Scattering from dielectric structures above impedance surfaces andresistive sheets

Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods     

Electromagnetic Scattering From Multilayer Rough Surfaces With Arbitrary Dielectric Profiles for Remote Sensing of Subsurface Soil Moisture

Radar remote sensing of soil moisture content at low frequencies requires an accurate scattering model of realistic soils, which often involves multilayer rough surfaces and dielectric profiles. In this paper, a hybrid analytical/numerical solution to two-dimensional scattering from multilayer rough surfaces separated by arbitrary dielectric profiles based on the extended boundary condition method (EBCM) and scattering matrix technique is presented. The reflection and transmission matrices of rough interfaces are constructed using EBCM. The dielectric profiles are modeled as stacks of piecewise homogeneous dielectric thin layers, whose scattering matrices are computed by recursively cascading reflection and transmission matrices of individual dielectric interfaces. The interactions between the rough interfaces and stratified dielectric profiles are taken into account by applying the generalized scattering matrix technique. The scattering coefficients are obtained by combining the powers computed from the resulting Floquet modes of the overall system. The bistatic scattering coefficients are validated against existing analytical and numerical solutions. Field-collected soil moisture data are then used for numerical simulations to investigate the penetration capability at different frequencies and to address the potential of low-frequency radar systems in estimating deep soil moisture. In particular, soil moisture profiles during dry ground, wet ground, and wet subsurface layer conditions are examined. The results show that both backscattering coefficients and copolarized phase difference at low frequencies are sensitive to the roughness of subsurface interfaces and deep soil moisture. Also, much larger depth sensitivity can be achieved using copolarized phase difference than scattering coefficients     

Scattering from natural soils modeled by dielectric fractal profiles: the forward-backward approach

The forward-backward (FB) method is an efficient technique for numerical evaluation of electromagnetic scattering from rough surfaces. In its usual formulation, this technique can be only applied to perfectly or highly conducting surfaces. In addition, up to now FB has been employed to compute scattering from surfaces modeled by Gaussian stochastic processes with Gaussian or Pierson-Moscowitz spectra. Accordingly, this technique can be fruitfully used for numerical simulations of scattering from sea surfaces. However, in order to properly deal with natural soil surfaces, extension to the dielectric interface case and to fractal surface models is needed. Extension of the FB method to the dielectric interface case has been recently presented, whereas application to fractal surface models is presented here. Original contribution of the present paper is twofold. First of all, the FB method for dielectric profiles is framed within the theory of iterative methods for the solution of linear systems. In addition, application of the FB method to dielectric band-limited fractional Brownian motion fractal one-dimensional surfaces is explored. Numerical experiments show that, for most of realistic values of dielectric constant and fractal parameters actually encountered for natural soil profiles, the FB method is very rapidly convergent, and its results are in perfect agreement with "exact" ones (i.e. with results of method of moments solved via a direct method).     

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 interaction between a dielectriccylinder and a slightly rough surface

An electromagnetic scattering solution for the interaction between a dielectric cylinder and a slightly rough surface is presented in this paper. Taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary scattered fields from the composite target reduces to the evaluation of integrals involving the scattered fields from the cylinder and polarization currents of the rough surface induced by a plane wave. Basically, only the current distribution of isolated scatterers are needed to evaluate the interaction in the far-field region. The scattered field from the cylinder is evaluated in the near-field region using a stationary phase approximation along the cylinder axis. Also, the expressions for the polarization current induced within the top rough layer of the rough surface derived from the iterative solution of an integral equation are employed in this paper. A sensitivity analysis is performed for determining the dependency of the scattering interaction on the target parameters such as surface root mean square (RMS) height, dielectric constant, cylinder diameter, and length. It is shown that for nearly vertical cylinders, which is of interest for modeling of vegetation, the cross-polarized backscatter is mainly dominated by the scattering interaction between the cylinder and the rough surface. The accuracy of the theoretical formulation is verified by conducting polarimetric backscatter measurements from a lossy dielectric cylinder above a slightly rough surface. Excellent agreement between the theoretical prediction and experimental results is obtained     

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 combined steepest descent-fast multipole algorithm for the fastanalysis of three-dimensional scattering by rough surfaces

A new technique, the steepest descent-fast multipole method (SDFMM), is developed to efficiently analyze scattering from perfectly conducting random rough surfaces. Unlike other prevailing methods, this algorithm has linear computational complexity and memory requirements, making it a suitable candidate for analyzing scattering from large rough surfaces as well as for carrying out Monte Carlo simulations. The method exploits the quasiplanar nature of rough surfaces to efficiently evaluate the dyadic Green's function for multiple source and observation points. This is achieved through a combination of a Sommerfeld steepest descent integral and a multilevel fast multipole-like algorithm based on inhomogeneous plane wave expansions. The fast evaluation of the dyadic Green's function dramatically speeds up the iterative solution of the integral equation for rough surface scattering. Several numerical examples are presented to demonstrate the efficacy and accuracy of the method in analyzing scattering from extremely large finite rough surfaces     

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     

Radar images of rough surface scattering: comparison of numericaland analytical models

Rough surface scattering theories are investigated through analysis of radar images. Backscatter results from 10 GHz to 14 GHz under tapered wave illumination are considered for one-dimension (1D) random rough surface realizations which satisfy an impedance boundary condition. Back-projection tomography is applied to form two-dimensional (2D) synthetic aperture radar images from deterministic surface scattered field data at multiple incidence angles and frequencies. Numerical predictions of surface backscattered fields are obtained from an accelerated forward-backward (FB) method and the resulting images are compared with those obtained from approximate scattering theories such as the physical optics (PO) approximation, the small slope approximation (SSA), and the nonlocal SSA (NLSSA). The resulting radar images illustrate scattering sources associated with single and multiple scattering on the boundary, and a ray tracing analysis confirms the locations of time-delayed image points due to double reflections. For single scattering effects, the images demonstrate excellent agreement between analytical and numerical methods in both horizontal and vertical polarizations. For surfaces with RMS height 2.0 cm and correlation length 7.5 cm at normal incidence, multiple-scattering effects are observed and successfully captured when the lowest-order NLSSA is employed     

Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface

An analytical solution is presented for the electromagnetic scattering from a dielectric circular cylinder embedded in a dielectric half-space with a slightly rough interface. The solution utilizes the spectral (plane-wave) representation of the fields and accounts for all the multiple interactions between the rough interface and the. buried cylinder. First-order coefficients from the small perturbation method are used for computation of the scattered fields from the rough surface. The derivation includes both TM and TE polarizations and can be easily extended for other cylindrical buried objects (e.g., cylindrical shell, metallic cylinder). Several scattering scenarios are examined utilizing the new solution for a dielectric cylinder beneath a flat, sinusoidal, and arbitrary rough surface profile. Results indicate that the scattering pattern of a buried object below a slightly rough surface differs from the flat surface case only when the surface roughness spectrum contains a limited range of spatial frequencies. Furthermore, the illuminated area of the incident wave is seen to be a critical factor in the visibility of a buried object below a rough surface.     

TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

Rigorous formulation of scattering at a randomly varying impedanceplane: general case of oblique incidence

The problem of scattering of electromagnetic plane waves at one-dimensional surfaces (random gratings) is solved in the general case in which the incident wave vector does not lie on the main section of the cylindrical surface (oblique incidence). The scatterer is simulated by a plane boundary characterized by a coordinate-dependent impedance that varies along one of the two coordinates on the surface. This representation could be regarded as a canonical model of one-dimensional surfaces with height corrugations. A rigorous electromagnetic formalism for calculating the fields scattered at the impedance plane is presented. The fields above the scatterer are represented by spectral domain expansions. It is shown that the wave vectors of the scattered waves lie on the surface of a cone containing the direction of specular reflection and whose axis coincides with the direction of the grooves of the random grating. The theory is exemplified by calculating the angular distribution of the mean intensity scattered from an ensemble of surfaces with similar statistical parameters     

Mueller matrix elements that characterize scattering from coatedrandom rough surfaces

The Mueller matrix completely characterizes scattered electromagnetic waves. It relates the incident to the scattered Stokes vectors. The Mueller matrix, which contains intensity and relative phase data, is very useful for remote sensing. The Mueller matrix characterizing scattering from coated two-dimensional (2-D) random rough surfaces is obtained from full-wave solutions for the scattered fields considered in the companion paper. The general bistatic scattering case is considered in the analysis. However, for the numerical simulations presented here, the backscatter case is considered in particular, since backscatter is usually measured in remote sensing. The uniformly coated 2-D random rough surfaces are assumed here to be homogeneous and isotropic, with a Gaussian surface-height joint probability-density function. The diffuse incoherent and coherent contributions to the Mueller matrix elements are evaluated. The computer simulations of realistic models of relevant physical problems related to remote sensing of irregular stratified media can be used to determine the optimum modes of detection involving the selection of polarization, frequency, backscatter angle, and the specific Mueller matrix elements most sensitive to changes in medium parameters     

Electromagnetic scattering from a dielectric coated cylinder using OSRC-GMT

The electromagnetic scattering from a dielectric coated cylinder is analysed based on the generalised multipole technique (GMT) combined with the on-surface radiation condition (OSRC) for separating an open region of inhomogeneous media into the inside region of the homogeneous medium and the outside region of free space. The equivalent multipole sources inside which produce the outside scattered fields, are determined by the OSRC on the outer surface. Some numerical examples for calculating the RCS from the scatterer with concentrically circular or confocally elliptic cross-section are provided.<>     

Monte Carlo simulations of large-scale one-dimensional randomrough-surface scattering at near-grazing incidence: Penetrable case

Scattering from dielectric one-dimensional (1-D) random rough surfaces at near grazing incidence is studied for both TE and TM cases. To obtain accurate results at incidence angles of 80°-85°, we use long surface lengths of up to 1000 wavelengths. Numerical results are illustrated for dielectric surfaces corresponding to soil surfaces with various moisture contents. Results indicate that TM backscattering is much larger than that of TE backscattering. The ratio of TM to TE backscattering increases as a function of soil moisture and can be used as an indicator of soil moisture in remote sensing applications. However, the ratio of TM to TE backscattering is much lower than that predicted by the small perturbation method. To facilitate computation of scattering by such long surfaces, the previously developed banded-matrix iteration approach/canonical grid method (BMIA/CG) has been extended to dielectric surfaces. The numerical algorithm consists of translating the nonnear-field interaction to a flat surface and the interaction subsequently calculated by fast Fourier transform (FFT)     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

Depolarization of EM waves by slightly rough surfaces

Depolarization is obtained for the scattering of electromagnetic waves from a slightly rough surface using Rice's theory. In the plane of incidence, depolarization is a second-order effect. The results are applied to backscattering from a slightly rough sea using the Neumann spectrum for a fully developed sea. The expression for the depolarized scattered power is of the form obtained in multiple scattering investigations. Therefore, it can be inferred that depolarization from slightly rough surfaces is due to multiple scattering. For the sea, depolarization increases with wind speed and with the magnitude of the complex dielectric constant of the surface.     

Electromagnetic scattering from a buried cylinder in layered media with rough interfaces

A solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder.     

Studies of the cylinder-ground double bounce scattering mechanismin forest backscatter models

An integration methodology is presented for computing fields backscattered by the cylinder-ground double bounce scattering mechanism, in which randomly tilted, finite length dielectric cylinders stand on a slightly rough lossy surface, Based on the Stratton-Chu integral technique, incorporating exact solutions of fields scattered by the cylinders, the method yields like- and cross-polarized responses and polarization phase differences. Numerical results are reported     

Forward-backward method with spectral acceleration for scattering from Layered rough surfaces

A fast method of moments is presented to calculate electromagnetic wave scattering from layered one-dimensional rough surfaces. The formulation is provided for M stratified homogeneous regions, separated by M-1 rough surfaces, and solved using point matching and pulse basis functions. Compared to the single surface case, the solution of scattering from M-1 surfaces requires significantly more memory and computational time. To facilitate the solution, the forward-backward method with spectral acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. The numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. The accuracy, efficiency, and convergence of the method are then studied for various rough surfaces and layer permittivities.