Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

A rapid boundary perturbation algorithm for scattering by families of rough surfaces

In this paper we describe a novel algorithm for the computation of scattering returns by families of rough surfaces. This algorithm makes explicit use of the fact that some scattering profiles of engineering interest (e.g., traveling ocean waves) come in branches parameterized analytically by a bifurcation quantity. Our approach delivers recursions which not only can be implemented to yield a rapid, robust and high-order numerical scheme, but also give a new proof of analyticity of scattering quantities with respect to the bifurcation parameter of the surface family. The real advantage of this new approach is that it computes, in one step, the scattered field for all possible members of the family of surfaces. By contrast, other state-of-the-art schemes must restart when the returns from a new surface are desired, so that the cost of our new approach is greatly advantaged when the number of samples of the family reaches even modest values. Numerical results which verify the accuracy of our approach and demonstrate their utility in computing grating efficiencies scattered by traveling surface ocean waves are presented.     

A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

相位微扰法在粗糙面光散射中的应用

根据粗糙面散射理论，用相位微扰法推导出了从随机粗糙介质表面散射的激光雷达散射截面的理论计算公式，计算了几种粗糙表面样品在１．０６μｍ下的单位面积激光雷达散射截面，数值结果与实验数据基本吻合。     

The SSA+ for scattering from dielectric surfaces at very low grazing angles

Previously we developed a practical model for scattering from randomly-rough surfaces at very low grazing angles for the Dirichlet problem which was found to give good numerical results. In this paper, we derive the expression for the bistatic scattering cross-section for the non-local small slope approximation for dielectric interfaces. We then extend our practical model to dielectric surfaces based on this result. We discuss numerical results for scattering at low forward grazing angles for a Gaussian roughness spectrum with an angle of incidence of 80^○.     

A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

Abstract

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

三维随机粗糙面与目标复合电磁散射的FDTD方法

用时域有限差分方法(FDTD)研究三维周期性延拓的随机粗糙面与上方目标复合电磁散射.用周期性延拓消除数值计算中截取有限大小粗糙面产生的边缘效应,讨论一个周期单元粗糙面的边长与其相关长度之间的关系.给出在FDTD方法中向粗糙面加载入射波的方法,建立了粗糙面上单个三维目标的复合散射FDTD计算模型.数值结果给出粗糙面与目标散射的近场分布,应用近远场变换得到全方位散射角的双站散射系数.比较了三维与二维散射模型的区别.结果显示当粗糙面上放置目标时,其后向散射显著增强.     

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.     

随机Gauss粗糙面上三维导体目标散射差场的随机泛函解析计算方法

提出一种解析的随机泛函方法(SFA),计算导体Gauss粗糙面上三维导体目标的复合电磁散射.推导粗糙面的随机Green函数,用一种新的四路径模型描述面体复合散射机理,用SFA求解双站差场雷达散射截面.以导体球目标为算例,与其他数值计算方法比较后验证了SFA的有效性与准确性,同时讨论了粗糙度、体目标尺寸以及距离粗糙面高度等参量变化对结果的影响,给出复杂形状体目标的双站差场雷达散射截面的空间角分布. 关键词： 随机泛函方法 粗糙面随机Green函数 差场雷达散射截面 面体复合散射     

A new bistatic model for electromagnetic scattering from perfectly conducting random surfaces: numerical evaluation and comparison with SPM

This paper is a companion to our previous contribution deriving a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. We evaluate this model numerically and compare it with an 'exact' numerical solution of the scattering problem. This comparison shows good agreement between our approximation and numerical solution for a wide range of incident and scattering angles. However, for horizontal-incident horizontal-scattered polarization (HH-pol), the model exhibits strong deviation from the 'exact' solution for near-grazing scattering angles. The model shows a similar divergence at HH-pol when compared with the small-perturbation method (SPM). The cause of this divergence is explained. During the SPM comparison, we noticed that the integral equation method model also does not reproduce the SPM limit except for forward and backscatter geometries. We propose in this paper a simple modification of our model to ensure agreement with the bistatic SPM approximation when applicable, and show that the modified model also yields close agreement with numerical computations even when the surface roughness does not satisfy the SPM condition.     

Scattering of a Narrow Pulsed Wave Beam by a Randomly Rough,Locally Lambertian Surface under Conditions of Strong Shadowing

We consider the problem of scattering of a narrow pulsed wave beam irradiating a randomly rough surface in the atmosphere under conditions of strong shadowing of one surface element by another. Expressions for the average power recorded by a receiver are obtained for the case where a locally Lambertian surface with Gaussian distribution of heights and slopes is irradiated by a delta impulse. It is shown that the shadowing and the atmospheric turbulence give rise to a considerable distortion of the received optical signal. The obtained analytical expressions for the received power are in good agreement with the results of numerical calculations.     

Double-scatter Mueller matrices for vector electromagnetic scattering from single grooves and lines on a silicon surface

A recently developed numerical method is used to calculate the single- and double-scattered Mueller matrices for scattering of vector-electromagnetic waves from rough surfaces. Calculations are performed for the case of a single groove and a single rib on a silicon surface and results are compared to the published experimental results. The calculated results show good agreement with the experimental results for the groove case and poorer agreement with the rib case, probably due to errors in the experimental construction of the rib. It is found that, for the cases studied here, variations of the sign with scatter angle in individual Mueller matrix elements are associated with the presence of double- (or multiple-)scattered light, as has been found previously for scalar diffraction calculations in Gaussian randomly rough surfaces.     

随机粗糙表面光散射场分布特性的机理研究

为了研究随机粗糙表面光散射分布特性机理,采用线性滤波法生成高斯分布随机粗糙表面,以基尔霍夫近似作为电磁场边界条件,采用蒙特卡罗方法数值计算了一组金属和一组电介质粗糙表面在S偏振光和P偏振光照射下的散射光强度空间分布。计算结果显示:金属表面与电介质表面的散射光分布宽度、散射峰值、散射峰位置三个散射特征存在显著差异,经过分析发现这种特征差异的产生机理是由表面面元的斜率分布和面元反射率共同因素导致,与数值计算结果对比,二者具有良好的一致性。