Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensionalscattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction     

Multifrequency reconstruction of moderately rough interfaces viaquasi-ray Gaussian beams

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms of B-splines. The profile estimation problem is posed as a parameter optimization problem, which is solved using a multiresolution continuation method via frequency hopping. Numerical experiments establish that the algorithm is efficient and yields accurate reconstructions throughout most of the illuminated region even in noisy environments, losing accuracy only in regions with very weak illumination     

Short-pulse three-dimensional scattering from moderately rough surfaces: a comparison between narrow-waisted Gaussian beam algorithms and FDTD

In this paper, with reference to short-pulse three-dimensional scattering from moderately rough surfaces, we present a comparison between Gabor-based narrow-waisted Gaussian beam (NW-GB) and finite-difference time-domain (FDTD) algorithms. NW-GB algorithms have recently emerged as an attractive alternative to traditional (ray-optical) high-frequency/short-pulse approximate methods, whereas FDTD algorithms are well-established full-wave tools for electromagnetic wave propagation and scattering. After presentation of relevant background material, results are presented and discussed for realistic parameter configurations, involving dispersive soils and moderately rough surface profiles, of interest in pulsed ground penetrating radar applications. Results indicate a generally satisfying agreement between the two methods, which tends to improve for slightly dispersive soils. Computational aspects are also compared.     

二维粗糙面两束波束散射特性研究

基于Kirchhoff近似,推导两束波束散射强度相关系数的表达式,数值计算漫射强度及散射强度相关系数随角度差、相关长度及粗糙度变化情况。结果表明:散射角对粗糙表面相干散射强度与光滑表面相干散射强度的比值有影响,当两束波束的入射角、方位角均相等,意味着两束波束相互重合且散射强度比值为单波束比值的四倍;当两束波束的入射角、方位角中有一个角度不相等,由散射场干扰效应的影响,相干散射强度比值都会减小。相关长度的变化与漫射强度和散射强度相关系数均成正比;随着入射角度差增大,漫射强度的后向散射效应增强,且散射强度相关系数变小,说明两束波束的干扰越严重;随着散射角的增大,总散射强度受干扰项散射强度影响较大,则后向散射效应增强。     

高斯介质粗糙面电磁散射的小斜率近似方法

基于小斜率近似方法推导了极坐标系下介质粗糙面的双站散射系数和后向散射系数计算公式.为验证小斜率近似方法的准确性,针对二维高斯介质粗糙面,计算了双站散射系数并将得到的数值结果与实验测量数据和基尔霍夫近似方法计算结果进行了对比分析,结果表明:小斜率近似方法的结果和实验数据吻合较好.同时对不同入射角下散射系数的角分布及粗糙度和均方根斜率对散射系数的影响进行了讨论分析.     

Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams

An adaptive framework is presented for ultra-wideband ground penetrating radar imaging of shallow-buried low-contrast dielectric objects in the presence of a moderately rough air-soil interface. The proposed approach works with sparse data and relies on recently developed Gabor-based narrow-waisted quasi-ray Gaussian beam algorithms as fast forward scattering predictive models. First, a nonlinear inverse scattering problem is solved to estimate the unknown coarse-scale roughness profile. This sets the stage for adaptive compensation of clutter-induced distortion in the underground imaging problem, which is linearized via Born approximation and subsequently solved via various pixel-based and object-based techniques. Numerical simulations are presented to assess accuracy, robustness and computational efficiency for various calibrated ranges of problem parameters. The proposed approach has potential applications to antipersonnel land mine remediation.     

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).     

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     

MMW scattering by rough lossy dielectric cylinders and tree trunks

The millimeter-wave (MMW) radar backscatter response of a rough, lossy, dielectric cylinder is examined both analytically and experimentally. Models for both the coherent and incoherent components of the scattered field are developed based on the geometric-optics approximation. The accuracy of the analytical models and their applicability in predicting the backscatter response of tree trunks are determined experimentally by measuring the radar backscatter at 95 GHz from a rough conducting cylinder and from a section of a tree trunk. In both cases, very good agreement was achieved between the model predictions and the measurements     

Scattering of a Gaussian beam by a dielectric rectangular cylinder

For purpose of finding the dielectric constant, a new expression of the beam scattering is obtained by using the boundary element method (BEM) with extended boundary conditions. Comparison between with and without the resonant condition was made for the total scattered power. To find the accuracy, convergence property of the total scattered power versus divided number has been examined. To check the boundary conditions at the corner of the scatter, the electric field difference between inner and outer side has also been calculated and confirmed. The total electric field distributions in space are illustrated for the plane and beam wave. Microwave experiments was also performed     

电介质粗糙表面光散射特性

为了研究电介质随机表面散射特性的物理产生机制,采用基于Kirchhoff近似的Monte-Carlo方法进行了数值计算,得到了一组不同粗糙程度的电介质随机表面在s线偏振光入射时的散射光强度空间分布.所有表面自相关长度相同.结果表明,随均方根高度的增加,散射光强度空间分布呈现峰值衰减、展宽和向后向移动的特征.对这些散射特...     

手征涂覆球对高斯波束的散射

在广义米理论的基础上,通过把入射高斯波束、散射场和内部场用适当的球矢量波函数展开,给出了一种求解手征涂覆球对高斯波束散射的解析方法。待定的展开系数可由从边界条件得到的线性方程组求出。对于波束的区域近似模型,给出了微分散射截面的数值结果。结果表明：与介质涂覆的情况相比,手征涂覆对微分散射截面和散色场的极化特性都产生了较大的影响。     

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     

Electromagnetic scattering by a two-dimensional wedge composed ofconductor and lossless dielectric

Electromagnetic scattering by two-dimensional wedges composed of perfectly conducting and lossless dielectric material is considered. Heuristic geometrical theory of diffraction type diffraction coefficients are presented and a hybrid moment-method/physical-optics technique is developed to verify the accuracy of the proposed diffraction coefficients. The purpose is to show that the heuristic approach can yield acceptably accurate results for a number of composite wedge geometries, rather than to present rigorous diffraction coefficients for the composite wedge per se. Calculated results are presented in which the results obtained by means of the two methods are compared. Very good agreement is achieved for a variety of wedge geometries     

High frequency scattering of a Gaussian beam by a conducting cylinder

When the radius of the cylinder is much larger than the wavelength, an approximate expression for the scattering of a Gaussian beam by a conducting cylinder is obtained by using Watson transformation. The beam fields in shadow region and illuminated region are, respectively, derived from residue theorem and stationary phase method. In order to check the theory, comparisons for scattering pattern and field variation in space were made. Numerical examples of the scattering patterns forw/lambda geqleq a_{0}/lambda gg 1 (w, a_{0} lambdabeing the beamwidth, the radius of cylinder, and the wavelength) are also illustrated.     

Transient scattering from two-dimensional dielectric cylinders ofarbitrary shape

The problem of transient scattering by arbitrarily shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time technique. The dielectric problem is approached via the surface equivalence principle. Two coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution     

A hybrid FEM-based procedure for the scattering from photoniccrystals illuminated by a Gaussian beam

We provide an efficient numerical procedure for evaluating the field scattered by two-dimensional (2-D) photonic crystals when they are illuminated by Gaussian beams. In particular, the incident Gaussian beam is interpreted as a spectrum of both homogeneous and inhomogeneous plane waves. The scattering of each plane wave is analyzed by resorting to a hybrid technique combining the finite-element method (FEM) with a Floquet modal expansion. Moreover, by applying the standard saddle point method, the evaluation of the field at a specific point of the exterior medium is reduced to the contribution of the fundamental Floquet mode of a single plane wave belonging to the incident spectrum, strongly enhancing the numerical efficiency     

三维介质粗糙面上导体目标散射的解析-数值混合算法

推导出二维介质粗糙面与其上三维导体目标复合散射的耦合积分方程,提出目标散射的数值矩量法(Method of Moment,MoM)与粗糙面散射的基尔霍夫解析近似法(Kirchhoff Approximation,KA)相结合的混合迭代算法.理论推导表明:当目标距离粗糙面的高度满足条件时,目标的离散单元在粗糙面上任意一点的散射场满足局部平面波关系,利用粗糙面局部面元的反射和透射关系,得出粗糙面感应场的KA解析计算式.由于粗糙表面的感应场用KA解析计算,只需对目标的感应电流进行一次数值积分,无需数值求解粗糙面的积分方程,节省大量的存储空间和运算时间,能在理论上十分简明、数值计算上十分有效地求解三维体目标与面目标组合的复合散射问题.讨论了目标与粗糙面相互作用的互耦迭代算法的有效性和收敛性.结合Monte-Carlo方法产生随机粗糙面样本,数值分析Gauss介质粗糙面上方的规则导体球或任意不规则六面体的散射,讨论了粗糙面的介电参数和目标几何形状等对双站散射的影响.     

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