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     

水泥路面激光散射特性研究

为了通过激光散射特性识别不同粗糙程度水泥路面,设计了路面粗糙度测量系统.使用千分表测量水泥路面高度分布,计算高度均方根与相关长度.根据以上参量采用功率谱频域滤波生成随机粗糙表面以模拟水泥路面,通过切平面近似将粗糙面离散为大量微面元,由菲涅耳公式计算本地场,利用蒙特卡罗方法获取不同偏振光入射条件下粗糙面双向与后向散射光强...     

On the analysis of statistical distributions of UWB signal scattering by random rough surfaces based on Monte Carlo simulations of Maxwell equations

The field strength level of received signal and its statistical distributions are important in the study of signal propagation and scattering for wireless communication and remote sensing. In this paper, the scattering by random rough surface is analyzed by solving the solution of Maxwell equation. The method of moments is used to discretize the integral equation into the matrix equation. The sparse-matrix canonical grid method, which is a fast matrix solver, is applied in the analysis. Conjugate gradient (CG) method is adopted to solve the solution of matrix equation. With the solution of Maxwell equations, the magnitude of the scattered field is then used to predict the field statistics. Both time harmonic scattering and ultrawide-band (UWB) scattering are considered. For the time domain response, the electromagnetic scattered field in the vicinity of center of rough surfaces is first calculated in the frequency domain. Then the time domain signal is obtained by mean of the Fourier transform. The fading statistics are compared with that of the Rayleigh and Nakagami distributions. Results reveal that UWB signal exhibits less fading than the narrow band signal.     

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     

随机粗糙面上目标散射差值计算的快速互耦迭代方法

用粗糙面上方有目标和无目标时空间散射场的差值计算的雷达散射截面,称为差场雷达散射截面.本文推导TE波入射下电场积分方程(EFIE),直接求解散射差场.本文提出目标与粗糙面之间的互耦迭代的计算方法,散射场纳入了目标与粗糙面之间复杂的相互作用,给出了迭代过程中纳入的粗糙面长度的选择.用Monte-Carlo方法,计算了P-M谱粗糙海面上方二维圆柱和方柱的散射,说明目标的几何结构对散射方向图的影响.     

Fast iterative approach to difference scattering from the target above a rough surface

The difference field radar cross section (d-RCS) has been defined to analyze the scattering from the target above a rough surface, which takes account of scattering from the target and multiinteractions of the target and underlying rough surface. The d-RCS removes the effect of the finite illuminated surface length under the tapered wave incidence. In this paper, the electric field integral equations (EFIEs) of the difference-induced current J/sub sd/ on the rough surface and the induced current J/sub o/ on the target are derived. A small section of rough surface toward the target in the specular direction is taken to speed up computation of the scattering contribution E/sub s0/ from the moderate rough surface to the target. Then, an iterative approach is developed to solve the EFIEs of the induced currents, directly, and yields the bistatic d-RCS. A finite rough surface length for numerical iteration is taken, corresponding to the dependence on the maximum scattering angle. Using the Monte Carlo method to generate rough surface, the bistatic d-RCS of the target, e.g., a cylinder or a square column, above a Pierson-Morkowitz rough surface is numerically simulated. The induced currents on the target and the d-RCS are discussed, and compared with the case of the target in free-space.     

Effects of a Rough Boundary Surface on Polarization of the Scattered Field from an Inhomogeneous Medium

The effect of surface roughness on the polarization of the scattered field is studied by combining the standard Kirchhoff method for rough surface scattering with the radiative transfer method for volume scattering using the Rayleigh phase function. Corresponding cases of pure surface scattering from a homogeneous layer and volume scattering from a plane inhomogeneous layer are also computed to serve as points of reference. In each case the degree of polarization DP, polarization ratio PR, locations on the Poincaré sphere of copolarization nulls CN, and cross-polarization nulls XN are computed. It is found that for pure surface scattering PR between 0-20° incidence angles is quite sensitive to change in surface roughness. However, when both surface and volume scattering are present, CN by colatitude or DP between 0-15° incidence angles and CN or XN by longitude at large incidence angles (>60°) are better indicators of change in surface roughness. Since XN changes insignificantly in pure surface scattering, it appears that a significant change in it can serve as an indicator for the presence of volume scattering. Also, in pure surface or volume scattering, the variations of DP and CN by colatitude are monotone with the incidence angle, while in the combined surface and volume scattering DP has a minimum and CN by colatitude has a maximum. This character offers the possibility of separating combined surface and volume scattering from pure surface or volume scattering.     

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.     

太赫兹低频段随机粗糙金属板散射特性研究

该文提出了一种高效混合近似算法计算太赫兹频段无限薄金属板的电磁散射特性。在太赫兹低频段,金属目标可以被视为具有微粗糙表面的理想导体,散射场可以分为相干场和非相干场。该文采用物理光学法结合截断劈增量长度绕射系数法和微扰法来计算金属板的电磁散射分布。基于蒙特卡洛方法,分别利用多层快速多极子和提出的混合算法计算太赫兹低频段金属板的雷达散射截面,仿真结果表明该文提出的混合算法能够高效快速地给出太赫兹低频段金属板的电磁散射特性。      

A theory of wave scattering from an inhomogeneous layer with an irregular interface

Bistatic wave scattering from a layer of Rayleigh scatterers with an irregular interface is investigated by combining the doubling method in volume scattering with the Kirchhoff method in rough surface scattering. Theoretical results are shown illustrating the effect of the rough interface. It is found that for scattered and incident angles near the vertical, the rough interface causes a substantial increase relative to the plane interface in both the like and cross-scattering coefficients over all azimuth angles. However, for large scattered and incident angles, the reverse is true except for azimuth angles around the specular direction. It is interesting to note that while one dominant peak of the like polarized scattering coefficient occurs along the specular direction, two dominant peaks of the cross-polarized scattering coefficient may appear symmetrically with respect to the specular direction. In backscattering, the surface roughness causes a peak to appear in both the like and cross-scattering coefficients at near vertical incidence and also a decrease of these coefficients at large incidence angles.     

Backscattering from a randomly rough dielectric surface

A backscattering model for scattering from a randomly rough dielectric surface is developed. Both like- and cross-polarized scattering coefficients are obtained. The like-polarized scattering coefficients contain single scattering terms and multiple scattering terms. The single scattering terms are shown to reduce to the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients increases with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces     

The use of fractals for modeling EM waves scattering from rough seasurface

A rough surface model based on fractal geometry is presented for the study of surface scattering. In particular, the Pierson-Moskowitz spectrum is incorporated into this model to represent a fully developed sea surface. The Kirchoff approximation is used to evaluate the scattered field from this rough surface. Some interconnection are found between the surface model developed and the statistical characteristics of the scattered field. These include: 1) the relationship between the surface correlation length and the surface fractal dimension; 2) the relationship between the shape parameter of the K-distribution and the surface fractal dimension; 3) the mean value of the scattered amplitude as a function of the surface fractal dimension; and 4) the effect of the incident angle on the scattered field     

Wave scattering from a large sphere with rough surface

Wave scattering from a rough perfectly conducting sphere is considered. Use is made of the reformulated current method in which the object is replaced by a current distribution radiating into an unbounded media. The scattered field components are obtained in terms of the joint characteristic function defining the roughness.     

A new approach to the analysis of rough surface scattering

A novel approach to the problem of scattering by a randomly rough surface is developed based on combining normalization and the method of smoothing. Previous uses of smoothing have been forced to assume small surface heights in order to guarantee the dominance of the scattered field by its average or specular part. The term that causes the average scattered field to be so sensitive to the height is identified, and is normalized out of the basic integral equation. Smoothing is then applied to the normalized integral equation with a subsequent reintroduction of the normalizing factor after smoothing. The results are shown to extend beyond existing approximations, and they contain none of the divergent integral behavior that has recently been observed with a pure second order iterative approximation. An examination of the conditions under which the technique provides very accurate results shows that it is essentially an extension of the so-called composite surface scattering model     

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。      

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     

Bidirectional Analytic Ray Tracing for Fast Computation of Composite Scattering From Electric-Large Target Over a Randomly Rough Surface

The bidirectional analytic ray tracing (BART) method is developed to rapidly calculate composite scattering from three-dimensional (3D) electrically large complex targets above a randomly rough surface. Ray tracing is carried out both along the incident (forward) direction and converse direction of scattering (backward) recording different orders of ray illumination on each facet or edge of the target and surface. Once a pair of forward and backward rays meet on a facet/edge, a scattering term is constructed using the diffused scattering/diffraction of this facet/edge and all reflections occurred on the tracing paths. The rough surface is modeled with “rough facets” including coherent scattering and diffused incoherent scattering, which can be directly calculated according to the IEM (integral equation method) of a randomly rough surface. Analytic tracing of polygon ray tubes is developed to precisely calculate the illumination and shadowing of facets, which exempt large patches of the target from any finer meshing. It significantly reduces the complexity relevant to the target electric-size. Higher orders of scattering and, in particular, interactions between the target and rough surface are then taken into account. The accuracy and performance of BART is validated and evaluated by comparing with exact computational electromagnetic methods for electrically small targets. Numerical examples of angularly composite scattering from a three-dimensional electrically large, e.g., a ship-like target over a randomly rough surface are presented and discussed.      

室内粗糙面的太赫兹散射特性研究

运用改进型菲涅尔方程和基尔霍夫近似方法分别研究室内不同粗糙面的太赫兹波反射和散射.根据改进型菲涅尔反射理论,得到了在水平和垂直两种极化状态下,不同入射角、不同粗糙面及不同频率的反射系数,分析了以上参数变化对反射系数的影响和物理意义.同时,基于基尔霍夫近似理论,得到了在水平和垂直两种极化状态下,不同入射角和方位角、不同散射角、不同粗糙面的散射系数,获得了散射系数随以上参数变化而产生的数值结果,并分析了仿真结果的物理意义.     

Scattering of electromagnetic waves by rough perfectly conducting circular cylinders

A numerical method is proposed for computing the normalized correlation functions of the real and imaginary parts of the field scattered from a statistically rough perfectly conducting circular cylinder. The deviation of the surface from its mean radius is assumed to be small. The correlation function of the far-field is related to the correlation function of the scattering object by an integral equation. Far-field correlation functions are found for two types of surface correlation functions: the delta function and a periodic exponential function.     

A Novel Method to Analyze Electromagnetic Scattering of Complex Objects

The finite-difference time-domain (FD-TD) method is proposed as a means of accurately computing electromagnetic scattering by arbitrary-shaped extremely complex metal or dielectric objects excited by an external plane wave. In the proposed method, one first uses the FD-TD method to compute the near total fields within a rectangular volume which fully encloses the object. Then, an electromagnetic-field equivalence principle is invoked at a virtual surface of this rectangular volume to transform the tangential near scattered fields to the far field. To verify the feasibility of this method, the surface currents, near scattered fields, far scattered fields, and radar cross section of two canonical two-dimensional objects are presented. For these cases, it is shown that the FD-TD method provides magnitude of current and field predictions which are within ± 2.5 percent and further phase values within ± 30 of values predicted by the method of moments ( MOM) at virtually every point including in shadow regions.