used to effectively enhance other types of images such as the visible and medical images.
Lee, Sunghoon Ivan; Mortazavi, Bobak; Hoffman, Haydn A; Lu, Derek S; Li, Charles; Paak, Brian H; Garst, Jordan H; Razaghy, Mehrdad; Espinal, Marie; Park, Eunjeong; Lu, Daniel C; Sarrafzadeh, Majid
2016-01-01
Predicting the functional outcomes of spinal cord disorder patients after medical treatments, such as a surgical operation, has always been of great interest. Accurate posttreatment prediction is especially beneficial for clinicians, patients, care givers, and therapists. This paper introduces a prediction method for postoperative functional outcomes by a novel use of Gaussian process regression. The proposed method specifically considers the restricted value range of the target variables by modeling the Gaussian process based on a truncated Normal distribution, which significantly improves the prediction results. The prediction has been made in assistance with target tracking examinations using a highly portable and inexpensive handgrip device, which greatly contributes to the prediction performance. The proposed method has been validated through a dataset collected from a clinical cohort pilot involving 15 patients with cervical spinal cord disorder. The results show that the proposed method can accurately predict postoperative functional outcomes, Oswestry disability index and target tracking scores, based on the patient's preoperative information with a mean absolute error of 0.079 and 0.014 (out of 1.0), respectively. PMID:25423659
Buis, Arjan
2016-01-01
Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm – Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable. PMID:27695626
Approximating Gaussian mixture model or radial basis function network with multilayer perceptron.
Patrikar, Ajay M
2013-07-01
Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN.
Strain-rate dependent shear viscosity of the Gaussian core model fluid.
Ahmed, Alauddin; Mausbach, Peter; Sadus, Richard J
2009-12-14
Nonequilibrium molecular dynamics simulations are reported for the shear viscosity of the Gaussian core model (GCM) fluid over a wide range of densities, temperatures and strain rates. A transition from Newtonian and non-Newtonian behavior is observed in all cases for sufficiently high strain rates. On the high-density side of the solid region where re-entrant melting occurs, the shear viscosity decreases significantly when the density is increased at constant temperature and Newtonian behavior persists until very high strain rates. This behavior, which is attributed to particle overlap, is in contrast to the monotonic increase in shear viscosity with density observed for the Lennard-Jones potential. Contrary to the behavior of normal fluids, the viscosity is observed to increase with increasing temperatures at high densities. This reflects a peculiarity of the GCM, namely the approach to the "infinite-density ideal-gas limit." The behavior is also consistent with viscosity measurements of cationic surfactant solutions. In contrast to other potentials, the shear viscosities for the Gaussian core potential at low to moderate strain rates are obtained with modest statistical uncertainties. Zero shear viscosities extrapolated from the nonequilibrium simulations are in good agreement with equilibrium Green-Kubo calculations.
NASA Astrophysics Data System (ADS)
Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
2016-10-01
As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.
Coherent beam combination of fiber lasers with a strongly confined waveguide: numerical model.
Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin
2012-08-20
Self-imaging properties of fiber lasers in a strongly confined waveguide (SCW) and their application in coherent beam combination (CBC) are studied theoretically. Analytical formulas are derived for the positions, amplitudes, and phases of the N images at the end of an SCW, which is important for quantitative analysis of waveguide CBC. The formulas are verified with experimental results and numerical simulation of a finite difference beam propagation method (BPM). The error of our analytical formulas is less than 6%, which can be reduced to less than 1.5% with Goos-Hahnchen penetration depth considered. Based on the theoretical model and BPM, we studied the combination of two laser beams based on an SCW. The effects of the waveguide refractive index and Gaussian beam waist are studied. We also simulated the CBC of nine and 16 fiber lasers, and a single beam without side lobes was achieved.
Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan
2015-06-20
A theoretical formulation of the spherical-wave two-frequency mutual coherence function (MCF) for a propagation path characterized by a complex ABCD matrix with anisotropic atmospheric turbulence existing somewhere is developed. A specialization of this formulation leads to an expression for the two-frequency MCF of an equivalent pulsed Gaussian beam propagating in weak anisotropic atmospheric turbulence along a horizontal line-of-sight path; relevant closed-form analytical solutions under both near- and far-field conditions are obtained. The small- and large-scale solutions for both the plane- and spherical-wave spatial-coherence radii in either horizontal or vertical direction are derived. Analysis shows that the formula for the on-axis two-frequency MCF of a pulsed Gaussian beam under the weak-turbulence condition in both the near- and far-field regions is distinguished from that applicable in the strong-turbulence limit only by whether the turbulence-induced beam broadening can be thought of as negligible. Under both the near- and far-field conditions, the turbulence-induced increment of the mean-square temporal-pulse half-width is proportional to the effective anisotropy factor of turbulence. The MCF becomes statistically anisotropic due to the anisotropy of turbulence. For the spatial coherence radius of either a plane or spherical wave propagating along a horizontal line-of-sight path in anisotropic atmospheric turbulence, the corresponding small-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient depending only on the effective anisotropy factor of turbulence. The corresponding large-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient that depends on both the effective anisotropy factor and spectral index of turbulence.
Bayesian estimation of airborne fugitive emissions using a Gaussian plume model
NASA Astrophysics Data System (ADS)
Hosseini, Bamdad; Stockie, John M.
2016-09-01
A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of deposition and concentration. We cast this source inversion problem within the Bayesian framework, and use a forward model based on a Gaussian plume solution. We present three alternate models for constructing the prior distribution on the emission rates as functions of time. Next, we present an industrial case study in which our framework is applied to estimate the rate of fugitive emissions of lead particulates from a smelter in Trail, British Columbia, Canada. The Bayesian framework not only provides an approximate solution to the inverse problem, but also quantifies the uncertainty in the solution. Using this information we perform an uncertainty propagation study in order to assess the impact of the estimated sources on the area surrounding the industrial site.
Prediction of Filamentous Sludge Bulking using a State-based Gaussian Processes Regression Model.
Liu, Yiqi; Guo, Jianhua; Wang, Qilin; Huang, Daoping
2016-01-01
Activated sludge process has been widely adopted to remove pollutants in wastewater treatment plants (WWTPs). However, stable operation of activated sludge process is often compromised by the occurrence of filamentous bulking. The aim of this study is to build a proper model for timely diagnosis and prediction of filamentous sludge bulking in an activated sludge process. This study developed a state-based Gaussian Process Regression (GPR) model to monitor the filamentous sludge bulking related parameter, sludge volume index (SVI), in such a way that the evolution of SVI can be predicted over multi-step ahead. This methodology was validated with SVI data collected from one full-scale WWTP. Online diagnosis and prediction of filamentous bulking sludge with real-time SVI prediction was tested through a simulation study. The results showed that the proposed methodology was capable of predicting future SVIs with good accuracy, thus providing sufficient time for predicting and controlling filamentous sludge bulking. PMID:27498888
Adaptive hybrid likelihood model for visual tracking based on Gaussian particle filter
NASA Astrophysics Data System (ADS)
Wang, Yong; Tan, Yihua; Tian, Jinwen
2010-07-01
We present a new scheme based on multiple-cue integration for visual tracking within a Gaussian particle filter framework. The proposed method integrates the color, shape, and texture cues of an object to construct a hybrid likelihood model. During the measurement step, the likelihood model can be switched adaptively according to environmental changes, which improves the object representation to deal with the complex disturbances, such as appearance changes, partial occlusions, and significant clutter. Moreover, the confidence weights of the cues are adjusted online through the estimation using a particle filter, which ensures the tracking accuracy and reliability. Experiments are conducted on several real video sequences, and the results demonstrate that the proposed method can effectively track objects in complex scenarios. Compared with previous similar approaches through some quantitative and qualitative evaluations, the proposed method performs better in terms of tracking robustness and precision.
Prediction of Filamentous Sludge Bulking using a State-based Gaussian Processes Regression Model
Liu, Yiqi; Guo, Jianhua; Wang, Qilin; Huang, Daoping
2016-01-01
Activated sludge process has been widely adopted to remove pollutants in wastewater treatment plants (WWTPs). However, stable operation of activated sludge process is often compromised by the occurrence of filamentous bulking. The aim of this study is to build a proper model for timely diagnosis and prediction of filamentous sludge bulking in an activated sludge process. This study developed a state-based Gaussian Process Regression (GPR) model to monitor the filamentous sludge bulking related parameter, sludge volume index (SVI), in such a way that the evolution of SVI can be predicted over multi-step ahead. This methodology was validated with SVI data collected from one full-scale WWTP. Online diagnosis and prediction of filamentous bulking sludge with real-time SVI prediction was tested through a simulation study. The results showed that the proposed methodology was capable of predicting future SVIs with good accuracy, thus providing sufficient time for predicting and controlling filamentous sludge bulking. PMID:27498888
Spatial location priors for Gaussian model based reverberant audio source separation
NASA Astrophysics Data System (ADS)
Duong, Ngoc QK; Vincent, Emmanuel; Gribonval, Rémi
2013-12-01
We consider the Gaussian framework for reverberant audio source separation, where the sources are modeled in the time-frequency domain by their short-term power spectra and their spatial covariance matrices. We propose two alternative probabilistic priors over the spatial covariance matrices which are consistent with the theory of statistical room acoustics and we derive expectation-maximization algorithms for maximum a posteriori (MAP) estimation. We argue that these algorithms provide a statistically principled solution to the permutation problem and to the risk of overfitting resulting from conventional maximum likelihood (ML) estimation. We show experimentally that in a semi-informed scenario where the source positions and certain room characteristics are known, the MAP algorithms outperform their ML counterparts. This opens the way to rigorous statistical treatment of this family of models in other scenarios in the future.
Li, Lin; Li, Chuan; Alexov, Emil
2014-05-01
Traditional implicit methods for modeling electrostatics in biomolecules use a two-dielectric approach: a biomolecule is assigned low dielectric constant while the water phase is considered as a high dielectric constant medium. However, such an approach treats the biomolecule-water interface as a sharp dielectric border between two homogeneous dielectric media and does not account for inhomogeneous dielectric properties of the macromolecule as well. Recently we reported a new development, a smooth Gaussian-based dielectric function which treats the entire system, the solute and the water phase, as inhomogeneous dielectric medium (J Chem Theory Comput. 2013 Apr 9; 9(4): 2126-2136.). Here we examine various aspects of the modeling of polar solvation energy in such inhomogeneous systems in terms of the solute-water boundary and the inhomogeneity of the solute in the absence of water surrounding. The smooth Gaussian-based dielectric function is implemented in the DelPhi finite-difference program, and therefore the sensitivity of the results with respect to the grid parameters is investigated, and it is shown that the calculated polar solvation energy is almost grid independent. Furthermore, the results are compared with the standard two-media model and it is demonstrated that on average, the standard method overestimates the magnitude of the polar solvation energy by a factor 2.5. Lastly, the possibility of the solute to have local dielectric constant larger than of a bulk water is investigated in a benchmarking test against experimentally determined set of pKa's and it is speculated that side chain rearrangements could result in local dielectric constant larger than 80.
FastGGM: An Efficient Algorithm for the Inference of Gaussian Graphical Model in Biological Networks
Ding, Ying; Fang, Zhou; Sun, Zhe; MacDonald, Matthew L.; Sweet, Robert A.; Wang, Jieru; Chen, Wei
2016-01-01
Biological networks provide additional information for the analysis of human diseases, beyond the traditional analysis that focuses on single variables. Gaussian graphical model (GGM), a probability model that characterizes the conditional dependence structure of a set of random variables by a graph, has wide applications in the analysis of biological networks, such as inferring interaction or comparing differential networks. However, existing approaches are either not statistically rigorous or are inefficient for high-dimensional data that include tens of thousands of variables for making inference. In this study, we propose an efficient algorithm to implement the estimation of GGM and obtain p-value and confidence interval for each edge in the graph, based on a recent proposal by Ren et al., 2015. Through simulation studies, we demonstrate that the algorithm is faster by several orders of magnitude than the current implemented algorithm for Ren et al. without losing any accuracy. Then, we apply our algorithm to two real data sets: transcriptomic data from a study of childhood asthma and proteomic data from a study of Alzheimer’s disease. We estimate the global gene or protein interaction networks for the disease and healthy samples. The resulting networks reveal interesting interactions and the differential networks between cases and controls show functional relevance to the diseases. In conclusion, we provide a computationally fast algorithm to implement a statistically sound procedure for constructing Gaussian graphical model and making inference with high-dimensional biological data. The algorithm has been implemented in an R package named “FastGGM”. PMID:26872036
Synthetic ECG Generation and Bayesian Filtering Using a Gaussian Wave-Based Dynamical Model
Sayadi, Omid; Shamsollahi, Mohammad B.; Clifford, Gari D.
2011-01-01
In this paper, we describe a Gaussian wave-based state space to model the temporal dynamics of electrocardiogram (ECG) signals. It is shown that this model may be effectively used for generating synthetic ECGs as well as separate characteristic waves (CWs) such as the atrial and ventricular complexes. The model uses separate state variables for each CW, i.e. P, QRS and T, and hence is capable of generating individual synthetic CWs as well as realistic ECG signals. The model is therefore useful for generating arrhythmias. Simulations of sinus bradycardia, sinus tachycardia, ventricular flutter, atrial fibrillation, and ventricular tachycardia are presented. In addition, discrete versions of the equations are presented for a model-based Bayesian framework for denoising. This framework, together with an extended Kalman filter (EKF) and extended Kalman smoother (EKS), were used for denoising the ECG for both normal rhythms and arrhythmias. For evaluating the denoising performance the signal-to-noise ratio (SNR) improvement of the filter outputs and clinical parameter stability were studied. The results demonstrate superiority over a wide range of input SNRs, achieving a maximum 12.7 dB improvement. Results indicate that preventing clinically relevant distortion of the ECG is sensitive to the number of model parameters. Models are presented which do not exhibit such distortions. The approach presented in this paper may therefore serve as an effective framework for synthetic ECG generation and model-based filtering of noisy ECG recordings. PMID:20720288
Mendels, Dan; Tessler, Nir
2014-09-18
Using Monte Carlo simulations, we investigate the thermoelectric properties of disordered organic semiconductors under the premise of the Gaussian disorder model and its variants. In doing so, we provide much needed additional dimensions for comparison between these theoretical frameworks and real systems beyond those based on extensively studied charge-transport properties and aim to provide a frame-of-reference for rising interest in these systems for thermoelectric-based applications. To illustrate the potential existing in the implementation of combined transport and thermoelectric investigation, we discuss strategies to experimentally deduce a system's DOS shape and the temperature dependence of its transport energy (which can discern hopping transport from multiple trapping transport), infer whether a system's activation energy originates from inherent energetic disorder or a polaron activation energy (while deducing the given polaron activation energy), and discerning whether a system's energetic disorder is spatially correlated or accompanied by off-diagonal disorder. PMID:26276340
NASA Astrophysics Data System (ADS)
Liu, Sijia; Sa, Ruhan; Maguire, Orla; Minderman, Hans; Chaudhary, Vipin
2015-03-01
Cytogenetic abnormalities are important diagnostic and prognostic criteria for acute myeloid leukemia (AML). A flow cytometry-based imaging approach for FISH in suspension (FISH-IS) was established that enables the automated analysis of several log-magnitude higher number of cells compared to the microscopy-based approaches. The rotational positioning can occur leading to discordance between spot count. As a solution of counting error from overlapping spots, in this study, a Gaussian Mixture Model based classification method is proposed. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) of GMM are used as global image features of this classification method. Via Random Forest classifier, the result shows that the proposed method is able to detect closely overlapping spots which cannot be separated by existing image segmentation based spot detection methods. The experiment results show that by the proposed method we can obtain a significant improvement in spot counting accuracy.
Ma, Rubao; Xu, Weichao; Zhang, Yun; Ye, Zhongfu
2014-01-01
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment. PMID:25393286
Identification of Ligand Binding Sites of Proteins Using the Gaussian Network Model
Tuzmen, Ceren; Erman, Burak
2011-01-01
The nonlocal nature of the protein-ligand binding problem is investigated via the Gaussian Network Model with which the residues lying along interaction pathways in a protein and the residues at the binding site are predicted. The predictions of the binding site residues are verified by using several benchmark systems where the topology of the unbound protein and the bound protein-ligand complex are known. Predictions are made on the unbound protein. Agreement of results with the bound complexes indicates that the information for binding resides in the unbound protein. Cliques that consist of three or more residues that are far apart along the primary structure but are in contact in the folded structure are shown to be important determinants of the binding problem. Comparison with known structures shows that the predictive capability of the method is significant. PMID:21283550
Ma, Rubao; Xu, Weichao; Zhang, Yun; Ye, Zhongfu
2014-01-01
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
NASA Astrophysics Data System (ADS)
Hughes, James M.; Rockmore, Daniel N.; Wang, Yang
2014-02-01
Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.
SAR amplitude probability density function estimation based on a generalized Gaussian model.
Moser, Gabriele; Zerubia, Josiane; Serpico, Sebastiano B
2006-06-01
In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena. PMID:16764268
Chialvo, Ariel A.; Vlcek, Lukas
2014-11-01
We present a detailed derivation of the complete set of expressions required for the implementation of an Ewald summation approach to handle the long-range electrostatic interactions of polar and ionic model systems involving Gaussian charges and induced dipole moments with a particular application to the isobaricisothermal molecular dynamics simulation of our Gaussian Charge Polarizable (GCP) water model and its extension to aqueous electrolytes solutions. The set comprises the individual components of the potential energy, electrostatic potential, electrostatic field and gradient, the electrostatic force and the corresponding virial. Moreover, we show how the derived expressions converge to known point-based electrostatic counterparts when the parameters, defining the Gaussian charge and induced-dipole distributions, are extrapolated to their limiting point values. Finally, we illustrate the Ewald implementation against the current reaction field approach by isothermal-isobaric molecular dynamics of ambient GCP water for which we compared the outcomes of the thermodynamic, microstructural, and polarization behavior.
About a solvable mean field model of a Gaussian spin glass
NASA Astrophysics Data System (ADS)
Barra, Adriano; Genovese, Giuseppe; Guerra, Francesco; Tantari, Daniele
2014-04-01
In a series of papers, we have studied a modified Hopfield model of a neural network, with learned words characterized by a Gaussian distribution. The model can be represented as a bipartite spin glass, with one party described by dichotomic Ising spins, and the other party by continuous spin variables, with an a priori Gaussian distribution. By application of standard interpolation methods, we have found it useful to compare the neural network model (bipartite) from one side, with two spin glass models, each monopartite, from the other side. Of these, the first is the usual Sherrington-Kirkpatrick model, the second is a spin glass model, with continuous spins and inbuilt highly nonlinear smooth cut-off interactions. This model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses. The purpose of this paper is to give a synthetic description of the most peculiar aspects, by stressing the necessary novelties in the treatment. In particular, it will be shown that the control of the infinite volume limit, according to the well-known Guerra-Toninelli strategy, requires in addition one to consider the involvement of the cut-off interaction in the interpolation procedure. Moreover, the control of the ergodic region, the annealed case, cannot be directly achieved through the standard application of the Borel-Cantelli lemma, but requires previous modification of the interaction. This remark could find useful application in other cases. The replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique. However, this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated. A very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one. The definite sign of the error term shows that the replica solution is optimal. Then
NASA Technical Reports Server (NTRS)
Picco, C. E.; Shavers, M. R.; Victor, J. M.; Duron, J. L.; Bowers, W. h.; Gillis, D. B.; VanBaalen, M.
2009-01-01
LIDAR systems that maintain a constant beam spot size on a retroreflector in order to increase the accuracy of bearing and ranging data must use a software controlled variable position lens. These systems periodically update the estimated range and set the position of the focusing lens accordingly. In order to precisely calculate the r NOHD for such a system, the software method for setting the variable position lens and gaussian laser propagation can be used to calculate the irradiance at any point given the range estimation. NASA s Space Shuttle LIDAR, called the Trajectory Control Sensor (TCS), uses this configuration. Analytical tools were developed using Excel and VBA to determine the radiant energy to the International Space Station (ISS) crewmembers eyes while viewing the shuttle on approach and departure. Various viewing scenarios are considered including the use of through-the-lens imaging optics and the window transmissivity at the TCS wavelength. The methodology incorporates the TCS system control logic, gaussian laser propagation, potential failure mode end states, and guidance from American National Standard for the Safe Use of Lasers (ANSI Z136.1-2007). This approach can be adapted for laser safety analyses of similar LIDAR systems.
Blakeslee, Barbara; Cope, Davis; McCourt, Mark E
2016-03-01
The Oriented Difference of Gaussians (ODOG) model of brightness (perceived intensity) by Blakeslee and McCourt (Vision Research 39:4361-4377, 1999), which is based on linear spatial filtering by oriented receptive fields followed by contrast normalization, has proven highly successful in parsimoniously predicting the perceived intensity (brightness) of regions in complex visual stimuli such as White's effect, which had been believed to defy filter-based explanations. Unlike competing explanations such as anchoring theory, filling-in, edge-integration, or layer decomposition, the spatial filtering approach embodied by the ODOG model readily accounts for the often overlooked but ubiquitous gradient structure of induction which, while most striking in grating induction, also occurs within the test fields of classical simultaneous brightness contrast and the White stimulus. Also, because the ODOG model does not require defined regions of interest, it is generalizable to any stimulus, including natural images. The ODOG model has motivated other researchers to develop modified versions (LODOG and FLODOG), and has served as an important counterweight and proof of concept to constrain high-level theories which rely on less well understood or justified mechanisms such as unconscious inference, transparency, perceptual grouping, and layer decomposition. Here we provide a brief but comprehensive description of the ODOG model as it has been implemented since 1999, as well as working Mathematica (Wolfram, Inc.) notebooks which users can employ to generate ODOG model predictions for their own stimuli.
Modal identification based on Gaussian continuous time autoregressive moving average model
NASA Astrophysics Data System (ADS)
Xiuli, Du; Fengquan, Wang
2010-09-01
A new time-domain modal identification method of the linear time-invariant system driven by the non-stationary Gaussian random force is presented in this paper. The proposed technique is based on the multivariate continuous time autoregressive moving average (CARMA) model. This method can identify physical parameters of a system from the response-only data. To do this, we first transform the structural dynamic equation into the CARMA model, and subsequently rewrite it in the state-space form. Second, we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive (CAR) model by virtue of the Girsanov theorem, under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time. Then, based on the relation between the CAR model and the CARMA model, we present the exact maximum likelihood estimators of parameters of the CARMA model. Finally, the modal parameters are identified by the eigenvalue analysis method. Numerical results show that the method we introduced here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.
Cummings, P.; Thomas, A. G. R.
2011-05-15
Critical to the performance of any future accelerator based on the laser wakefield accelerator is the response of the system to perturbations from ideal. In this paper, we use particle-in-cell simulation using a modified version of the OSIRIS 2.0 framework to demonstrate that comatic optical aberrations in a nominally Gaussian laser pulse are self-corrected by the plasma response, leading to stable propagation and therefore little variation in peak energy, energy spread, or peak current of the accelerated bunch, even for serious aberrations. However, the comatic aberration does lead to enhanced transverse beam emittance in the direction of the coma. Although this may be deleterious to the performance of an accelerator, one useful outcome is that the increased oscillation amplitude of electrons in the wake structure may lead to increased synchrotron radiation emission, which would be partially polarized in the direction of coma.
Huang, Jiayao; Liang, Zijie; Deng, Fu; Yu, Weihao; Zhao, Ruihuang; Chen, Bo; Yang, Xiangbo; Deng, Dongmei
2015-11-01
The propagation of right-hand circularly polarized Airy-Gaussian beams (RHCPAiGBs) through slabs of right-handed materials (RHMs) and left-handed materials (LHMs) is investigated analytically and numerically with the transfer matrix method. An approximate analytical expression for the RHCPAiGBs passing through a paraxial ABCD optical system is derived on the basis of the Huygens diffraction integral formula. The intensity and the phase distributions of the RHCPAiGBs through RHMs and LHMs are demonstrated. The influence of the parameter χ_{0} on the propagation of RHCPAiGBs through RHM and LHM slabs is investigated. The RHCPAiGBs possess transverse-momentum currents, which shows that the physics underlying this intriguing accelerating effect is that of the combined contributions of the transverse spin and transverse orbital currents. Additionally, we go a step further to explore the radiation force including the gradient force and scattering force of the RHCPAiGBs.
Small signal gain based on analytic models of thin intense electron beams
NASA Astrophysics Data System (ADS)
James Elliott, C.; McVey, Brian; Schmitt, Mark
1991-07-01
We develop the free electron laser theory of the effective energy distribution and the small signal gain for a thin electron beam. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. These ideas extend previous work of Colson et al., Dattoli et al., Scharlemann, and others in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (i) electron beams with separate betatron matching in each plane. (ii) those with aspect ratio matching, and (iii) crossed matched beams. Manifestations of these symmetries include elliptical cross-sections and electron beams that have modulated spatial profiles. For these we derive analytical expressions for effective energy distributions. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Thus, the effective energy distribution for a 1:4 ribbon electron beam is nearly equivalent to a distribution for a beam of circular cross-section. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernel. Emittance, energy spread, diffraction, and gain may be interpreted as limiting the length over which the bunching contributions of the propagating electric fields downstream are important. Fifth, three-dimensional profiles of the optical fields are computed. This work is complementary to the recent work of Yu, Krinsky and Gluckstern in that ours always describes the transition from low gain to high gain for a thin beam and not
Atomic forces for geometry-dependent point multipole and gaussian multipole models.
Elking, Dennis M; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G
2010-11-30
In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry-dependent multipole models. In this study, atomic force expressions for geometry-dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives partial derivative D(m'm)(l)/partial derivative Omega. The force equations can be applied to electrostatic models based on atomic point multipoles or gaussian multipole charge density. Hydrogen-bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry-dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry-dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry-dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry-dependent multipole models.
IntegriSense molecular image sequence classification using Gaussian mixture model
NASA Astrophysics Data System (ADS)
He, Tiancheng; Xue, Zhong; Lu, Kongkuo; Valdivia y Alvarado, Miguel; Wong, Stephen T.
2012-03-01
Targeted fluorescence imaging agents such as IntegriSense 680 can be used to label integrin αvβ3 expressed in tumor cells and to distinguish tumor from normal tissues. Coupled with endomicroscopy and image-guided intervention devices, fluorescence contrast captured from the fiber-optic imaging technique can be used in a Minimally Invasive Multimodality Image Guided (MIMIG) system for on-site peripheral lung cancer diagnosis. In this work, we propose an automatic quantification approach for IntegriSense-based fluorescence endomicroscopy image sequences. First, a sliding time-window is used to calculate the histogram of the frames at a given timepoint, also denoted as the IntegriSense signal. The intensity distributions of the endomicroscopy image sequences can be briefly classified into three groups: high, middle and low intensities, which might correspond to tumor, normal tissue, and background (air) tissues within the lungs, respectively. At a given time-point, the histogram calculated from the sliding time-window is fit with a Gaussian mixture model, and the average and standard deviation (std), as well as the weight of each Gaussian distribution can be identified. Finally, a threshold can be used to the weighting parameter of the high intensity group for tumor information detection. This algorithm can be used as an automatic tumor detection tool from IntegriSense-based endomicroscopy. In experiments, we validated the algorithm using 20 IntegriSense-based fluorescence endomicroscopy image sequences collected from 6 rabbit experiments, where VX2 tumor was implanted into the lung of each rabbit, and image-guided endomicroscopy was performed. The automatic classification results were compared with manual results, and high sensitivity and specificity were obtained.
Dynamic Modelling of Aquifer Level Using Space-Time Kriging and Sequential Gaussian Simulation
NASA Astrophysics Data System (ADS)
Varouchakis, Emmanouil A.; Hristopulos, Dionisis T.
2016-04-01
Geostatistical models are widely used in water resources management projects to represent and predict the spatial variability of aquifer levels. In addition, they can be applied as surrogate to numerical hydrological models if the hydrogeological data needed to calibrate the latter are not available. For space-time data, spatiotemporal geostatistical approaches can model the aquifer level variability by incorporating complex space-time correlations. A major advantage of such models is that they can improve the reliability of predictions compared to purely spatial or temporal models in areas with limited spatial and temporal data availability. The identification and incorporation of a spatiotemporal trend model can further increase the accuracy of groundwater level predictions. Our goal is to derive a geostatistical model of dynamic aquifer level changes in a sparsely gauged basin on the island of Crete (Greece). The available data consist of bi-annual (dry and wet hydrological period) groundwater level measurements at 11 monitoring locations for the time period 1981 to 2010. We identify a spatiotemporal trend function that follows the overall drop of the aquifer level over the study period. The correlation of the residuals is modeled using a non-separable space-time variogram function based on the Spartan covariance family. The space-time Residual Kriging (STRK) method is then applied to combine the estimated trend and the residuals into dynamic predictions of groundwater level. Sequential Gaussian Simulation is also employed to determine the uncertainty of the spatiotemporal model (trend and covariance) parameters. This stochastic modelling approach produces multiple realizations, ranks the prediction results on the basis of specified criteria, and captures the range of the uncertainty. The model projections recommend that in 2032 a part of the basin will be under serious threat as the aquifer level will approximate the sea level boundary.
Exponential Gaussian approach for spectral modeling: The EGO algorithm I. Band saturation
NASA Astrophysics Data System (ADS)
Pompilio, Loredana; Pedrazzi, Giuseppe; Sgavetti, Maria; Cloutis, Edward A.; Craig, Michael A.; Roush, Ted L.
2009-06-01
Curve fitting techniques are a widespread approach to spectral modeling in the VNIR range [Burns, R.G., 1970. Am. Mineral. 55, 1608-1632; Singer, R.B., 1981. J. Geophys. Res. 86, 7967-7982; Roush, T.L., Singer, R.B., 1986. J. Geophys. Res. 91, 10301-10308; Sunshine, J.M., Pieters, C.M., Pratt, S.F., 1990. J. Geophys. Res. 95, 6955-6966]. They have been successfully used to model reflectance spectra of powdered minerals and mixtures, natural rock samples and meteorites, and unknown remote spectra of the Moon, Mars and asteroids. Here, we test a new decomposition algorithm to model VNIR reflectance spectra and call it Exponential Gaussian Optimization (EGO). The EGO algorithm is derived from and complementary to the MGM of Sunshine et al. [Sunshine, J.M., Pieters, C.M., Pratt, S.F., 1990. J. Geophys. Res. 95, 6955-6966]. The general EGO equation has been especially designed to account for absorption bands affected by saturation and asymmetry. Here we present a special case of EGO and address it to model saturated electronic transition bands. Our main goals are: (1) to recognize and model band saturation in reflectance spectra; (2) to develop a basic approach for decomposition of rock spectra, where effects due to saturation are most prevalent; (3) to reduce the uncertainty related to quantitative estimation when band saturation is occurring. In order to accomplish these objectives, we simulate flat bands starting from pure Gaussians and test the EGO algorithm on those simulated spectra first. Then we test the EGO algorithm on a number of measurements acquired on powdered pyroxenes having different compositions and average grain size and binary mixtures of orthopyroxenes with barium sulfate. The main results arising from this study are: (1) EGO model is able to numerically account for the occurrence of saturation effects on reflectance spectra of powdered minerals and mixtures; (2) the systematic dilution of a strong absorber using a bright neutral material is not
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2016-10-01
Stemming from the law of the conservation of energy in an elastic medium, this work extends the scope of the previous analysis for a scatterer immersed in a nonviscous liquid [F. G. Mitri, Ultrasonics 62, 20-26 (2015)] to the case of a (viscous) fluid circular cylinder cross-section encased in a homogeneous, isotropic, elastic matrix. Analytical expressions for the absorption, scattering, and extinction efficiencies (or cross-sections) are derived for "elastic-sheets" (i.e., finite beams in 2D propagating in elastic media) of arbitrary wavefront, in contrast to the ideal case of plane waves of infinite extent. The mathematical expressions are formulated in generalized partial-wave series expansions in cylindrical coordinates involving the beam-shape coefficients of finite elastic-sheet beams with arbitrary wavefront, and the scattering coefficients of the fluid cylinder encased in the elastic matrix. The analysis shows that in elastodynamic scattering, both the scattered L-wave as well as the scattered T-wave contribute to the time-averaged scattered efficiency (or power). However, the extinction efficiency only depends on the scattering coefficients characterizing the same type (L or T) as the incident wave. Numerical computations for the (non-dimensional energy) efficiency factors such as the absorption, scattering, and extinction efficiencies of a circular cylindrical viscous fluid cavity embedded in an elastic aluminum matrix are performed for nonparaxial focused Gaussian and Airy elastic-sheet beams with arbitrary longitudinal and transverse normally-polarized (shear) wave incidences in the Rayleigh and resonance regimes. A series of elastic resonances are manifested in the plots of the efficiencies as the non-dimensional size parameters for the L- and T-waves are varied. As the beam waist for the nonparaxial Gaussian beam increases, the plane wave result is recovered, while for a tightly focused wavefront, some of the elastic resonances can be suppressed
Sabaeian, Mohammad; Jalil-Abadi, Fatemeh Sedaghat; Rezaee, Mostafa Mohammad; Motazedian, Alireza; Shahzadeh, Mohammadreza
2015-02-01
In this work, the effect of temperature increase on the efficiency of a double-pass cavity type II second-harmonic generation (SHG) is investigated. To this end, a depleted wave model describing the continuous-wave SHG process with fundamental Gaussian waves was developed. First, six coupled equations were proposed to model a double-pass cavity to generate the second harmonic of a Gaussian fundamental wave in type II configuration. Then, the effect of temperature increase in the nonlinear crystal due to the optical absorption was modeled. To do this, a mismatched phase arising from changes in refractive indices was added to the coupled equations. Although the nondepleted assumption is usually used in such problems, a simultaneous solving of coupled equations with assumption of fundamental beam depletion was performed. The results were obtained by a homemade code written in Intel Fortran, and show how the efficiency of the SHG process decreases when the crystal is warmed up by 5, 10, and 15 K. Dramatic reductions in SHG efficiency were observed due to small changes in temperature. The results show excellent agreement with the experimental data [Opt. Commun.173, 311-314 (2000)]. PMID:25967798
Model fitting of kink waves in the solar atmosphere: Gaussian damping and time-dependence
NASA Astrophysics Data System (ADS)
Morton, R. J.; Mooroogen, K.
2016-09-01
Aims: Observations of the solar atmosphere have shown that magnetohydrodynamic waves are ubiquitous throughout. Improvements in instrumentation and the techniques used for measurement of the waves now enables subtleties of competing theoretical models to be compared with the observed waves behaviour. Some studies have already begun to undertake this process. However, the techniques employed for model comparison have generally been unsuitable and can lead to erroneous conclusions about the best model. The aim here is to introduce some robust statistical techniques for model comparison to the solar waves community, drawing on the experiences from other areas of astrophysics. In the process, we also aim to investigate the physics of coronal loop oscillations. Methods: The methodology exploits least-squares fitting to compare models to observational data. We demonstrate that the residuals between the model and observations contain significant information about the ability for the model to describe the observations, and show how they can be assessed using various statistical tests. In particular we discuss the Kolmogorov-Smirnoff one and two sample tests, as well as the runs test. We also highlight the importance of including any observational trend line in the model-fitting process. Results: To demonstrate the methodology, an observation of an oscillating coronal loop undergoing standing kink motion is used. The model comparison techniques provide evidence that a Gaussian damping profile provides a better description of the observed wave attenuation than the often used exponential profile. This supports previous analysis from Pascoe et al. (2016, A&A, 585, L6). Further, we use the model comparison to provide evidence of time-dependent wave properties of a kink oscillation, attributing the behaviour to the thermodynamic evolution of the local plasma.
NASA Astrophysics Data System (ADS)
Verpoorter, C.; Carrère, V.; Combe, J.-P.; Le Corre, L.
2009-04-01
Understanding of the uppermost layer of cohesive sediment beds provides important clues for predicting future sediment behaviours. Sediment consolidation, grain size, water content and biological slimes (EPS: extracellular polymeric substances) were found to be significant factors influencing erosion resistance. The surface spectral signatures of mudflat sediments reflect such bio-geophysical parameters. The overall shape of the spectrum, also called a continuum, is a function of grain size and moisture content. Composition translates into specific absorption features. Finally, the chlorophyll-a concentration derived from the strength of the absorption at 675 nm, is a good proxy for biofilm biomass. Bourgneuf Bay site, south of the Loire river estuary, France, was chosen to represent a range of physical and biological influences on sediment erodability. Field spectral measurements and samples of sediments were collected during various field campaigns. An ASD Fieldspec 3 spectroradiometer was used to produce sediment reflectance hyperspectra in the wavelength range 350-2500 nm. We have developed an automatic procedure based on the Modified Gaussian Model that uses, as the first step, the Spectroscopic Derivative Analysis (SDA) to extract from spectra the bio-geophysical properties on mudflat sediments (Verpoorter et al., 2007). This AMGM algorithm is a powerfull tool to deconvolve spectra into two components, first gaussian curves for the absorptions bands, and second a straight line in the wavenumber range for the continuum. We are investigating the possibility of including other approaches, as the inverse gaussian band centred on 2800 nm initially developed by Whiting et al., (2006) to estimate water content. Additionally, soils samples were analysed to determine moisture content, grain size (laser grain size analyses), organic matter content, carbonate content (calcimetry) and clay content. X-ray diffraction analysis was performed on selected non
Evaluation of realtime spray drift using RTDrift Gaussian advection-diffusion model.
Lebeau, Frédéric; Verstraete, Arnaud; Schiffers, Bruno; Destain, Marie-France
2009-01-01
A spray drift model was developed to deliver real time information to the pesticide applicator. The sprayer is equipped with sensors to deliver real time measurement of operational parameters as spray pressure, boom height, horizontal boom movements and geolocalization. The spray droplet size spectrum as a function of pressure was characterized using PDI measurements. Wind speed and direction were measured using a sprayer mounted 2-D ultrasonic anemometer. For each successive boom position, a diffusion-advection Gaussian tilting plume model is used to compute the spray drift deposits downwind. Drift is computed independently for each droplet classes and each nozzle based on the operating parameters. Field trials were performed on a test plot in various wind conditions. The ground drift was measured for different drift distances using fluorimetry analysis. Results show that drift deposits are mainly affected by wind speed and direction what was correctly accounted for by the model. Short distance drift deposits values were overestimated by the model while long distance drift was underestimated. It appears that this most probably origins from embarked wind speed measurements and diffusion parameter. It is concluded that a treatment of embarked wind speed and diffusion measurement should be used to minimize these errors. PMID:20218507
A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems
NASA Astrophysics Data System (ADS)
Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Hashemi Golpayegani, S. Mohammad Reza; Almasganj, Farshad
2015-02-01
As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.
Li, Baoyue; Bruyneel, Luk; Lesaffre, Emmanuel
2014-05-20
A traditional Gaussian hierarchical model assumes a nested multilevel structure for the mean and a constant variance at each level. We propose a Bayesian multivariate multilevel factor model that assumes a multilevel structure for both the mean and the covariance matrix. That is, in addition to a multilevel structure for the mean we also assume that the covariance matrix depends on covariates and random effects. This allows to explore whether the covariance structure depends on the values of the higher levels and as such models heterogeneity in the variances and correlation structure of the multivariate outcome across the higher level values. The approach is applied to the three-dimensional vector of burnout measurements collected on nurses in a large European study to answer the research question whether the covariance matrix of the outcomes depends on recorded system-level features in the organization of nursing care, but also on not-recorded factors that vary with countries, hospitals, and nursing units. Simulations illustrate the performance of our modeling approach.
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Franco-Pedroso, Javier; Ramos, Daniel; Gonzalez-Rodriguez, Joaquin
2016-01-01
In forensic science, trace evidence found at a crime scene and on suspect has to be evaluated from the measurements performed on them, usually in the form of multivariate data (for example, several chemical compound or physical characteristics). In order to assess the strength of that evidence, the likelihood ratio framework is being increasingly adopted. Several methods have been derived in order to obtain likelihood ratios directly from univariate or multivariate data by modelling both the variation appearing between observations (or features) coming from the same source (within-source variation) and that appearing between observations coming from different sources (between-source variation). In the widely used multivariate kernel likelihood-ratio, the within-source distribution is assumed to be normally distributed and constant among different sources and the between-source variation is modelled through a kernel density function (KDF). In order to better fit the observed distribution of the between-source variation, this paper presents a different approach in which a Gaussian mixture model (GMM) is used instead of a KDF. As it will be shown, this approach provides better-calibrated likelihood ratios as measured by the log-likelihood ratio cost (Cllr) in experiments performed on freely available forensic datasets involving different trace evidences: inks, glass fragments and car paints. PMID:26901680
Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control
Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.
1997-01-01
One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.
NASA Astrophysics Data System (ADS)
Kuyuk, H. S.; Yildirim, E.; Dogan, E.; Horasan, G.
2012-08-01
Two unsupervised pattern recognition algorithms, k-means, and Gaussian mixture model (GMM) analyses have been applied to classify seismic events in the vicinity of Istanbul. Earthquakes, which are occurring at different seismicity rates and extensions of the Thrace-Eskisehir Fault Zone and the North Anatolian Fault (NAF), Turkey, are being contaminated by quarries operated around Istanbul. We have used two time variant parameters, complexity, the ratio of integrated powers of the velocity seismogram, and S/P amplitude ratio as classifiers by using waveforms of 179 events (1.8 < M < 3.0). We have compared two algorithms with classical multivariate linear/quadratic discriminant analyses. The total accuracies of the models for GMM, k-means, linear discriminant function (LDF), and quadratic discriminant function (QDF) are 96.1%, 95.0%, 96.1%, 96.6%, respectively. The performances of models are discussed for earthquakes and quarry blasts separately. All methods clustered the seismic events acceptably where QDF slightly gave better improvements compared to others. We have found that unsupervised clustering algorithms, for which no a-prior target information is available, display a similar discriminatory power as supervised methods of discriminant analysis.
A Gaussian mixture model for definition of lung tumor volumes in positron emission tomography
Aristophanous, Michalis; Penney, Bill C.; Martel, Mary K.; Pelizzari, Charles A.
2007-11-15
The increased interest in {sup 18}F-fluorodeoxyglucose (FDG) positron emission tomography (PET) in radiation treatment planning in the past five years necessitated the independent and accurate segmentation of gross tumor volume (GTV) from FDG-PET scans. In some studies the radiation oncologist contours the GTV based on a computed tomography scan, while incorporating pertinent data from the PET images. Alternatively, a simple threshold, typically 40% of the maximum intensity, has been employed to differentiate tumor from normal tissue, while other researchers have developed algorithms to aid the PET based GTV definition. None of these methods, however, results in reliable PET tumor segmentation that can be used for more sophisticated treatment plans. For this reason, we developed a Gaussian mixture model (GMM) based segmentation technique on selected PET tumor regions from non-small cell lung cancer patients. The purpose of this study was to investigate the feasibility of using a GMM-based tumor volume definition in a robust, reliable and reproducible way. A GMM relies on the idea that any distribution, in our case a distribution of image intensities, can be expressed as a mixture of Gaussian densities representing different classes. According to our implementation, each class belongs to one of three regions in the image; the background (B), the uncertain (U) and the target (T), and from these regions we can obtain the tumor volume. User interaction in the implementation is required, but is limited to the initialization of the model parameters and the selection of an 'analysis region' to which the modeling is restricted. The segmentation was developed on three and tested on another four clinical cases to ensure robustness against differences observed in the clinic. It also compared favorably with thresholding at 40% of the maximum intensity and a threshold determination function based on tumor to background image intensities proposed in a recent paper. The parts of
NASA Technical Reports Server (NTRS)
Kattawar, G. W.
1980-01-01
The multipole expansion obtained by Morita et al. (1968) of the Gaussian laser beam used to levitate an aerosol particle in order that its complete phase matrix may be measured is compared with that of Tsai and Pogorzelski (1975) in order to demonstrate the effect of the incorrect expansion used by Morita. Errors incurred by the use of an equation in which one side satisfies the scalar wave equation while the other side does not and can be reduced to a plane wave amplitude are calculated as functions of the inverse of the wave number times the beam waist, the wave number times the radial spherical coordinate and the angular spherical coordinate. Errors on the order of a few percent, considered undetectable are obtained in the squared-field amplitudes due to the expansion, however, they are found to become significant (several tens of percent) when the angle is zero. It is concluded that the expansion of Morita should only be used in the regions where the spherical angle is less than 0.01 and its product with the wave number and the radial spherical coordinate is less than unity.
RNA-Seq Count Data Modelling by Grey Relational Analysis and Nonparametric Gaussian Process
Nguyen, Thanh; Bhatti, Asim; Yang, Samuel; Nahavandi, Saeid
2016-01-01
This paper introduces an approach to classification of RNA-seq read counts using grey relational analysis (GRA) and Bayesian Gaussian process (GP) models. Read counts are transformed to microarray-like data to facilitate normal-based statistical methods. GRA is designed to select differentially expressed genes by integrating outcomes of five individual feature selection methods including two-sample t-test, entropy test, Bhattacharyya distance, Wilcoxon test and receiver operating characteristic curve. GRA performs as an aggregate filter method through combining advantages of the individual methods to produce significant feature subsets that are then fed into a nonparametric GP model for classification. The proposed approach is verified by using two benchmark real datasets and the five-fold cross-validation method. Experimental results show the performance dominance of the GRA-based feature selection method as well as GP classifier against their competing methods. Moreover, the results demonstrate that GRA-GP considerably dominates the sparse Poisson linear discriminant analysis classifiers, which were introduced specifically for read counts, on different number of features. The proposed approach therefore can be implemented effectively in real practice for read count data analysis, which is useful in many applications including understanding disease pathogenesis, diagnosis and treatment monitoring at the molecular level. PMID:27783633
Highway traffic segmentation using super-resolution and Gaussian mixture model
NASA Astrophysics Data System (ADS)
Yousef, Amr Hussein; Flora, Jeff; Iftekharuddin, Khan
2013-09-01
One benefit of employing computer vision techniques to extract individual vehicles from a highway traffic scene is the abundance of networked, traffic surveillance cameras that may be leveraged as the input video. However, the acquisition sensors that are monitoring the highway traffic will have very limited quality. Additionally, video streams are heavily compressed, causing noise and, in some cases, visible artifacts to be introduced into the video. Further challenges are presented by external environmental and weather conditions, such as rain, fog, and snow, that cause video blurring or noise. The resulting output of a segmentation algorithm yields poorer results, with many vehicles undetected or partially detected. Our goal is to extract individual vehicles from a highway traffic scenes using super-resolution and the utilization of Gaussian mixture model algorithm (GMM). We used a speeded-up enhanced stochastic Wiener filter for SR reconstruction and restoration. It can be used to remove artifacts and enhance the visual quality of the reconstructed images and can be implemented efficiently in the frequency domain. The filter derivation depends on the continuous-discrete-continuous (CDC) model that represents most of the degradations encountered during the image-gathering and image-display processes. Then, we use GMM followed by the clustering of individual vehicles. Individual vehicles are detected from the segmented scene through the use of a series of morphological operations, followed by two-dimensional connected component labeling. We evaluate our hybrid approach quantitatively in the segmentation of the extracted vehicles.
Gaussian functional approximation to 't Hooft's extension of the linear Σ model
NASA Astrophysics Data System (ADS)
Nakamura, Issei; Dmitrašinović, V.
2012-03-01
We apply a self-consistent relativistic mean-field variational “Gaussian functional” (or optimized one-loop perturbation theory, or Hartree+RPA) approximation to the extended Nf=2 linear σ model with spontaneously and explicitly broken chiral SUR(2)×SUL(2)×UA(1)≡O(4)×O(2) symmetry. We set up the self-consistency, or gap equations that dress up the bare fields with “cactus tree” loop diagrams, and the Bethe-Salpeter equations that provide further dressing with one-loop irreducible diagrams. In a previous publication [V. Dmitrašinović and I. Nakamura, J. Math. Phys. (N.Y.)JMAPAQ0022-2488 44, 2839 (2003).10.1063/1.1576907] we have already shown the ability of this approximation to create composite (i.e., bound and/or resonance) states. With explicit SUR(2)×SUL(2)×UA(1) chiral symmetry breaking first we consider how the UA(1) symmetry induced scalar-pseudoscalar meson mass relation that is known to hold in fermionic chiral models is modified by the bosonic gap equations. Then we solve the gap and Bethe-Salpeter equations numerically and discuss the solutions’ properties and the particle content of the theory. We show that in the strong-coupling regime two, sometimes even three solutions to the η meson channel Bethe-Salpeter equation may coexist.
Wu, Chuanli; Gao, Yuexia; Hua, Tianqi; Xu, Chenwu
2016-01-01
Background It is challenging to deal with mixture models when missing values occur in clustering datasets. Methods and Results We propose a dynamic clustering algorithm based on a multivariate Gaussian mixture model that efficiently imputes missing values to generate a “pseudo-complete” dataset. Parameters from different clusters and missing values are estimated according to the maximum likelihood implemented with an expectation-maximization algorithm, and multivariate individuals are clustered with Bayesian posterior probability. A simulation showed that our proposed method has a fast convergence speed and it accurately estimates missing values. Our proposed algorithm was further validated with Fisher’s Iris dataset, the Yeast Cell-cycle Gene-expression dataset, and the CIFAR-10 images dataset. The results indicate that our algorithm offers highly accurate clustering, comparable to that using a complete dataset without missing values. Furthermore, our algorithm resulted in a lower misjudgment rate than both clustering algorithms with missing data deleted and with missing-value imputation by mean replacement. Conclusion We demonstrate that our missing-value imputation clustering algorithm is feasible and superior to both of these other clustering algorithms in certain situations. PMID:27552203
iGNM 2.0: the Gaussian network model database for biomolecular structural dynamics
Li, Hongchun; Chang, Yuan-Yu; Yang, Lee-Wei; Bahar, Ivet
2016-01-01
Gaussian network model (GNM) is a simple yet powerful model for investigating the dynamics of proteins and their complexes. GNM analysis became a broadly used method for assessing the conformational dynamics of biomolecular structures with the development of a user-friendly interface and database, iGNM, in 2005. We present here an updated version, iGNM 2.0 http://gnmdb.csb.pitt.edu/, which covers more than 95% of the structures currently available in the Protein Data Bank (PDB). Advanced search and visualization capabilities, both 2D and 3D, permit users to retrieve information on inter-residue and inter-domain cross-correlations, cooperative modes of motion, the location of hinge sites and energy localization spots. The ability of iGNM 2.0 to provide structural dynamics data on the large majority of PDB structures and, in particular, on their biological assemblies makes it a useful resource for establishing the bridge between structure, dynamics and function. PMID:26582920
Exploring Bias and Uncertainty in Gaussian Mixture Models of Young, Massive Star Clusters
NASA Astrophysics Data System (ADS)
Elrod, Aunna; Clarkson, William I.
2016-06-01
Mixture models are important for studies of star clusters observed against a foreground or background field population. By directly estimating both the distribution parameters of the components and the component fractions (and thus the formal membership probabilities), the populations of interest can be fit directly without recourse to binning. Gaussian Mixtures are a highly popular choice when modeling star clusters, and their determination using the Expectation Maximization algorithm, or its extension to cases with strongly varying measurement uncertainty (e.g. Bovy et al.’s Extreme Deconvolution) now appears in some statistics textbooks.Here we describe our Monte Carlo study to estimate the effect of the choice of instrumental setup, particularly different field of views, on parameter recovery for simulated star clusters under a variety of situations. We simulate observations of a Young, Massive Cluster like those near the Galactic Center, focusing mainly on scenarios where the same cluster is observed from ground and from space. We characterize the bias and uncertainty that might be introduced when using this fairly recent yet increasingly popular technique across heterogenous instrumental setups.
Laser beam scintillation beyond the turbulent atmosphere A numerical computation
NASA Technical Reports Server (NTRS)
Bufton, J. L.; Taylor, L. S.
1976-01-01
The extended Huygens-Fresnel formulation for propagation through turbulence is used to examine scintillation of a finite laser beam. The method is demonstrated analytically for propagation beyond a weak Gaussian phase screen. A numerical integration technique is used to extend the results to a more realistic turbulence model. Results are compared with existing Gaussian beam propagation theory.
Laser beam modeling in optical storage systems
NASA Technical Reports Server (NTRS)
Treptau, J. P.; Milster, T. D.; Flagello, D. G.
1991-01-01
A computer model has been developed that simulates light propagating through an optical data storage system. A model of a laser beam that originates at a laser diode, propagates through an optical system, interacts with a optical disk, reflects back from the optical disk into the system, and propagates to data and servo detectors is discussed.
Atomic Forces for Geometry-Dependent Point Multipole and Gaussian Multipole Models
Elking, Dennis M.; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G.
2010-01-01
In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise due to 1) the transfer of torque between neighboring atoms, and 2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry-dependent multipole models. In the current study, atomic force expressions for geometry-dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives ∂Dlm′m/∂Ω. The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen bonded dimers are used to test the inter-molecular electrostatic energies and atomic forces calculated by geometry-dependent multipoles fit to the ab initio electrostatic potential (ESP). The electrostatic energies and forces are compared to their reference ab initio values. It is shown that both static and geometry-dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, while geometry-dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry-dependent multipole models. PMID:20839297
Measuring the Mass of Kepler-78b Using a Gaussian Process Model
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew; Haywood, Raphaëlle
2015-08-01
Kepler-78b is a transiting planet that is 1.2 times the size of Earth and orbits a young K dwarf every 8 hours. Two teams independently reported the mass of Kepler-78b based on radial velocity measurements using the HIRES and HARPS-N spectrographs. We modeled these datasets using a nonparametric Gaussian process (GP) regression. We considered three kernel functions for our GP models to account for the activity from the young host star. All three kernel functions gave consistent Doppler amplitudes. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel that gives a Doppler amplitude of 1.86 ± 0.25 m s-1. The mass of 1.87+0.27/-0.26 M⊕ is as precise than can be measured with either data set (a 2.5-σ improvement on the HIRES data). Reanalyzing only the HIRES data with a GP model, we reach a Doppler signal uncertainty equivalent with the previous study using slightly more than half of the HIRES measurements. Our GP model is the first analysis of the RVs for this active star that accounts for the continuously varying, quasi-periodic stellar activity signal. Based on our mass and the radius measurement from transit photometry, Kepler- 78b has a bulk density of 6.0+1.9/-1.4 g cm-3. We estimate that Kepler-78b is 32 ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Hierarchical heuristic search using a Gaussian mixture model for UAV coverage planning.
Lin, Lanny; Goodrich, Michael A
2014-12-01
During unmanned aerial vehicle (UAV) search missions, efficient use of UAV flight time requires flight paths that maximize the probability of finding the desired subject. The probability of detecting the desired subject based on UAV sensor information can vary in different search areas due to environment elements like varying vegetation density or lighting conditions, making it likely that the UAV can only partially detect the subject. This adds another dimension of complexity to the already difficult (NP-Hard) problem of finding an optimal search path. We present a new class of algorithms that account for partial detection in the form of a task difficulty map and produce paths that approximate the payoff of optimal solutions. The algorithms use the mode goodness ratio heuristic that uses a Gaussian mixture model to prioritize search subregions. The algorithms search for effective paths through the parameter space at different levels of resolution. We compare the performance of the new algorithms against two published algorithms (Bourgault's algorithm and LHC-GW-CONV algorithm) in simulated searches with three real search and rescue scenarios, and show that the new algorithms outperform existing algorithms significantly and can yield efficient paths that yield payoffs near the optimal.
Argenti, Fabrizio; Bianchi, Tiziano; Alparone, Luciano
2006-11-01
In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori MIAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation.
Chaddad, Ahmad
2015-01-01
This paper presents a novel method for Glioblastoma (GBM) feature extraction based on Gaussian mixture model (GMM) features using MRI. We addressed the task of the new features to identify GBM using T1 and T2 weighted images (T1-WI, T2-WI) and Fluid-Attenuated Inversion Recovery (FLAIR) MR images. A pathologic area was detected using multithresholding segmentation with morphological operations of MR images. Multiclassifier techniques were considered to evaluate the performance of the feature based scheme in terms of its capability to discriminate GBM and normal tissue. GMM features demonstrated the best performance by the comparative study using principal component analysis (PCA) and wavelet based features. For the T1-WI, the accuracy performance was 97.05% (AUC = 92.73%) with 0.00% missed detection and 2.95% false alarm. In the T2-WI, the same accuracy (97.05%, AUC = 91.70%) value was achieved with 2.95% missed detection and 0.00% false alarm. In FLAIR mode the accuracy decreased to 94.11% (AUC = 95.85%) with 0.00% missed detection and 5.89% false alarm. These experimental results are promising to enhance the characteristics of heterogeneity and hence early treatment of GBM. PMID:26136774