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J T Johnson - One of the best experts on this subject based on the ideXlab platform.
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scattering of electromagnetic waves from 3d multilayer random rough surfaces based on the second order Small Perturbation method energy conservation reflectivity and emissivity
Journal of The Optical Society of America A-optics Image Science and Vision, 2017Co-Authors: Mohammadreza Sanamzadeh, Leung Tsang, J T Johnson, R. J. BurkholderAbstract:A theoretical investigation of energy conservation, reflectivity, and emissivity in the scattering of electromagnetic waves from 3D multilayer media with random rough interfaces using the second-order Small Perturbation method (SPM2) is presented. The approach is based on the extinction theorem and develops integral equations for surface fields in the spectral domain. Using the SPM2, we calculate the scattered and transmitted coherent fields and incoherent fields. Reflected and transmitted powers are then found in the form of 2D integrations over wavenumber in the spectral domain. In the integrand, there is a summation over the spectral densities of each of the rough interfaces with each weighted by a corresponding kernel function. We show in this paper that there exists a “strong” condition of energy conservation in that the kernel functions multiplying the spectral density of each interface obey energy conservation exactly. This means that energy is conserved independent of the roughness spectral densities of the rough surfaces. Results of this strong condition are illustrated numerically for up to 50 rough interfaces without requiring specification of surface roughness properties. Two examples are illustrated. One is a multilayer configuration having weak contrasts between adjacent layers, random layer thicknesses, and randomly generated permittivity profiles. The second example is a photonic crystal of periodically alternating permittivities of larger dielectric contrast. The methodology is applied to study the effect of roughness on the brightness temperatures of the Antarctic ice sheet, which is characterized by layers of ice with permittivity fluctuations in addition to random rough interfaces. The results show that the influence of roughness can significantly increase horizontally polarized thermal emission while leaving vertically polarized emissions relatively unaffected.
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Microwave Thermal Emission Characteristics of a Two-Layer Medium With Rough Interfaces Using the Second-Order Small Perturbation Method
IEEE Geoscience and Remote Sensing Letters, 2017Co-Authors: R. J. Burkholder, J T Johnson, M. Sanamzadeh, L. TsangAbstract:The second-order Small Perturbation method is applied to investigate brightness temperature corrections caused by the rough interfaces of a two-layer medium. The spectral weighting functions of the two rough interfaces are extracted from the solution, and their properties examined. It is found that the functions are identical for the two interfaces as the spectral variable approaches zero, indicating an identical weighting of the surface height variance on each interface and an additive effect on the brightness temperature at nadir. Sample results for some realistic scenarios show that surface roughness in a two-layer medium can increase or decrease the observed brightness temperature at shallower angles, and in the case of a wideband measurement, can shift the interference pattern in frequency.
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scattering and transmission of waves in multiple random rough surfaces energy conservation studies with the second order Small Perturbation method
Progress in Electromagnetics Research-pier, 2016Co-Authors: Tianlin Wang, Leung Tsang, J T JohnsonAbstract:Energy conservation is an important consideration in wave scattering and transmission from random rough surfaces and is particularly important in passive microwave remote sensing. In this paper, we study energy conservation in scattering from layered random rough surfaces using the second order Small Perturbation method (SPM2). SPM2 includes both first order incoherent scattering and a second order correction to the coherent fields. They are combined to compute the total reflected and transmitted powers, as a sum of integrations over wavenumber kx, in which each integration includes the surface power spectra of a rough interface weighted by an emission kernel function (assuming the roughness of each interface is uncorrelated). We calculate the corresponding kernel functions which are the power spectral densities for one-dimensional (1D) surfaces in 2D scattering problems and examine numerical results for the cases of 2 rough interfaces and 51 rough interfaces. Because it is known that the SPM when evaluated to second order conserves energy, and it can be applied to second order for arbitrary surface power spectra, energy conservation can be shown to be satisfied for each value of kx in the kernel functions. The numerical examples show that energy conservation is obeyed for any dielectric contrast, any layer configuration and interface, and arbitrary roughness spectra. The values of reflected or transmitted powers predicted, however, are accurate only to second order in Small surface roughness.
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A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces
IEEE Transactions on Geoscience and Remote Sensing, 2012Co-Authors: Metin Aytekin Demir, J T Johnson, Tom J. ZajdelAbstract:Predictions of the fourth-order Small Perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fields and incoherent ensemble-averaged normalized radar cross sections (NRCSs) up to the third and the fourth order in surface rms heights, respectively, are reviewed. It is shown that the fourth-order NRCS includes distinct contributions from upper and lower interface roughnesses, as well as an “interaction” term that couples the upper and lower interface roughnesses. A comparison with NRCS values computed using the “numerically exact” method of moments in the full bistatic scattering pattern is shown for verification, and NRCS values at the second and the fourth order are compared in order to assess the convergence of the SPM series. Although the number of parameters inherent in the two-layer rough surface scattering problem makes an exhaustive study of scattering effects difficult, several illustrative examples are presented to capture a range of scattering behaviors. The results emphasize the importance of interactions between the rough surfaces in producing cross-polarized backscattering and also indicate an increased significance of fourth-order contributions in the two-layer geometry as compared to the single-layer case.
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fourth and higher order Small Perturbation solution for scattering from dielectric rough surfaces
Journal of The Optical Society of America A-optics Image Science and Vision, 2003Co-Authors: Metin Aytekin Demir, J T JohnsonAbstract:A recursive solution of the Small-Perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.
A A Maznev - One of the best experts on this subject based on the ideXlab platform.
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boundary scattering of phonons specularity of a randomly rough surface in the Small Perturbation limit
Physical Review B, 2015Co-Authors: A A MaznevAbstract:Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the Small Perturbation approach. In the limiting case of a large correlation length $L$ compared with the acoustic wavelength, the specularity reduction is given by $4\eta^2k^2$, where $\eta$ is the RMS roughness and $k$ is the acoustic wavevector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a Small correlation length, the specularity reduction is found to be proportional to $\eta^2k^4L^2$, with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of $L$. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.
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boundary scattering of phonons specularity of a randomly rough surface in the Small Perturbation limit
Physical Review Letters, 2015Co-Authors: A A MaznevAbstract:Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the Small-Perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity reduction is given by 4η 2 k 2 ,w here η is the rms roughness and k is the acoustic wave vector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman’s equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a Small correlation length, the specularity reduction is found to be proportional to η 2 k 4 L 2 , with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of L. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson’s ratio of the medium approaches 1/ 2a s ar esult of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman’s formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.
Metin Aytekin Demir - One of the best experts on this subject based on the ideXlab platform.
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A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces
IEEE Transactions on Geoscience and Remote Sensing, 2012Co-Authors: Metin Aytekin Demir, J T Johnson, Tom J. ZajdelAbstract:Predictions of the fourth-order Small Perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fields and incoherent ensemble-averaged normalized radar cross sections (NRCSs) up to the third and the fourth order in surface rms heights, respectively, are reviewed. It is shown that the fourth-order NRCS includes distinct contributions from upper and lower interface roughnesses, as well as an “interaction” term that couples the upper and lower interface roughnesses. A comparison with NRCS values computed using the “numerically exact” method of moments in the full bistatic scattering pattern is shown for verification, and NRCS values at the second and the fourth order are compared in order to assess the convergence of the SPM series. Although the number of parameters inherent in the two-layer rough surface scattering problem makes an exhaustive study of scattering effects difficult, several illustrative examples are presented to capture a range of scattering behaviors. The results emphasize the importance of interactions between the rough surfaces in producing cross-polarized backscattering and also indicate an increased significance of fourth-order contributions in the two-layer geometry as compared to the single-layer case.
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fourth and higher order Small Perturbation solution for scattering from dielectric rough surfaces
Journal of The Optical Society of America A-optics Image Science and Vision, 2003Co-Authors: Metin Aytekin Demir, J T JohnsonAbstract:A recursive solution of the Small-Perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.
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Fourth and higher order Small Perturbation solution for scattering from dielectric rough surfaces
IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC CNC URSI North American Radio Sci. Meeting (Cat., 2003Co-Authors: Metin Aytekin Demir, J T JohnsonAbstract:The Small Perturbation method (SPM) for scattering from a rough surface involves a Perturbation series in surface height for scattered fields. In this paper, the systematic procedure is applied to construct a complete, recursive, and arbitrary order solution for scattered fields in the SPM method. Sample results from the fourth order theory are presented in terms of the fourth-order reflection coefficient correction The fourth order solution also allows computation of backscattered cross-polarized fields at sixth order, and the fourth order emitted power from a rough surface for passive remote sensing analysis.
Richard Dusseaux - One of the best experts on this subject based on the ideXlab platform.
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electromagnetic wave scattering from rough layered interfaces analysis with the Small Perturbation method and the Small slope approximation
Progress in Electromagnetics Research B, 2014Co-Authors: Abla Berrouk, Richard Dusseaux, Saddek AfifiAbstract:We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the Small Perturbation method and the Small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic fleld in each medium is represented by a Rayleigh expansion and a Perturbation method is used for solving the boundary value problem and determining the flrst-order scattering amplitudes by recurrence relations. The scattering amplitude under the flrst-order Small slope approximation are deduced from results derived from the flrst-order Small Perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented. The study of electromagnetic wave scattering from rough layered interfaces has many applications in remote sensing, communication techniques, civil engineering, geophysics and optics. Several models give the average scattered fleld and the average intensity. Analytical methods are based on physical approximations and give closed-form formulae for the flrst- and second-order moments of the scattered fleld. Exact methods estimate the average scattered fleld and the average intensity from the results over many realizations of rough layered interfaces. In this paper, we propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using two analytical models: the flrst-order Small Perturbation method (SPM) and the flrst-order Small slope approximation (SSA). Elson was one of the flrst authors to develop a vector theory of scattering from a stratifled medium. This vector theory allows the angular distribution of scattered light to be determined and can be used with correlated or uncorrelated surface roughness (1,2). The SPM has been used for the study of light scattering from multilayer optical coatings (1{5) and many authors have also implemented a perturbative theory for analyzing remote sensing problems (6{12). The Small slope approximation (SSA1) has an extended domain of applicability (13{15) which includes the domain of the Small-Perturbation method that is only valid for surfaces with Small roughness (16) and the domain of the Kirchhofi approximation that is applicable to surfaces with long correlation length (17,18). In the present paper, the structure under consideration is a stack of several rough one-dimensional interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fleld in each region is represented by a continuous spectrum of plane waves, the amplitudes of which are found by matching the boundary conditions
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Electromagnetic Scattering From 3D Layered Structures With Randomly Rough Interfaces: Analysis With the Small Perturbation Method and the Small Slope Approximation
IEEE Transactions on Antennas and Propagation, 2014Co-Authors: Saddek Afifi, Richard Dusseaux, Abla BerroukAbstract:We propose a theoretical study on the electromagnetic wave scattering from three-dimensional layered structures with an arbitrary number of rough interfaces by using the Small Perturbation method and the Small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not, isotropic or not. The electromagnetic field in each medium is represented by a continuum of plane waves and a Perturbation theory is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitudes under the first-order Small slope approximation are deduced from results derived from the first-order Small Perturbation method. We analyze with the Small slope approximation model the combined influence of the anisotropy and cross-correlation upon the electromagnetic signature of a natural stratified structure.
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On the Co-Polarized Scattered Intensity Ratio of Rough Layered Surfaces: The Probability Law Derived From the Small Perturbation Method
IEEE Transactions on Antennas and Propagation, 2012Co-Authors: Saddek Afifi, Richard DusseauxAbstract:We determine the probability law of the ratio between the co-polarized intensities scattered from a stack of two two-dimensional rough interfaces in the incidence plane. Calculations are carried out within the framework of the first-order Small Perturbation method. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters and has an infinite average and an infinite variance. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle and the cross-spectral density upon this probability law.
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effect of the illumination length on the statistical distribution of the field scattered from one dimensional random rough surfaces analytical formulae derived from the Small Perturbation method
Waves in Random and Complex Media, 2007Co-Authors: Richard Dusseaux, R De OliveiraAbstract:We consider a dielectric plane surface with a local cylindrical Perturbation illuminated by a monochromatic plane wave. The Perturbation is represented by a random function assuming values with a Gaussian probability density with zero mean value. Outside the Perturbation zone, the scattered field can be represented by a superposition of a continuous spectrum of outgoing plane waves. The stationary phase method leads to the asymptotic field, the angular dependence of which is given by the scattering amplitudes of the propagating plane waves. The Small Perturbation method applied to the Rayleigh integral and the boundary conditions gives a first-order approximation of the scattering amplitudes. We show that the real part and the imaginary part of the scattering amplitudes are Gaussian stochastic variables with zero mean values and unequal variances. The values of variances depend on the length of the Perturbation zone. In most cases, the probability density function for the amplitude is a Hoyt distribution ...
Saddek Afifi - One of the best experts on this subject based on the ideXlab platform.
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electromagnetic wave scattering from rough layered interfaces analysis with the Small Perturbation method and the Small slope approximation
Progress in Electromagnetics Research B, 2014Co-Authors: Abla Berrouk, Richard Dusseaux, Saddek AfifiAbstract:We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the Small Perturbation method and the Small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic fleld in each medium is represented by a Rayleigh expansion and a Perturbation method is used for solving the boundary value problem and determining the flrst-order scattering amplitudes by recurrence relations. The scattering amplitude under the flrst-order Small slope approximation are deduced from results derived from the flrst-order Small Perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented. The study of electromagnetic wave scattering from rough layered interfaces has many applications in remote sensing, communication techniques, civil engineering, geophysics and optics. Several models give the average scattered fleld and the average intensity. Analytical methods are based on physical approximations and give closed-form formulae for the flrst- and second-order moments of the scattered fleld. Exact methods estimate the average scattered fleld and the average intensity from the results over many realizations of rough layered interfaces. In this paper, we propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using two analytical models: the flrst-order Small Perturbation method (SPM) and the flrst-order Small slope approximation (SSA). Elson was one of the flrst authors to develop a vector theory of scattering from a stratifled medium. This vector theory allows the angular distribution of scattered light to be determined and can be used with correlated or uncorrelated surface roughness (1,2). The SPM has been used for the study of light scattering from multilayer optical coatings (1{5) and many authors have also implemented a perturbative theory for analyzing remote sensing problems (6{12). The Small slope approximation (SSA1) has an extended domain of applicability (13{15) which includes the domain of the Small-Perturbation method that is only valid for surfaces with Small roughness (16) and the domain of the Kirchhofi approximation that is applicable to surfaces with long correlation length (17,18). In the present paper, the structure under consideration is a stack of several rough one-dimensional interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fleld in each region is represented by a continuous spectrum of plane waves, the amplitudes of which are found by matching the boundary conditions
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Electromagnetic Scattering From 3D Layered Structures With Randomly Rough Interfaces: Analysis With the Small Perturbation Method and the Small Slope Approximation
IEEE Transactions on Antennas and Propagation, 2014Co-Authors: Saddek Afifi, Richard Dusseaux, Abla BerroukAbstract:We propose a theoretical study on the electromagnetic wave scattering from three-dimensional layered structures with an arbitrary number of rough interfaces by using the Small Perturbation method and the Small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not, isotropic or not. The electromagnetic field in each medium is represented by a continuum of plane waves and a Perturbation theory is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitudes under the first-order Small slope approximation are deduced from results derived from the first-order Small Perturbation method. We analyze with the Small slope approximation model the combined influence of the anisotropy and cross-correlation upon the electromagnetic signature of a natural stratified structure.
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On the Co-Polarized Scattered Intensity Ratio of Rough Layered Surfaces: The Probability Law Derived From the Small Perturbation Method
IEEE Transactions on Antennas and Propagation, 2012Co-Authors: Saddek Afifi, Richard DusseauxAbstract:We determine the probability law of the ratio between the co-polarized intensities scattered from a stack of two two-dimensional rough interfaces in the incidence plane. Calculations are carried out within the framework of the first-order Small Perturbation method. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters and has an infinite average and an infinite variance. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle and the cross-spectral density upon this probability law.
