A new bistatic model for electromagnetic scattering from randomly rough surfaces

In this paper we propose a bistatic model for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Green's function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) and the integral equation model for second-order multiple scattering (IEM2M). Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross- and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Green's function. It is expected that our result for the complementary scattering coefficient is more accurate and more general, even when the effect of the error function related terms is neglected. As a result, the proposed model is expected to have wider applicability with a better accuracy. Numerical simulations are provided to demonstrate the validity of the proposed model.     

An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces

Based on the local configuration angle division to select the corresponding method for electromagnetic scattering calculation from rough sea surface,this paper presents an angular cutoff composite model:when the local scattered angle is in the specular region that is given by an approximately 20 degrees cone around the specular direction,the Kirchhoff approximation is applied to evaluate the specular reflection,which dominates the total scattering in this region;the small perturbation method is employed to handle the diffuse reflection which is predominant as the local scattered angle is situated out of the specular region.Numerical results are compared with those of experimental and theoretical models in several configurations as a function of incident angle,wind speed,wind direction.The comparison of numerical results of other experimental and theoretical models in several configurations shows that the new composite model is robust to give accurate numerical evaluations for the sea surface scattering.     

Low-grazing angles scattering of electromagnetic waves from one-dimensional natural surfaces: Rigorous and approximate theories

We present a rigorous model, based on a specific boundary integral formalism for the wave scattering from rough, one-dimensional, dielectric or conducting surfaces at low-grazing incidence and scattering angles. Even though this so-called Grazing Method of Moment is, from a numerical cost point of view, independent of the incidence, it remains very numerically demanding. We thus propose an extrapolation technique for faster monostatic diagram computation, based on the theoretical behavior of the scattering amplitude at low-grazing angles. This technique is compared to the GMoM and to some approximate models, for surfaces with Gaussian spectrum as well as for sea surface.     

Investigation of light scattering from rough periodic surfaces — numerical solutions

The Beckmann scalar scattering model based on the Kirchhoff approximation was used to investigate the scattering of light from periodic surfaces whose roughness amplitude is comparable to, and greater than, the illumination wavelength. Solutions by numerical integration were obtained for surfaces of different profiles and of different roughnesses. It was found that the scattering patterns from these surfaces were very different at large roughness amplitudes. As the incident angle was varied on a given surface, it was also observed that the intensity of any individual diffraction order oscillated and the degree of oscillation was directly related to roughness. By utilizing this property, a new procedure could be developed for surface roughness assessment.     

On the accuracy of perturbative solutions to wave scattering from rough closed surfaces

The method of small perturbations is applied to the problem of plane-wave scattering from a soft circular surface with sinusoidal roughness. Rayleigh-theory and extinction-theorem perturbative solutions of arbitrary order are developed, and they are compared to each other as well as to an exact solution. A numerical study yields quantitative information about effects associated with the use of the Rayleigh hypothesis, about the merit of higher-order solutions, and about the reliability of the error criteria that measure a posteriori the conformity of perturbative solutions to the boundary condition. It is shown that the accuracy of perturbative solutions depends not only on the height, but also on the slope, of surface corrugations. Moreover, it is shown that the Rayleigh hypothesis does not affect the accuracy of far-field perturbative calculations. The mean extinction error is proposed as a measure for the error of the extinction-theorem perturbative solution.     

White light scattering from non-Gaussian rough surfaces

Optics and Spectroscopy - A method is proposed for calculating the spectral correlation function of light intensity scattered from non-Gaussian rough surfaces. The correlation function of a...     

弹性波在固体自由粗糙平界面上的散射

利用散射幅度矩阵的概念来处理弹性波在粗糙界面弹性介质中的散射问题。利用微扰近似解边界方程,对散射幅度进行求解,得到了散射幅度的0阶、1阶和2阶解。同时分析了粗糙起伏高度符合高斯分布时,散射幅度的数学期望值和方差,它们分别代表平均场和声场在偏离镜面方向的起伏。最后进行了实验。     

Non-local small-slope approximation for wave scattering from rough surfaces

A new general analytical approach to solving the problems of wave scattering from rough surfaces, referred to as the non-local small-slope approximation (NLSSA), is suggested. It is formulated in the general form both for vector and scalar waves. This approach is valid for an arbitrary wavelength of radiation provided that the slopes of the undulations are small enough. The NLSSA represents a generalization of the small-slope approximation to situations where double scattering (in the optical sense) appears. It is demonstrated that with appropriate approximations the NLSSA of the lowest order reduces to the small-slope approximation of the second order.     

An approach to the scattering of electromagnetic waves by rough metal surfaces

Summary A method to describe the scattering of an electromagnetic wave by a rough metal surface whose imperfections are not small with respect to the wave-length is proposed. The surface is simulated as a plane uniformly covered by hemispheres of equal radii, the material is supposed to be a good conductor and the incident wave to propagate normally to the plane. The use of an addition theorem for spherical waves together with some statistical considerations allows the boundary conditions to come out in a simple form.

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Riassunto Si propone un metodo per il calcolo dello scattering della radiazione elettromagnetica da parte di una superficie metallica rugosa avente imperfezioni non piccole rispetto alla lunghezza d’onda. La superficie è schematizzata mediante un piano ricoperto uniformemente da semisfere di egual raggio. Si suppone che il materiale sia buon conduttore (abbastanza da giustificare l’approssimazione di Leontovich) e che la radiazione incida normalmente al piano. L’uso di un teorema di addizione per le onde sferiche insieme ad alcune considerazioni di carattere statistico permette di scrivere le condizioni al contorno in forma semplice.

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Резюме Предлагается метод для описания рассеяния электромагнитной волны на шероховатой металлической поверхности, неоднородности которой не являются малыми по сравнению с длиной волны. Поверхность представляется в виде плоскости, покрытой равномерно полусферами одинакового радиуса. Предполагается, что материал поверхности представляет хороший проводник, а падающая волна распространяется нормально к плоскости. Использование теоремы дополнительности для сферических волн и статистического описания позволяет записать граничные условия в простой форме.

     

A Markovian approach to atomic scattering from rough surfaces

Atomic scattering intensities from surfaces in a rough state are calculated, in the hard wall model, separating a form (or geometrical) factor from a statistical factor and neglecting all the edge effects. Attention has been paid more to the statistics than to the scattering problem. In principle only incoherent scattering occurs from a rough surface. This incoherent line shape is calculated for square and hexagonal lattices under the basic assumption that the surface level is a Markov process in two dimensions.     

Light scattering from rough surfaces with superimposed periodic structures

0 ), where K is the wave vector of the periodic structure and λ₀ is the correlation length for random roughness. The surface height h of the periodic structure plays a less important role in the suppression of the diffuse scattering, but it gives an oscillating term in grating scattering intensity that can produce the “rainbowing” (or coloration) effect for such a surface. In practice, this may result in increased visual brightness of textured metallic surfaces and also in a new and interesting method of surface coloration control. The rapid development of focused beam texturing technologies leaves no doubt that patterns with a given spatial frequency and amplitude can be easily produced in experiments. Received: 16 January 1997/Revised version: 19 June 1997     

Exact multiple scattering of waves from random rough surfaces

The exact multiple scattering theory of waves scattered from a random rough surface is presented. We give an iterative series for the mean scattered intensity (I (Q)) for all order in the statistics. We show that the coherent intensity for large correlation distances approaches the value obtained in the Kirchhoff approximation by Beckmann. Also we prove that a “white noise” surface reflects specularly the whole incident intensity.     

Multiple light scattering from metal and dielectric rough surfaces

Abstract

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Multiple light scattering from metal and dielectric rough surfaces

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Implementation and validation of the curvilinear coordinate method for the scattering of electromagnetic waves from two-dimensional dielectric random rough surfaces

The curvilinear coordinate method is applied for analysing 2-D dielectric random rough surfaces. The theory is based on Maxwell's equations written in a non-orthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered fields within two media are expanded as linear combinations of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The coherent and incoherent intensities are estimated by averaging the scattering amplitudes over several realizations. The theory is verified by comparison with results obtained by other exact method. A discussion on the C-method and the Sparse-Matrix CAnonical Grid method is proposed in terms of accuracy and computation time.     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型。利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度。数值计算模型中,将冰面认为是局部阻抗表面,直接代入起伏冰面局部反射系数进行散射声场的计算,避免了解析计算模型中对反射系数的近似处理。对比分析了数值和解析计算模型在小粗糙起伏冰面、大粗糙起伏冰面及不同声波入射角和不同声波频率时的散射强度。相比解析模型计算结果,数值模型计算结果与实测结果更吻合。     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型。利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度。数值计算模型中,将冰面认为是局部阻抗表面,直接代入起伏冰面局部反射系数进行散射声场的计算,避免了解析计算模型中对反射系数的近似处理。对比分析了数值和解析计算模型在小粗糙起伏冰面、大粗糙起伏冰面及不同声波入射角和不同声波频率时的散射强度。相比解析模型计算结果,数值模型计算结果与实测结果更吻合。     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

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.     

Field transformational approach to three-dimensional scattering from two-dimensional rough surfaces

In 1985, Tappert and Nghiem-Phu introduced a field-transformation technique for computing rough surface scattering from a parabolic equation model utilizing a split-step Fourier marching algorithm. The approach was based on a two-dimensional parabolic equation with a standard operator approximation that was capable of computing scattering from a one-dimensional rough surface. Although this approach has been used extensively and effectively, extensions of this approach to higher order approximations or three-dimensional propagation have only recently been investigated. In this work, the expressions that incorporate higher-order approximations and three-dimensional scattering from two-dimensional rough surfaces are presented. The implications of some computationally necessary approximations are also provided.