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     

Electromagnetic Scattering From Multilayer Rough Surfaces With Arbitrary Dielectric Profiles for Remote Sensing of Subsurface Soil Moisture

Radar remote sensing of soil moisture content at low frequencies requires an accurate scattering model of realistic soils, which often involves multilayer rough surfaces and dielectric profiles. In this paper, a hybrid analytical/numerical solution to two-dimensional scattering from multilayer rough surfaces separated by arbitrary dielectric profiles based on the extended boundary condition method (EBCM) and scattering matrix technique is presented. The reflection and transmission matrices of rough interfaces are constructed using EBCM. The dielectric profiles are modeled as stacks of piecewise homogeneous dielectric thin layers, whose scattering matrices are computed by recursively cascading reflection and transmission matrices of individual dielectric interfaces. The interactions between the rough interfaces and stratified dielectric profiles are taken into account by applying the generalized scattering matrix technique. The scattering coefficients are obtained by combining the powers computed from the resulting Floquet modes of the overall system. The bistatic scattering coefficients are validated against existing analytical and numerical solutions. Field-collected soil moisture data are then used for numerical simulations to investigate the penetration capability at different frequencies and to address the potential of low-frequency radar systems in estimating deep soil moisture. In particular, soil moisture profiles during dry ground, wet ground, and wet subsurface layer conditions are examined. The results show that both backscattering coefficients and copolarized phase difference at low frequencies are sensitive to the roughness of subsurface interfaces and deep soil moisture. Also, much larger depth sensitivity can be achieved using copolarized phase difference than scattering coefficients     

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     

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.     

Renormalization of EM fields in application to large-angle scattering from randomly continuous media and sparse particle distributions

The conventional wave-integral equation in electromagnetic scattering, consisting of a sum of directly received vacuum field plus a scattered field that sums weighted vacuum spherical waves from each scatterer, is replaced by one in which renormalized fields containing part of the multiply scattered energy replace the vacuum fields. A first-order approximation in the renormalized equation is applied to bistatic (large-angle) scattering from weak random fluctuations of the permittivity in a distant volume, and to a sparse monodisperse distribution of isotropic particles to yield scattering cross sections with extended validity for the direct polarization. A similar correction is introduced for the cross polarization in the case of backscatter. Differences with other calculations are noted.     

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 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.     

Fully polarimetric bistatic radar scattering behavior of forestedhills

The bistatic radar scattering measurements of forested hills were performed at grazing incidence and at azimuth scattering angles from 28° to 66° from the forward scatter plane. Using pulse-to-pulse switching between orthogonal transmitted polarizations, the radar simultaneously measures two orthogonally polarized components of the scattered wave to obtain full polarimetric information about the scattering process. These are the first fully polarimetric terrain clutter measurements to be conducted at large bistatic angles. The complete Stokes matrix, computed by averaging successive realizations of the polarization scattering matrix, is used to examine the polarization sensitivity of the bistatic clutter. It is found that the polarization state of the EM wave scattered out of the plane of incidence strongly depends on the polarization orientation of the incident electric field. Unlike the monostatic case, these two incident wave polarization states are found to produce substantially different scattered wave behavior when trees are viewed at large bistatic angles. Scattered fields resulting from vertically oriented incident fields are found to be highly polarized and to produce bistatic clutter power levels that are strongly dependent on the polarization of the receiving antenna. In contrast, horizontally oriented incident fields are found to produce weakly polarized scattered waves with bistatic clutter power levels that are insensitive to the polarization of the receiving antenna     

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     

Experimental studies of bistatic scattering from two-dimensionalconducting random rough surfaces

Despite the recent development of analytical and numerical techniques for problems of scattering from two-dimensional rough surfaces, very few experimental studies were available for verification. The authors present the results of millimeter-wave experiments on scattering from two-dimensional conducting random rough surfaces with Gaussian surface roughness statistics. Machine-fabricated rough surfaces with controlled roughness statistics were examined. Special attention was paid to surfaces with large rms slopes (ranging from 0.35 to 1.00) for which enhanced backscattering is expected to take place. Experimentally, such enhancement was indeed observed in both the copolarized and cross-polarized returns. In addition, it was noticed that at moderate angles of incidence, the scattering profile as a function of observation angle is fairly independent of the incident polarization and operating frequency. This independence justifies the use of the geometric optics approximation embodied in the Kirchhoff formulation for surfaces with large surface radius of curvature. When compared with the experimental data, this analytical technique demonstrates good agreement with the experimental data     

Full-wave solutions for the scattered radiation fields from rough surfaces with arbitrary slope and frequency

Full-wave solutions are derived for the scattered radiation fields from rough surfaces with arbitrary slope and electromagnetic parameters. These solutions bridge the wide gap that exists between the perturbational solutions for rough surfaces with small slopes and the quasi-optics solutions. Thus it is shown, for example, that for good conducting boundaries the backscattered fields, which are dependent on the polarization of the incident and scattered fields at low frequencies, become independent of polarization at optical frequencies. These solutions are consistent with reciprocity, energy conservation, and duality relations in electromagnetic theory. Since the full-wave solutions account for upward and downward scattering, shadowing and multiple scatter are considered. Applications to periodic structures and random rough surfaces are also presented.     

Calculations of the Microwave Brightness Temperature of Rough Soil Surfaces: Bare Field

A model for simulating the remotely sensed microwave brightness temperatures of soils with rough surfaces is developed. The surface emissivity of the soil media is calculated from one minus its reflectivity, which is obtained by the integration of the bistatic scattering coefficients for rough soil surfaces. The soil brightness temperature is obtained from the product of the surface emissivity and the effective soil temperature, which is calculated with measured soil moisture profiles and soil temperature profiles at various soil depths. The roughness of a soil surface is characterized by two parameters, the surface height standard deviation a and its horizontal correlation length l. The model calculations are compared to the measured angular variations of the polarized brightness temperatures at both L-band (1.4 GHz) and C-band (5 GHz) frequencies. A nonlinear least squares fitting method is used to match the model calculations with the data, and the best fit results produce the parameter values of a and l that best characterize the surface roughness. The effect of rough surface shadowing is also incorporated into the model by introducing a shadowing function S(?), which represents the probability that a point on a rough surface is not shadowed by other parts of the surface. The model results for horizontal polarization are in excellent agreement with the data, both qualitatively and quantitatively. For vertical polarization, some discrepancies exist between the calculations and data. Possible causes of the discrepancy are discussed.     

Numerical simulation of scattering from three-dimensional randomlyrough surfaces

Randomly rough surface patches in three dimensions are generated on the computer. The FD-TD method is used to compute scattering from surface patches by converting the Maxwell's equations into difference equations using a central difference approximation for the space and time derivatives. The volume of grids above the rough surface is divided into the total field and the scattered field regions. In between these two regions, obliquely incident waves are generated. To reduce computation, the volume of grids is chosen to be small, and a transformation is used to convert the scattered field into far zone fields for bistatic scattering coefficient calculations. Possible errors near the edge of the surface due to the use of a relatively small volume are suppressed by introducing a windowing function. Very good agreements are obtained between the results obtained by this method and those calculated by an integral equation method (IEM) for scattering from randomly rough perfectly conducting and dielectric surfaces     

Optimal time-domain detection of a deterministic target buriedunder a randomly rough interface

We consider pulsed plane-wave scattering from targets buried under a rough air-ground interface. The properties of the interface are parametrized as a random process with known statistics, and therefore the fields scattered from a particular surface constitute one realization of an ensemble, characterized by corresponding statistics. Moreover, since the fields incident upon a buried target must first penetrate the rough interface, they and the subsequent scattered fields are random processes as well. Based on this understanding, an optimal detector is formulated, accounting for the clutter and target-signature statistics (the former due to scattering at the rough surface, and the latter due to transmission); the statistics of these two processes are in general different. The detector performance is compared to that of a matched filter, which assumes the target signature is known exactly (i.e., nonrandom). The results presented here, as a function of angle and polarization, demonstrate that there is often a significant gain in detector performance if the target signature is properly treated as a random process     

Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface

An analytical solution is presented for the electromagnetic scattering from a dielectric circular cylinder embedded in a dielectric half-space with a slightly rough interface. The solution utilizes the spectral (plane-wave) representation of the fields and accounts for all the multiple interactions between the rough interface and the. buried cylinder. First-order coefficients from the small perturbation method are used for computation of the scattered fields from the rough surface. The derivation includes both TM and TE polarizations and can be easily extended for other cylindrical buried objects (e.g., cylindrical shell, metallic cylinder). Several scattering scenarios are examined utilizing the new solution for a dielectric cylinder beneath a flat, sinusoidal, and arbitrary rough surface profile. Results indicate that the scattering pattern of a buried object below a slightly rough surface differs from the flat surface case only when the surface roughness spectrum contains a limited range of spatial frequencies. Furthermore, the illuminated area of the incident wave is seen to be a critical factor in the visibility of a buried object below a rough surface.     

Electromagnetic wave scattering by a system of two spheroids ofarbitrary orientation

An exact solution to the problem of the scattering of a plane electromagnetic wave by two perfectly conducting arbitrarily oriented prolate spheroids is obtained by expanding the incident and scattered electric fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions, the field scattered by one spheroid is expressed in terms of its spheroidal coordinates, using rotational-translational addition theorems for vector spheroidal wave functions. The column matrix of the scattered field expansion coefficients is equal to the product of a square matrix which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident-field expansion coefficients. The unknown scattered-field expansion coefficients are obtained by solving the associated set of simultaneous linear equations. Numerical results for the bistatic and backscattering cross sections for prolate spheroids with various axial ratios and orientations are presented     

不同类型土壤地面与其上方目标散射特性研究

针对超低空目标与地面复合电磁散射的问题,以某型巡航导弹作为超低空目标的典型代表,研究了不同类型土壤地面与其上方巡航导弹的散射特性。在考虑不同类型土壤组成成分的基础上,采用四成分土壤介电模型计算其介电常数,分析了土壤介电常数与土壤类型和土壤湿度的关系;以二维高斯粗糙面模拟地面环境,引入锥形入射波克服粗糙面的边缘衍射,应用基于物理意义的双网格法(Physics Based Two Grid, PBTG)结合稀疏矩阵规范网格法(Sparse Matrix Canonical Grid, SMCG)仿真分析了土壤类型、入射波频率与极化等因素对地面环境电磁散射特性的影响;基于目标与环境的复合表面积分方程,研究了不同类型土壤地面与巡航导弹的复合散射特性。分析表明:巡航导弹与粗糙面相互作用,使三种类型土壤地面的散射系数均有所增大。研究成果为不同类型土壤地面环境遥感探测及其上方超低空目标的探测提供了理论参考。     

Oblique scattering from lossy periodic surfaces with applicationsto anechoic chamber absorbers

Plane wave scattering from lossy, periodic surfaces with periodicity in one direction is considered for arbitrary polarization and incidence angles. The material is assumed to be homogeneous and characterized by complex values of permittivity and permeability. Muller-type coupled integral equations are derived for the surface electric and magnetic currents. The power reflection coefficient is defined in terms of the scattered far fields. The integral equations are solved by the boundary element method (BEM) with constant elements. Arbitrary surfaces are accommodated by approximating the actual profile by means of linear segments. Other speed-up techniques are utilized to generate a numerically efficient solution. Substantial comparison is made for special cases to verify the formulation. The reflection coefficient is calculated for a variety of surface shapes. A new profile shape is presented that results in a lower reflection coefficient than the commonly used triangular shape     

Scattering cross sections for composite models of non-Gaussian rough surfaces for which decorrelation implies statistical independence

The full wave approach is used to determine the scattering cross sections for composite models of non-Gaussian rough surfaces. It is assumed in this work that the rough surface heights become statistically independent when they decorrelate, thus no delta function type specular term appears in the expressions for the scattered fields. The broad family of non-Gaussian surfaces considered range in the limit from exponential to Gaussian. It is seen that for small angles of incidence the like polarized cross sections have the same dependence on the specific form of the surface height joint probability density, but for large angles the scattering cross sections for the horizontally polarized waves are much more sensitive to the specific form of the joint probability density. On the other hand the shadow functions are rather insensitive to the specific form of the joint probability density.     

多频段典型地表的双站雷达散射回波预测

双站雷达在反隐身、超低空防御方面具有独特优势,但双站测量装置较为复杂,地表参数的准确获取工作耗时耗力,且精度难以保证,地表双站雷达散射数据极其匮乏。为解决上述问题,该文以L/S/X/Ku波段裸土、水泥地和粗糙沙地后向散射实测数据为例,忽略地表的精细结构,采用等效面散射模型和遗传算法反演了各地表的等效介电常数和粗糙度参数,获取其等效参数统计特征,实现对地表双站雷达散射回波的预测。结果表明:该等效面散射模型保证了地表的后向和双站散射回波预测精度;地表双站雷达散射回波随入射波频率的增大而增大;随散射角的增大先增大而后减小,并在镜像方向出现最大值;随散射方位角的增大,地表散射回波先减小而后增大,HH极化双站散射回波的最小值一般出现在 方位角处,而VV极化双站散射回波的最小值位置随入射角的增大从 方位角向小角度方向偏移,并与入射波频率、地表湿度以及粗糙度参数相关,该双站散射特性可用于地表参数的反演以及目标的反隐身研究。