Three-dimensional subsurface analysis of electromagnetic scatteringfrom penetrable/PEC objects buried under rough surfaces: use of thesteepest descent fast multipole method

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine     

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.     

用角相关函数识别随机粗糙面上散射目标的有限元解法

研究随机粗糙面上有散射目标时散射场求解的有限元数值方法，并提出用散射场角相关函数在非记忆线上的增强，来识别粗糙面上散射目标的存在。给出了随机粗糙面上无散射目标和有效射目标时散射场角有关函数的特征性变化。     

随机粗糙地面与下方目标复合电磁散射研究

利用MOM 研究了不同土壤类型的有耗介质粗糙地面与其下方埋藏金属目标的复合电磁散射问题,在数值计算中,引入了锥形入射波以减少粗糙面模拟中由于人为截断所引起的计算误差。当给定入射波频率、土壤成分及土壤温度和土壤湿度后,可以根据相关模型计算出土壤的相对介电常数。数值结果以二维无限长导体圆柱为例,利用 Monte-Carlo 方法统计计算了双站复合散射截面随土壤湿度、均方根高度的变化情况,并做了详细分析及讨论。     

Electromagnetic scattering from a buried cylinder in layered media with rough interfaces

A solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder.     

Analytical, experimental, and numerical studies of angular memorysignatures of waves scattered from one-dimensional rough surfaces

It is known that a change in the direction of an incident wave on a random medium is “remembered” by the angular correlation characteristics of the scattered waves. This “memory effect” is studied for rough-surface scattering by means of theoretical [second-order Kirchhoff approximation (KA)], numerical (Monte Carlo simulations), and experimental (millimeter-wave range) approaches. The second-order KA has been found to be effective for wave scattering from very rough surfaces with large radii of curvature and high slopes (0.5-1.5). Although the second-order KA is based on a number of approximations including the geometrical optics approximation and the approximate forms of the shadowing functions, excellent agreement with Monte Carlo simulations and millimeter-wave experiments was achieved. The results are presented in a form of memory signatures which clearly exhibit the important features of this effect     

Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects

A three-dimensional polarimetric analysis of the two-layered rough ground with and without buried objects is investigated here. A rigorous electromagnetic surface integral-equation-based model is used in this analysis. The statistical average of the polarimetric scattering matrix elements is computed based on the Monte Carlo simulations for both the vertically and horizontally polarized incident waves. The results show a significant impact on the scattered intensities due to the two-layer nature of the ground. However, these intensities show almost no difference between the ground signature with or without the object. On the other hand, the statistical average of the covariance matrix elements shows a distinct difference between these two signatures despite the small size of the buried object.     

复杂陆地粗糙面及其上方坦克目标复合散射研究

研究了复杂陆地粗糙面及其上方坦克目标的复合散射特性.基于Monte Carlo方法,利用高斯谱函数模拟不同统计特性的陆地表面,运用加权反正切函数滤波处理以构造边界和连接相邻区域,构建了复杂陆地分区域复合粗糙面的几何模型.提出了一种快速精确求解复杂陆地粗糙面及其上方坦克目标复合散射的混合方法,利用迭代物理光学法求解目标与环境间的多次耦合,运用等效电磁流法修正棱边绕射.分析了复杂陆地粗糙面的散射特性,研究了入射角、均方根高度、相关长度和粗糙面表面结构对复合散射特性的影响.本研究为探测复杂环境上方的坦克目标提供了理论基础,数值仿真结果对雷达目标的探测与识别具有借鉴意义.     

Monte Carlo simulations for clutter statistics in minefields: AP-mine-like-target buried near a dielectric object beneath 2-D random rough ground surfaces

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.     

目标与复杂地海面复合电磁散射研究现状综述

目标与复杂地海环境复合电磁散射研究一直是电磁领域一大重要课题.该方面研究在复杂背景中的目标探测（地海上方低飞导弹、飞机,海上舰船目标,地上坦克目标等）、资源勘探（浅层地下矿物质勘探）等领域发挥着巨大作用,使得该领域的研究变得紧迫且具有实际意义.大多数的目标都处在粗糙地海背景中,当电磁波入射到目标时,由于粗糙背景的存在,电磁波会与粗糙背景发生相互作用,对回波造成影响,进一步干扰目标本身的散射.在粗糙面上飞行、行驶目标及粗糙面下掩埋、半掩埋目标引起的电磁散射与其在自由空间中的散射特性是非常不同的,粗糙背景的作用很大程度上增加了目标探测和识别的不确定性.     

Scattering from multiple objects buried beneath two-dimensional random rough surface using the steepest descent fast multipole method

Generalized formulations are presented to analyze the electric field scattered from multiple penetrable shallow objects buried beneath two-dimensional random rough surfaces. These objects could have different materials, shapes, or orientations. In addition, their separation distance may range from a fraction of a wavelength to several wavelengths. The fast algorithm, steepest descent fast multipole method (SDFMM), is used to compute the unknown electric and magnetic surface currents on the rough ground surface and on the buried objects. Parametric investigations are presented to study the effect of the objects proximity, orientations, materials, shapes, the incident waves polarization, and the ground roughness on the scattered fields. A significant interference is observed between the objects when they are separated by less than one free space wavelength. Even when the clutter due to the rough ground is removed, the return from the second object, can be dominating causing a possible false alarm in detecting the target. The results show that the distortion in target signature significantly increases with the increase of both the proximity to a clutter item and the ground roughness.     

Scattering from a metallic object embedded near the randomly roughsurface of a lossy dielectric

Two-dimensional electromagnetic scattering from a perfectly conducting target embedded near the randomly rough surface of an isotropic lossy dielectric is investigated. The randomly rough surface is illuminated by a finite width beam from an antenna in the free space above the surface, with off-normal incidence. Standard integral equation methods are applied and include all subsurface interactions between the object and rough surface. For a chosen embedded target, Monte Carlo simulations are performed for a selection of ensembles of rough surface types intended to be suggestive of natural ground. Far field scattering coefficient distributions and corresponding synthetic images suggest when the buried object should be discernible. Sensitivities are explored in terms of surface type, polarization of the incident field, depth and orientation of target, soil characteristics, incidence angle, and beamwidth. Many of the scattering features identified should also apply in 3D     

An FDTD near- to far-zone transformation for scatterers buried instratified grounds

The finite-difference time-domain (EDTD) technique is being used with increasing frequency for modeling the scattering characteristics of buried objects. The FDTD has, for some time, been able to model the near-zone scattered fields of buried objects due to near-zone sources. This is adequate for modeling the scattered returns of ground-based ground-penetrating radar, but not for airborne radar. This paper describes an FDTD-compatible technique whereby far-zone scattered fields of objects buried in a stratified ground can be calculated. This technique uses the equivalence principle to model a buried object in terms of equivalent electric and magnetic currents. The fields radiated by these currents in the presence of a stratified ground are then calculated using the reciprocity theorem and the well-known field equations for plane waves in a stratified media. Numerical results are presented that show excellent agreement between this technique and both analytical and numerical results     

The scattering from curved rough surfaces of an EM wave transmitted through a turbulent medium

A generalized analysis of electromagnetic (EM) wave scattering from rough surfaces yields an expression for mean scattered power flux which is the spatial Fourier transform of the product of three transfer functions: 1) the optical transfer function (OTF) of the propagating medium; 2) the joint characteristic function of the surface roughness; and 3) a coherence involving the mean surface and the wave profile. The solution is applicable to moderately rough surfaces which have rms slopes less than a few degrees. The solution is applied to laser scattering from aluminum and titanium surfaces where the medium is the atmosphere. The randomly rough surface consists of independent "roughness" and "waviness" components which possess a Gaussian autocorrelation. The deterministic surface is quadratic; the laser profile, Gaussian. The atmospheric OTF is modeled into a Gaussian form. For typical parameters, the result decouples into a specular term (depending on turbulence, wave profile, and known surface) and a diffuse component (depending on rough and known surfaces). A slightly spherical incident wave affects only the coherent term.     

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     

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.     

基于二维粗糙面模型的大地土壤表面散射特性研究

建立二维粗糙面模型研究了大地土壤表面对高频超视距雷达电磁波的散射特性.采用半经验公式计算了HF频段给定频率下土壤媒质在不同温度、湿度时的有效相对介电常数,并与微波频段下情形进行对比.采用Monte Carlo法结合高斯谱函数生成二维粗糙面模拟真实大地土壤表面,建立了土壤表面积分方程,采用锥形波入射消除人为截断粗糙面带来的边缘衍射,采用基于物理意义的双网格法(Physics Based Two Grid,PBTG)结合稀疏网格迭代法(Sparse Matrix Canonical Grid,SMCG)求解土壤表面的双站散射系数.研究了不同温度和湿度条件下,大地土壤表面对高频超视距雷达电磁波的散射特性.研究结果为高频超视距雷达遥感探测提供了理论参考.     

Acoustic and electromagnetic wave interaction: estimation of Doppler spectrum from an acoustically vibrated metallic circular cylinder

The idea of using acoustically induced Doppler spectra as a means of target detection and identification is introduced. An analytical solution for the calculation of the bistatic scattered Doppler spectrum from an acoustically excited, vibrating, metallic, circular cylinder is presented. First, the electromagnetic scattering solution of a slightly deformed circular cylinder is obtained using a perturbation method. Then, assuming the vibration frequency is much smaller than the frequency of the incident electromagnetic wave, a closed form expression for the time-frequency response of the bistatic scattered field is obtained which can be used directly for estimating the Doppler spectrum. The acoustic scattering solution for an incident acoustic plane wave upon a solid elastic cylinder is applied to give the displacement of the cylinder surface as a function of time. Results indicate that the scattered Doppler frequencies correspond to the mechanical vibration frequencies of the cylinder, and the sidelobe Doppler spectrum level is, to the first order, linearly proportional to the degree of deformation and is a function of bistatic angle. Moreover, the deformation in the cylinder, and thus the Doppler sidelobe level, only becomes sizeable near frequencies of normal modes of free vibration in the cylinder. Utilizing the information in the scattered Doppler spectrum could provide an effective means of buried object identification, where acoustic waves are used to excite the mechanical resonances of a buried object.     

Bistatic Scattering From a Three-Dimensional Object Over a Randomly Rough Surface Using the FDTD Algorithm

A numerical finite-difference time-domain approach for electromagnetic scattering from an object over a randomly rough surface in three-dimensional (3-D) model is developed. Rough surface is truncated in numerical simulation by using the periodic surface extension, and one period of the rough surface with dependence of the correlation length is used for scattering computation. Generation of the incident wave upon the rough surface is presented. A numerical model and algorithm of a single object on or above a rough surface are developed. Polarized bistatic scattering from the object and rough surface is obtained based on numerical distribution of the near zone fields. Comparison with conventional two-dimensional model is also discussed.     

A Monte-Carlo FDTD Technique for Rough Surface Scattering

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique