Full wave vertically polarized bistatic radar cross sections forrandom rough surfaces-comparison with experimental and numerical results

The one-dimensionally rough surfaces considered in this paper are characterized by four-dimensional Gaussian joint probability density functions for the surface heights and slopes at two points. The expressions for the diffuse scattered fields are used to obtain the random rough cross sections. The full wave solutions are compared with the corresponding small perturbation results and the physical optics results. They are also compared with experimental and numerical results based on Monte Carlo simulations of rough surfaces. The earlier assumption that the surface heights and slopes can be considered to be uncorrelated are examined, and the impact of self shadow is considered in detail. The impact of the commonly used assumption that the radii of curvature is very large compared to the wavelength is also examined in detail. These results are in agreement with the duality and reciprocity relationships in electromagnetic theory     

Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope

Employing a variable coordinate system associated with the local features of two-dimensionally rough surfaces with arbitrary slope, full-wave solutions are derived for the depolarization of the scattered radiation fields. An outline of the analytical procedures used in the derivations of the solutions are presented. Furthermore, the engineer who is not familiar with them can also use the final result which is expressed as a definite integral whose integrand is given explicitly and in closed form. These full-wave solutions are compared with the quasi-optics solution and the iterative or perturbational solutions for slightly rough surfaces, and they are shown to bridge the wide gap that exists between them. The full-wave solutions are consistent with energy conservation, duality, and reciprocity relationships in electromagnetic theory. These solutions account for upward and downward scattering of the incident waves with respect to the horizontal reference plane, thus shadowing and multiple scattering are considered. Applications to two-dimensionally periodic structures and random rough surfaces are also presented. The fullwave solutions are examined for Brewster, grazing, and specular angles and backscatter. Special consideration is also given to good conducting boundaries.     

Coupling Between Guided Surface Waves, Lateral Waves, and the Radiation Fields by Rough Surfaces--Full-Wave Solutions

In this paper explicit expressions are presented for the guided surface waves and lateral waves that are excited when radiation fields are incident upon rough surfaces. Similarly, expressions are presented for the radiation fields scattered by rough surfaces that are excited by surface waves and lateral waves. In addition, coupling between the surface waves and the lateral waves due to surface irregularities is considered in detail. The solutions, which are based on a full-wave approach to the problem, are subject to the exact boundary conditions at the irregular interface. These are shown to be consistent with the reciprocity relationship in electromagnetic theory. The validity of the approximate impedance boundary condition is examined and consideration is given to excitation at the grazing incidence, the Brewster angle, and to waves incident at the critical angle for total internal reflection. Optimum conditions are determined for coupling between the radiation fields, the surface waves, and the Iateral waves incident upon irregular boundaries. Thus this work is applicable to problems of radio wave propagation near an irregular interface between two media and excitation of guided waves by irregular dielectric structures.     

Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles full-wave solutions

Explicit expressions are presented for the radiation fields scattered by rough surfaces. Both electric and magnetic dipole sources are assumed, thus excitations of both vertically and horizontally polarized waves are considered. The solutions are based on a full-wave approach which employs complete field expansions and exact boundary conditions at the irregular boundary. The scattering and depolarization coefficients axe derived for arbitrary incident and scatter angles. When the observation point is at the source these scattering coefficients are related to the backscatter cross section per unit area. Solutions based on the approximate impedance boundary condition are also given, and the suitability of these approximations are examined. The solutions are presented in a form that is suitable for use by engineers who may not be familiar with the analytical techniques and they may be readily compared with earlier solutions to the problem. The full-wave solutions are shown to satisfy the reciprocity relationships in electromagnetic theory, and they can be applied directly to problems of scattering and depolarization by periodic and random rough surfaces.     

Mueller matrix elements that characterize scattering from coatedrandom rough surfaces

The Mueller matrix completely characterizes scattered electromagnetic waves. It relates the incident to the scattered Stokes vectors. The Mueller matrix, which contains intensity and relative phase data, is very useful for remote sensing. The Mueller matrix characterizing scattering from coated two-dimensional (2-D) random rough surfaces is obtained from full-wave solutions for the scattered fields considered in the companion paper. The general bistatic scattering case is considered in the analysis. However, for the numerical simulations presented here, the backscatter case is considered in particular, since backscatter is usually measured in remote sensing. The uniformly coated 2-D random rough surfaces are assumed here to be homogeneous and isotropic, with a Gaussian surface-height joint probability-density function. The diffuse incoherent and coherent contributions to the Mueller matrix elements are evaluated. The computer simulations of realistic models of relevant physical problems related to remote sensing of irregular stratified media can be used to determine the optimum modes of detection involving the selection of polarization, frequency, backscatter angle, and the specific Mueller matrix elements most sensitive to changes in medium parameters     

THz全尺寸凸体粗糙目标雷达回波散射建模与成像仿真

回波仿真是研究雷达成像体制、算法及后续应用的前提条件,目标散射建模又是回波仿真的重要一环。在THz频段,目标常常具有超电大尺寸,这使得利用经典电磁计算方法面临现实困难。而波长的减小使得目标表面粗糙起伏成为不能忽略的因素,这使得传统基于点散射模型的回波生成手段难以适用。如何对目标进行THz散射建模及高效的雷达回波生成成为亟待解决的问题。该文提出了基于面片分级的半确定性建模方法,采用粗糙面全波法计算面片的散射场,再将各面片散射场转换至目标坐标系并相干叠加得到带有相位信息的雷达回波。利用小尺寸粗糙模型,通过与高频数值方法进行对比,验证了该文方法的有效性,并给出了全尺寸锥体的成像结果。初步解决了THz频段全尺寸凸体粗糙目标散射建模及回波生成问题,为后续成像体制和算法研发打下了基础。      

Excitation of Surface Waves and the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope

Surface waves as well as Iateral waves are excited when a rough surface is illuminated by the radiation fields. In view of shadowing, these terms of the complete field expansions contribute significantly to the total fields when the transmitter or receiver are near the rough surface. In this work explict expressions are derived for the coupling between the radiation fields and the surface waves which are guided at the irregular interface between two media. In the analysis, the slope of the rough surface is not restricted and the solutions for both the horizontally and vertically polarized waves are shown to satisfy reciprocity and duality relationships in electromagnetic theory. Special consideration is given to Brewster angles of incidence and scatter and stationary phase techniques. The fufl-wave solutions are also applied to random and periodic rough surfaces.     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

Full wave and physical optics solutions for scattered radiation fields by rough surfaces-energy and reciprocity relationships

Full wave and physical optics solutions for the scattered radiation fields from rough surfaces are compared. The full wave solutions involve complete expansions of the fields and exact boundary conditions. The solutions for the radiation fields axe provided in a form that can be readily compared with earlier solutions to the problem, and they can be applied directly to engineering problems without the need to carry out any of the analytic procedures encountered in the derivations. The surface impedance concept, reciprocity, and energy conservation relationships are considered in detail, and special consideration is given to grazing incidence and excitation at the Brewster angle. This work on irregular ground effects on radio wave propagation is relevant to problems of communication, navigation, and active remote sensing.     

Diffuse like and cross-polarized fields scattered from irregularlayered structures-full-wave analysis

The full-wave solution for scattering from two-dimensional (2-D) irregular layered structures is expressed as a sum of radiation fields, the lateral waves and the surface waves. Only the radiation far fields are considered in this work. The lateral waves and surface waves are ignored since excitations of plane waves are considered and the observation points are in the far fields. The scattering coefficients appearing in the full-wave generalized telegraphists' equations for irregular layered structures are proportional to the derivatives of the surface heights at each interface. Using a first-order iterative procedure to solve the generalized telegraphists' equations, the diffusely scattered fields from irregular layered structures are expressed as a sum of first-order fields scattered at each rough interface. In this paper, the like and cross-polarized diffuse scattered fields are derived for three medium irregular structures with 2-D rough interfaces. The thickness of the coating material or thin film between the two interfaces is arbitrary, however, in this work it is assumed to be constant. Thus, in this case, both interfaces are rough and there are five different scattering processes identified in the full-wave results. A physical interpretation is given to the five different scattering mechanisms that contribute to the diffusely scattered fields. This work can be used to provide realistic analytical models of propagation across irregular stratified media such as ice or snow covered terrain, remote sensing of coated rough surfaces, or the detection of buried objects in the presence of signal clutter from the rough interfaces     

Inversion of roughness profile of heterogeneous fractal surface using Gaussian beam incidence at low grazing angle

As a Gaussian beam is incident upon a rough surface at low grazing angle, the Helmholts scalar wave equation may be replaced by the parabolic approximate equation. As the incident field is known, the scattered field and surface current give the Volterra integral equation. Surface roughness profile can be formulated by the integral equation of the surface currents. These two coupled equations are applied to invert the roughness profile of heterogeneous fractal surface. Using Monte Carlo method, the fractal rough surfaces with a band-limited Weistrass-Manderbrot function are numerically simulated and the scattered fields along a line parallel to the mean surface are solved. The Gaussian beam incidence and scattered fields are used to progressively invert the surface roughness profile. Reconstructed profile and its inverted fractal dimension, roughness variance and correlation length are well matched with the simulated surfaces.     

Rigorous formulation of scattering at a randomly varying impedanceplane: general case of oblique incidence

The problem of scattering of electromagnetic plane waves at one-dimensional surfaces (random gratings) is solved in the general case in which the incident wave vector does not lie on the main section of the cylindrical surface (oblique incidence). The scatterer is simulated by a plane boundary characterized by a coordinate-dependent impedance that varies along one of the two coordinates on the surface. This representation could be regarded as a canonical model of one-dimensional surfaces with height corrugations. A rigorous electromagnetic formalism for calculating the fields scattered at the impedance plane is presented. The fields above the scatterer are represented by spectral domain expansions. It is shown that the wave vectors of the scattered waves lie on the surface of a cone containing the direction of specular reflection and whose axis coincides with the direction of the grooves of the random grating. The theory is exemplified by calculating the angular distribution of the mean intensity scattered from an ensemble of surfaces with similar statistical parameters     

THz频段粗糙导体圆锥的极化成像特性

太赫兹频段下粗糙导体表面会对电磁散射回波的幅度、相位、极化状态产生影响,为分析这一影响,以导体圆锥为例,研究了不同粗糙参数表面电磁散射在雷达图像中的表现规律。基于谱方法和坐标变换对粗糙圆锥面进行建模,利用高频电磁计算方法获得不同粗糙度导体圆锥样本多角度、多频点、全极化的单站散射场,基于转台模型,利用二重积分法获得目标二维像。从仿真结果可以看出,粗糙与理想光滑导体的圆锥图像存在明显差异,粗糙圆锥图像中能量分布偏离理想光滑情况下的强散射区域;随着粗糙度的增加,图像能量分布愈加均匀;相比于同极化图像,交叉极化图像更具反映目标轮廓信息的潜力。     

Scattering cross sections for composite rough surfaces using the unified full wave approach

The full wave approach is used to derive a unified formulation for the like and cross polarized scattering cross sections of composite rough surfaces for all angles of incidence. Earlier solutions for electromagnetic scattering by composite random rough surfaces are based on two-scale models of the rough surface. Thus, on applying a hybrid approach physical optics theory is used to account for specular scattering associated with a filtered surface (consisting of the large sonic spectral components of the surface) while perturbation theory is used to account for Bragg scattering associated with the surface consisting of the small scale spectral components. Since the full wave approach accounts for both specular point scattering and Bragg scattering in a self-consistent manner, the two-scale model of the rough surface is not adopted in this work. These unified full wave solutions are compared with the earlier solutions and the simplifying assumptions that are common to all the earlier solutions are examined. It is shown that while the full wave solutions for the like polarized scattering cross sections based on the two-scale model are in reasonably good agreement with the unified full wave solutions, the two solutions for the cross polarized cross sections differ very significantly.     

Mueller matrix calculation for a slab of random medium with bothrandom rough surfaces and discrete particles

A model for a slab of random medium containing both random rough surfaces and discrete scatterers is presented in this paper. The refractive indices of the surrounding media are different from the background refractive index of the random medium. Kirchhoff rough surface theory is used to derive the transmittivity and reflectivity matrices for the scattering of electromagnetic waves from the rough surfaces. These matrices are used to determine a pair of boundary conditions for the vector radiative transfer equation. The multiple scattering due to the discrete scatterers is computed by solving the radiative transfer equation numerically, including the rough surface scattering effect. Mueller matrices characterizing the random medium are constructed from the scattered Stokes vectors due to four independent polarized incident waves. The Mueller matrices are found to have symmetrical properties, and there are eight nonvanishing matrix elements     

Scattering and depolarization by rough surfaces near grazing angles--Full wave solutions

Using the full wave approach to rough surface scattering, the apparent singularity in the physical optics and perturbation expressions for the scattered fields is not encountered. The full wave expression for the far fields is shown to vanish in a continuous manner as the observer moves across a shadow boundary. Precise criteria are given for near grazing angles where uniform plane wave excitations cannot be assumed. Comparisons are made between the full wave and the physical optics and perturbation solutions. Since the full wave solution is shown to bridge the gap between the physical optics and perturbation solutions, it accounts for both specular and Bragg scattering. The full wave solutions satisfy reciprocity, duality, and realizability relationships in electromagnetic theory, and they are invariant to coordinate transformations.     

A numerical simulation of scattering from one-dimensionalinhomogeneous dielectric random surfaces

An efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient σ° is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists     

Scattering, transmission, and absorption by a rough resistive sheet - E polarization

Motivated by the use of thin conducting textiles in absorbers, the interaction of electromagnetic waves with a rough resistive sheet is examined. Expressions for the fields above and below the sheet are derived in terms of an equivalent current using Gaussian beam illumination. These field expressions are then used with equations derived from the conservation of energy to find the distribution of scattered, transmitted, and absorbed power using an exact numerical solution and the Kirchhoff approximation. As a consequence of the lack of refraction, the Kirchhoff single scattering solution produces strong coherent transmitted intensities at the forward angles with an attendant minimum in the incoherent intensity. A second minimum in the incoherent intensity is observed in the antispecular direction. Fields arising from multiple scattering interactions are observed independent of the Kirchhoff single scatter contributions at these angles for surfaces of large root-mean-square slope. An increase in the absorption in the sheet is also observed as surface roughness is increased. The increase in absorption is believed due to multiple scattering interactions on the surface.     

一维微粗糙面与其上方金属平板的复合电磁散射研究

研究了一维导体随机粗糙面与其上方金属平板的复合电磁散射。应用互易性原理使求解复合目标的二次散射场简化为求解包含平板上的极化电流和微粗糙面散射场的积分方程。利用物理光学近似和粗糙面微扰法分别计算了平板上的感应电流和粗糙面的电磁散射场,导出了复合散射模型单、双站散射的计算公式并给出了单站数值计算结果,讨论了后向复合散射截面随入射频率及平板尺寸、位置的变化关系。     

Depolarization of EM waves by slightly rough surfaces

Depolarization is obtained for the scattering of electromagnetic waves from a slightly rough surface using Rice's theory. In the plane of incidence, depolarization is a second-order effect. The results are applied to backscattering from a slightly rough sea using the Neumann spectrum for a fully developed sea. The expression for the depolarized scattered power is of the form obtained in multiple scattering investigations. Therefore, it can be inferred that depolarization from slightly rough surfaces is due to multiple scattering. For the sea, depolarization increases with wind speed and with the magnitude of the complex dielectric constant of the surface.