Parallel analysis of electromagnetic scattering from random rough surfaces

An efficient approach for simulation of random rough surface scattering is developed based on using a single integral equation formulation and a multilevel sparse-matrix canonical-grid method. Merits of the scheme are demonstrated using two wind-driven ocean surfaces, one which is very rough and the other large in size.     

On the universal behavior of scattering from a rough surface forsmall grazing angles

It is shown that for scattering from a plane of an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behavior. If the angle of incidence is fixed (in general, it should not be small), the diffuse component of the scattering cross section for the Dirichlet problem is proportional to &thetas;² where &thetas; is the (small) angle of elevation and for the Neumann problem it does not depend on &thetas;. For the backscattering case, these dependencies correspondingly become &thetas;⁴ and &thetas;⁰. The result is obtained from the structure of the equations that determine the scattering problem rather than the use of an approximation     

Application of stochastic second-degree method to electromagnetic scattering from randomly rough surfaces

Application of a stochastic second-degree method in combination with the banded matrix canonical grid (BMIA/CAG) method for two- dimensional electromagnetic scattering from PEC randomly rough surfaces is presented. This method can improve convergence while preserving the computational attractiveness of the BMIA/CAG method. Numerical examples illustrate the effectiveness of the proposed method.     

Monte Carlo simulation of electromagnetic scattering fromtwo-dimensional random rough surfaces

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory     

Bistatic scattering from three-dimensional layered rough surfaces

An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths.     

Bistatic specular scattering from rough dielectric surfaces

An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks<0.2 (where k=2π/λ and s is the RMS surface height) and for three rough surfaces with ks=0.5, 1.39, and 1.94, included observations over the range of incidence angles from 20° to 65° for both horizontal and vertical polarizations. For the coherent component, the reflectivity was found to behave in accordance with the prediction of the physical optics model, although it was observed that the Brewster angle exhibited a small negative shift with increasing roughness. The first-order solution of physical optics also provided good agreement with observations for hh-polarized incoherent scattering coefficient, but it failed to predict the behavior of the vv-polarized scattering coefficient in the angular range around the Brewster angle. A second-order solution is proposed which appears to partially address the deficiency of the physical optics model     

Wavelet-based simulations of electromagnetic scattering fromlarge-scale two-dimensional perfectly conducting random rough surfaces

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed     

Channeling phenomenon in electromagnetic forward scattering at low grazing

Channeling phenomenon is a type of forward scattering and multipath that occasionally occurs when a well-formed sea wave briefly reflects or focuses the out-of-plane energy toward the receiver, yielding a higher than expected, broadband power gain. A series of X-band, forward-scattering measurements in a large wave tank observed multiple channeling events at low grazing angles. The wave tank simulated a one-dimensional, 1/10th-scale Pierson-Moskowitz surface at sea states 0, 3, and 5. During the measurements, channeling events were observed under crosswind wave conditions when a properly constructed wave trough, coinciding with the radar's line of sight, channeled or focused the out-of-plane, forward-scattered energy toward the receiver. Presented is a summary of the channeling events observed and a physical model of the channeling phenomenon based on experimental observations and numerical simulations.     

Preconditioned iterative solution of scattering from rough surfaces

Extensions to the functionally identical forward-backward (FB) and method of ordered multiple interactions iterative techniques have been introduced that improve the convergence characteristics with specific scattering geometries. These extensions are shown to be mathematically equivalent to applying preconditioners to the discretized integral equation that is iteratively solved. The same preconditioners can be used with any iterative solution technique. Numerical examples show that the generalized minimal residual (GMRES) and bi-conjugate gradient-stable (BICGSTAB) algorithms give similarly rapid convergence when applied to a preconditioned discretized integral equation     

Forward-backward method for scattering from dielectric rough surfaces

The iterative forward-backward (FB) method is a recently proposed efficient technique for numerical evaluation of scattering from perfectly conducting rough surfaces. Extension of the method to include scattering from imperfect conducting surfaces, with a high imaginary part of the complex dielectric constant, has also been proposed. The FB method is further generalized to analyze scattering from dielectric rough surfaces with arbitrary complex dielectric constant. Electric and magnetic equivalent surface currents are split into forward and backward components and equations governing these current components are obtained. As a solution, an iterative scheme is proposed and its convergence rate is analyzed. Finally, the effectiveness of the method is assessed by comparing the obtained scattering results with "exact" ones, computed by employing the usual method of moments (MoM).     

A new theory for scattering of electromagnetic waves fromconducting or dielectric rough surfaces

The problem of electromagnetic scattering from a conducting or dielectric rough surface with arbitrary shape is studied. An exact solution, using a differential method, is provided for a plane wave with one-dimensional irregularity of the interface. The problem is reduced to the resolution of a linear system of partial differential equations with constant coefficients, and to the computation of eigenvalues and eigenvectors of a truncated infinite matrix. Numerical application is made to show the angular distribution of energy density in the case of an arbitrary profile of the scattering surface and its evolution when the nonperiodic profile tends to become periodic. The near field is computed on the interface and its enhancement in the illuminated region is observed. It increases with the height of the irregularity and with the frequency     

New results on coherent scattering from randomly rough conducting surfaces

An approximate solution for the average field scattered by a perfectly conducting randomly rough surface having a correlation length much smaller than the electromagnetic wavelength is presented. The analysis is based on the use of a substitute surface which gives rise to the same describing equations as the true surface relative to the average scattered field. The substitute surface comprises large nonoverlapping fiat areas having random elevations with respect to the mean planar surface and arbitrary correlation between adjacent areas. The average scattered field is shown to depend upon the number of interacting areas and the surface roughness. For a given range of surface roughness there is a specific number of interacting areas which dominate the average scattered field. It is demonstrated how this number can be computed and how a continuous curve of average scattered field as a function of surface roughness is obtained. Of particular importance is the quantitative correspondence established in this paper between the surface roughness and the degree of multiple interaction on the rough surface.     

大粗糙度表面激光散射特性实验研究

本文利用激光散射自动测量系统,对经喷丸处理后的钢基粗糙表面及其喷漆表面的后向激光雷达散射截面(LRCS)进行了测量。测量波长分别为λ=633nm和λ=904nm.在λ=904nm,利用粗糙面电磁散射理论的基尔霍夫方法对上述样片进行了理论计算,其中将粗糙表面视为双尺度模型,根据驻留相位法和标量近似法理论计算双尺度模型随机粗糙表面的散射强度角分布,其理论值与实验测量结果有较好的吻合。     

粗糙平面的激光散射特性研究

为了检测目标的边缘信息,采用激光扫描目标表面、通过回波信号变化来得到目标的边缘信息的方法,利用随机面元模型,分析了刚性随机粗糙平面的激光散射特点,建立了实用化的随机粗糙平面激光散射理论模型,并给出了正入射时几种情况下的激光散射图像,分析了平面目标的激光散射能量计算方法,仿真了光束在平面目标表面做正弦摆动时,光斑在不同位置的反射能量,利用激光信号的强度变化,采用峰(谷)检出法或者过零检出法就可以得到物体的边缘信息。结果表明,通过回波信号的变化,可以得到目标的边缘轮廓。     

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。     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

Analysis of scattering from rough surfaces at large incidenceangles using a periodic-surface moment method

The moment method is used to calculate electromagnetic backscattering from one-dimensionally rough surfaces at near-grazing incidence (angles of incidence up to 89°). A periodic representation of the scattering surface is used to prevent edge effects in the calculated scattering without the use of an artificial illumination weighting function. A set of universal series common to all elements of the moment interaction matrix are derived that allow the efficient application of the moment method to the periodic surface. Comparison with other moment method implementations demonstrates the efficiency of this approach. The scattering from surfaces with Gaussian roughness spectra is calculated at both horizontal and vertical polarizations, and the results are compared with the theoretical predictions of the small-perturbation method (SPM) and Kirchhoff approximation (KA). SPM shows the expected loss of accuracy in predicting the vertically polarized backscattering from small-roughness, short-correlation-length surfaces at large incidence angles. SPM accurately predicts the backscattering from the same type of surface at incidence up to 89° at horizontal polarization, KA provides accurate estimates of the scattering from long correlation-length surfaces as long as the incidence angle is small enough that surface self-shadowing does not occur. When shadowing occurs, KA severely underpredicts vertically polarized backscattering and less severely overpredicts backscattering at horizontal polarization     

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