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.     

分形随机粗糙表面的电磁散射研究

本文利用数值方法研究分形随机粗糙表面的电磁散射问题。 应用矩量法研究分形随机粗糙表面的电磁散射可以使我们获得较为精确的数值结果。但是,对于表面散射,应用矩量法时,表面未知变量的数目非常大,即使对于一维表面也需要几千个未知变量。当我们求解矩阵方程时,计算机对求解的问题有几个限制,一个是内存的限制,一个是速度的限制。为了克服内存的限制,发展了许多迭代数值算法。本文发展了一种新的数值迭代方法.利用这一方法,我们对分形随机粗糙表面的电磁散射问题进行了研究, 并与矩阵反演方法进行了比较.所得结果表明,这种新的迭代法具有很好的收敛性。     

The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory

Theoretical analyses of the scattering of the electromagnetic waves from rough surfaces have progressed using basically the Kirchhoff approach (KA) and the small perturbation method (SPM) of Rice. It is demonstrated that the latter method (SPM) is actually a special case of the former (KA). Reasons why SPM agrees with experimental data near grazing angle are given and arguments are made for the invalidity of the SPM second-order depolarized term.     

高阶基尔霍夫法求解导体粗糙表面的散射特性

在分析粗糙表面电磁散射特性的基础上,提出了一种考虑粗糙表面协方差函数Taylor展开的高阶基尔霍夫近似(KA)法,解决了经典KA近似的大逼近误差问题.应用9阶高度的KA和传统的KA,对比研究了不同照射频率和均方根高度下的后向散射系数,并比较了遮挡函数的修正效应.同时应用高、低阶KA计算了典型粗糙面的后向散射系数,并分别与测量值和矩量法的数值解进行了比较.结果表明,9阶表面高度展开的切平面KA不仅拓宽了KA的适用条件,还具有更高的精度范围,从而证明了高阶均方根高度展开的KA近似的有效性.     

An approach to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling

A new method to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling is derived. It can be utilized in conjunction with the concept of ray launching. Similar to the Kirchoff formulations, the approach is based on a tangential plane approximation, i.e., it is applicable to surfaces with gentle undulations, whose horizontal dimensions are large compared to the incident wavelength. However, in contrast to the Kirchoff models, which are only valid for either slightly rough or very rough surfaces, the proposed stochastic scattering approach includes both the coherent and incoherent components at the same time. The purely deterministic ray-based modeling is expanded by a "stochastic" component, allowing, for the first time, to account for nondeterministic scattering in ray-optical wave propagation modeling.     

A note on the scattering from a slightly rough surface

A Fourier transform approach is used to derive the bistatic radar scattering cross section of a slightly rough perfectly conducting infinite surface. A perturbation expansion is used to apply the boundary conditions, and the scattered fields are asympotically evaluated by means of the method of stationary phase. The resultant expression for the radar cross sectionsigma^{0}is shown to agree with that obtained using the method as outlined by Rice.     

小波变换在指数粗糙表面电磁散射中的应用

研究了小波变换在指数粗糙表面电磁散射中的应用.在用矩量法研究电磁散射问题时,基函数的选择是一个非常重要的步骤.不同的基函数对问题的求解规模影响很大.利用小波变换中二尺度方程关系,通过对大尺度基函数和小波基函数求解相应的矩阵方程,然后由小尺度基函数与大尺度基函数以及小波基函数的关系,求出对应于小尺度基函数的矩量法解.该方法的优点是减少了矩阵方程求解的规模.     

A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces

An exact alternative approach to the diagrammatic technique for treating scattering from rough surfaces is developed. The magnetic field integral equation for the current induced on the rough perfectly conducting surface is multiplied by a Fourier kernel involving all orders of surface height derivatives and their associated transform variables. Averages of this weighted equation are converted to convolations in the transform domain. The result of this operation is a singular integral equation of the first kind of infinite dimensions (because of the infinite number of height derivatives) for the stochastic Fourier transform of the current. A procedure is developed for estimating the effects of ignoring one or more surface height derivatives in terms of the range of validity of the resulting approximate solution. Special limiting cases of very gently undulating surfaces and uniformly rough surfaces are examined. New and illuminating results are obtained for the latter case.     

A study of scattering from an object below a rough surface

A numerical model is applied in a Monte Carlo study of scattering from a three dimensional penetrable object below a lossy dielectric rough interface. Both time and frequency domain results are investigated to illustrate the relative importance of coherent and incoherent scattering effects in the sample problem considered. Results show that introducing a reduced transmission coefficient is reasonable for object coherent scattering predictions in this example, and that incoherent object/surface interaction effects approximately follow a simple scaling behavior as surface roughness is increased.     

A heuristic algorithm for the bistatic radar cross section forrandom rough surface scattering

Examines a heuristic algorithm which guarantees reciprocity in the cross-section equations when the phase perturbation approximation is used. The results obtained using a Gaussian surface roughness spectrum are superior to those of either the phase perturbation or the reversed phase perturbation method and agree well with the exact results obtained using a Monte Carlo integral equation technique     

A numerical study of scattering from an object above a rough surface

A numerical model is applied in a Monte Carlo study of scattering from a three-dimensional penetrable object above a lossy dielectric rough interface. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. Both time-and frequency-domain results are investigated to illustrate the relative importance of coherent and incoherent scattering effects in the sample problem considered. Results show that a four-path model using a reduced-reflection coefficient can be reasonable for coherent scattering predictions and that incoherent object/surface interaction effects can make significant contributions to received cross sections.     

Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory

It is shown that the small amplitude limit of the mean backscatter cross section for a perfectly conducting random rough surface calculated from the first two terms in the iterative series solution of the surface current integral equation gives the same results as the small perturbation method. This demonstration resolves a long-standing controversy in rough surface scattering theory.     

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.     

Banded matrix iterative approach to Monte-Carlo simulations of scattering of waves by large-scale random rough surface problems: TM case

A banded matrix iterative approach is applied to study the scattering of a TM incident wave from a perfectly conducting one-dimensional random rough surface. It is accurate and is much faster than the full matrix inversion approach or the conjugate gradient method. Applications of this method to large-scale rough surface problems are illustrated.<>     

A surface integral equation approach to the scattering andabsorption of doubly periodic lossy structures

The scattering and absorption of a doubly periodic array of absorbers, either placed in free space, backed by a perfect conductor or by a half-infinite space with the same material properties as the elements forming the array, is analyzed with a surface integral equation approach (SIE). The use of a suitable periodic Green's function as kernel of the SIE reduces the formulation of the problem to a single absorber. A set of equivalent electric and magnetic currents on the surface of the absorber is discretised using Glisson functions and the SIE is solved with Galerkin's method. The validity and flexibility of the SIE approach is exemplified by comparing numerical results with measurement data for a family of commercially available absorbers     

Numerical simulation of scattering from rough surfaces: awavelet-based approach

In this paper, a preliminary study is carried out to demonstrate the application of wavelets for improving the computation time and reducing computational memory required for evaluating the statistics of the scattered field from rough surfaces using the method of moments (MoM) in conjunction with a Monte Carlo simulation. In specific, Haar and the first order B-spline wavelet basis functions are applied to the MoM formulation of one-dimensional rough surfaces in order to compare the computation time and sparsity for wavelets in the same family but of higher order. Since the scattering coefficient (the second moment of the backscatter field per unit area) is a gentle function of the surface parameters and the radar attributes, it is demonstrated that a relatively high thresholding level can be applied to the impedance matrix, which leads to a sparser impedance matrix and faster computation time. It is also shown that applying a high threshold level the coefficients of the high-order wavelets would increase out of proportion, however, the effect of these current components averages out when computing the scattering coefficients. The resulting sparse impedance matrices are solved efficiently using fast search routines such as the conjugate gradient method. A systematic study is carried out to investigate the effect of different threshold levels on the accuracy versus computing speed criterion. The computed scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solutions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time     

The dependence of rough surface scattering on surface height statistics and correlation function

Relationships between the statistical properties of a rough surface and the diffuse surface scattering are investigated. For a physical optics model, we consider the roughness dependence of the angular distribution of the diffuse scattering as a function of surface height statistics and form of the correlation function. This includes examining the characteristics of the diffuse scattering from a surface with heights that are still statistically dependent when decorrelated. Finally, we analyze the effect of correlation function on the scattering when the roughness is in the perturbation regime.     

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.     

A new unified full wave approach to evaluate the scatter crosssections of composite random rough surfaces

A new unified approach, based on the original full wave solutions, is presented to evaluate the like and cross polarized scattering cross sections of composite (multiple scale) random rough surfaces. The rough surfaces are assumed to be characterized by the Pieson-Moskowitz spectral density function. To account for the surface undulations, the incoherent radar cross sections are obtained by regarding the composite rough surface as an ensemble of pixels of arbitrary orientation