Application of the integral equation method of smoothing to random surface scattering

The integral equation method of smoothing (IEMS) is applied to the magnetic field integral equation (MFIE) weighted by the exponentialexp (jk_{1}zeta)wherezetais the stochastic surface height. An integral equation in coordinate space for the average of the product of the surface current and the exponential factor is developed. The exact closed-form solution of this integral equation is obtained based on the specularity of the average scattered field. The complex amplitude of the average scattered field is thus determined by an algebraic equation which clearly shows the effects of multiple scattering on the surface. In addition, it is shown how the incoherent scattered power can be obtained using this method. Comparisons with the Kirchhoff approximation and the dishonest approach are presented, and the first-order smoothing result is shown to be superior to both.     

Simplifications in the stochastic Fourier transform approach to random surface scattering

Further developments in the application of the stochastic Fourier transform approach (SFTA) to random surface scattering are presented. It is first shown that the infinite dimensional integral equation for the stochastic Fourier transform of the surface current can be reduced to the three dimensions associated with the random surface height and slopes. A three-dimensional integral equation of the second kind is developed for the average scattered field in stochastic Fourier transform space using conditional probability density functions. Various techniques for determining the transformed current (and, subsequently, the incoherent scattered power) from the average scattered field in stochastic Fourier transform space are developed and studied from the point of view of computational suitability. The case of vanishingly small surface correlation length is reexamined and the SFTA is found to provide erroneous results for the average scattered field due to the basic failure of the magnetic field integral equation (MFIE) in this limit.     

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.     

任意截面非均匀各向异性阻抗柱体的电磁散射

采用矩量法(MoM)结合阻抗边界条件研究了二维无限长任意形状截面非均匀各向异性阻抗柱体的电磁散射特性。散射场通过Stratton-Chu电场积分方程、电流连续性方程和二维格林函数予以求解。当柱体截面矢径的模等于恒定值时,目标退化为二维无限长圆柱,提出的计算方法仍然有效。计算得到的散射宽度结果与解析法、物理光学法(PO)的结果进行了比较,吻合良好。     

Synthesis of tapered resistive strips

A technique for synthesizing a resistive taper that generates desired bistatic scattering and backscattering patterns from a strip is outlined. Antenna synthesis techniques relate the scattered field to the induced surface current density. Physical optics approximations then relate the induced current to the resistivity. The taper is checked by computing the surface current density and scattered fields of the tapered resistive strip using the integral equation formulation and comparing with the physical optics results.     

一种求解目标内谐振时散射截面的有效方法

众所周知,在内谐振频率点上,用矩量法求解电场或磁场表面积分方程将得到不正确的表面电流。文中应用奇异值分解和正交化方法对由电场积分方程计算出的表面电流进行修正,从而得到目标表面上产生散射场的真实电流分布。文中计算了一无限长理想导体圆柱内谐振时的散射截面,所得结果与解析解一致,并对一无限长理想导体正方柱的后向散射截面进行了计算,结果表明本文方法是有效和准确的。     

A survey of the near-field far-field inverse scattering inverse source integral equation

The Kirchhoff direct integration of the scalar wave equation is reviewed, and some properties of the Kirchhoff surface integral are discussed, from the perspective of the inverse scattering inverse source problem. A modified Kirchhoff surface integral is introduced, leading to a Fredholm integral equation of the first kind for the unknown sources (induced by the incident field) inside a volume in terms of the (scattered) fields on the surface enclosing this volume. The properties and physical meaning of this integral equation are discussed. A generalization of this integral equation for the vector electromagnetic wave equations is presented.     

Scattering from cylinders with arbitrary surface impedance

This paper presents an integral equation method for the solution of the field scattered by a set of cylinders with arbitrary cross-sectional shape, and arbitrarily varying anisotropic surface impedance. The integral equations are given for an arbitrary source with arbitrary harmonic variation along the cylinder axis. The scattering problem can be solved for arbitrary three-dimensional sources by expansion of the source in a Fourier integral over the axial propagation constant. The integral equations have been programmed for a CDC 1604A computer. The program developed has been used to solve a great variety of scattering, antenna, and propagation problems, and, depending upon accuracy desired, will handle cylinders up to about 150-wavelengths total perimeter. Numerical results on scattering from cylinders with specific cross sections are presented to illustrate the utility of the program developed.     

Scattering of TE-polarized EM wave by discontinuity in groundeddielectric layer

The two-dimensional problem of EM wave interaction with a dielectric discontinuity in an infinite grounded dielectric layer is studied. An electric field integral equation (EFIE) for TE illumination has been derived based on the Green's function for the electric field produced by induced polarization currents in the discontinuity region. Impressed electric fields consist of either plane waves incident from space above the dielectric layer or surface waves supported by that layer. Method of Moments (MoM) numerical solutions for the induced electric field in the discontinuity region are implemented. The amplitudes of surface waves excited by excess discontinuity-region polarization currents are calculated, as well as the pattern of the scattered field and the associated scattering width. It is observed that the excitation of a surface-wave mode reduces the back scattered radiation for TE-polarized plane wave incidence. The accuracy of the theory is verified by comparison of numerical results with those of existing studies     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

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     

Integral equation for scattering by a dielectric

The determination of the scattered and transmitted transient electromagnetic waves produced by a uniform dielectric body is reduced to the solution of a singular integral equation of the first kind for one tangential vector field defined on the surface. All derivations are carried out within the heuristic approach to Green functions and delta functions. The electric and magnetic fields are expressed in terms of the sources, initial values, and the boundary values by means of the Green function for the scalar wave equation. The appropriate integral equation is derived, and the integrals for the scattered and transmitted fields are given. The simpler problem of scattering of scalar waves is developed first. Formulas for the scattering of monochromatic fields are also given in the scalar and electromagnetic cases when transmitted fields do not vanish.     

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.     

Sommerfeld and Zenneck wave propagation for a finitely conductingone-dimensional rough surface

Starting with Zenneck and Sommerfeld wave propagation over a flat finitely conducting surface has been extensively studied by Wait (see IEEE Antennas Propagat. Mag., vol.40, p.7-24, 1998) and many other authors. We examine propagation over a finitely conducting rough surface, also studied by many people including Feinberg (1944), Bass and Fuks (1979), and Barrick (see Radio Sci., vol.6, p.517-26, and vol.6., p.527-33). This paper extends the multiple scattering theories based on Dyson and Bethe-Salpeter equations and their smoothing approximations. The theory developed here applies to rough surfaces with small root-mean-square (RMS) heights (σ<0.1λ). We limit ourselves to the one-dimensional (1-D) rough surface with finite conductivity excited by a magnetic line source, which is equivalent to the Sommerfeld dipole problem in two dimensions (x-z plane). With the presence of finite roughness, the total field decomposes into the coherent field and the incoherent field. The coherent (average) field is obtained by using Dyson's equation, a fundamental integral equation based on the modified perturbation method. Once the coherent field has been obtained, we determine the Sommerfeld pole, the effective surface impedance, and the Zenneck wave for rough surfaces of small RMS heights. The coherent field is written in terms of the Fourier transform, which is equivalent to the Sommerfeld integral. Numerical examples of the attenuation function are compared to Monte Carlo simulations and are shown to contrast the flat and rough surface cases. Next, we obtain the general expression for the incoherent mutual coherence functions and scattering cross section for rough conducting surfaces     

Electromagnetic scattering from conducting circular cylinders inthe presence of a stratified anisotropic medium-TM case

Scattering by a conducting circular cylinder in the presence of a stratified ferrite medium is investigated analytically using a combined Green's function (G-function) and integral equation approach. The incident plane wave is polarized along the axis of the cylinder. The bias DC magnetic field is in the same direction. The G-function of the structure is developed by well-known techniques of matrix analysis, and the appropriate integral equation for the electric field is derived on the basis of the modified reciprocity theorem. Its solution is followed by numerical results presented in graphical form for both the current density induced on the scatterer's surface and the scattered far field. The possibility of controlling the scattering properties of the structure by varying the degree of anisotropy is also investigated. The main conclusion is that anisotropic materials can be used to control antenna radiation characteristics     

应用切比雪夫逼近快速求解目标宽带雷达散射截面

将切比雪夫逼近理论应用于目标宽带电磁散射特性分析中,通过求解给定频带内的切比雪夫节点和节点处的目标表面电流,实现了频带内任意频率点表面电流的快速预测,从而实现目标宽带雷达散射截面的快速计算.组合场积分方程的使用消除了内谐振问题.将计算结果与传统矩量法逐点计算的结果进行了比较,结果表明在不影响精度的前提下,该方法的计算效率大大提高.     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique     

On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Green's function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Green's function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.     

Determination of lines of constant phase in the near-field of ametallic cube and an airplane

A method is presented which enables one to calculate the scattered field very close to the surface of a perfectly conducting body as well as at the surface itself. The method is based on the representation of the scattered field by an integral over the surface current distribution. The integrand is treated by identity transformations that the singular terms can be integrated analytically, while the remaining nonsingular terms are integrated numerically. The surface current distribution is determined by the magnetic field integral equation. The theory is validated by experiments with the scattered field of a metallic cube with an edge length of a wavelength. The current distribution and the normal as well as the tangential electric field at the surface of the cube are measured by small probes, and the results are compared to those of the theory. The theoretical results of the current distributions are presented as gray value graphics-those of the near-field distribution of a cube and an airplane with the help of lines of constant phase     

二维分形粗糙面电磁散射的分形规律研究

采用二维归一化带限Brown分形函数来模拟二维分形粗糙面,利用基尔霍夫近似给出了该粗糙面的电磁散射场和散射强度方差的计算公式,主要讨论了散射场分布与分维的关系,获得了散射场波峰拟合线的斜率与分维D满足线性关系这一重要规律。