The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.

Electromagnetic scattering by surfaces of arbitrary shape

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

When time-domain electromagnetic-field equations are solved using finite-difference techniques in unbounded space, there must be a method limiting the domain in which the field is computed. This is achieved by truncating the mesh and using absorbing boundary conditions at its artificial boundaries to simulate the unbounded surroundings. This paper presents highly absorbing boundary conditions for electromagnetic-field equations that can be used for both two-and three-dimensional configurations. Numerical results are given that clearly exhibit the accuracy and limits of applicability of highly absorbing boundary conditions. A simplified, but equally accurate, absorbing condition is derived for two- dimensional time-domain electromagnetic-field problems.

Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations

An approach has been developed that involves the fit of a combination of three simple scattering mechanisms to polarimetric SAR observations. The mechanisms are canopy scatter from a cloud of randomly oriented dipoles, evenor double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants and Bragg scatter from a moderately rough surface. This composite scattering model is used to describe the polarimetric backscatter from naturally occurring scatterers. The model is shown to describe the behavior of polarimetric backscatter from tropical rain forests quite well by applying it to data from NASA/Jet Propulsion Laboratory's (JPLs) airborne polarimetric synthetic aperture radar (AIRSAR) system. The model fit allows clear discrimination between flooded and nonflooded forest and between forested and deforested areas, for example. The model is also shown to be usable as a predictive tool to estimate the effects of forest inundation and disturbance on the fully polarimetric radar signature. An advantage of this model fit approach is that the scattering contributions from the three basic scattering mechanisms can be estimated for clusters of pixels in polarimetric SAR images. Furthermore, it is shown that the contributions of the three scattering mechanisms to the HH, HV, and VV backscatter can be calculated from the model fit. Finally, this model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem.

A three-component scattering model for polarimetric SAR data

: The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes Such shapes are important in their own right and as a basis for synthesizing the radiation and scattering properties of more complex configurations Each shape is treated in a separate chapter whose contents are presented in stylized format for easy reference Emphasis is placed on results in the form of formulae and diagrams Although no detailed derivation are included, an outline of methods in scattering theory is given in the Introduction

Electromagnetic and acoustic scattering by simple shapes

Non-metallic materials and composites are now commonplace in modern vehicle construction, and the need to compute scattering and other electromagnetic phenomena in the presence of material structures has led to the development of new simulation techniques. This book describes a variety of methods for the approximate simulation of material surfaces, and provides the first comprehensive treatment of boundary conditions in electromagnetics. The genesis and properties of impedance, resistive sheet, conductive sheet, generalised (or higher order) and absorbing (or non-reflecting) boundary conditions are discussed. Applications to diffraction by numerous canonical geometries and impedance (coated) structures are presented, and accuracy and uniqueness issues are also addressed, high frequency techniques such as the physical and geometrical theories of diffraction are introduced, and more than130 figures illustrate the results, many of which have not appeared previously in the literature. Written by two of the authorities m the field, this
graduate-level text should be of interest to all scientists and engineers concerned with the analytical and numerical solution of electromagnetic problems.

Approximate boundary conditions in electromagnetics

It is shown how the exact electromagnetic boundary conditions at the surface of a material of large refractive index can be approximated to yield the usual impedance or Leontovich boundary conditions. These conditions relate the tangential components of the electric and magnetic fields (or the normal components and their normal derivatives) via a surface impedance which is a function only of the electromagnetic properties of the material. They are valid for surfaces whose radii of curvature are large compared with the penetration depth, and also for materials which are not homogeneous but whose properties vary slowly from point to point. As the refractive index (or conductivity) increases to infinity, the conditions go over uniformly to the conditions for perfect conductivity.

Impedance boundary conditions for imperfectly conducting surfaces

By using a computer program, the authors intend to compute quantities specifying the low frequency scattering behavior of rotationally symmetric bodies which are metallic (electromagnetic scattering), soft, or hard (acoustic scattering)

http://ieeexplore.ieee.org/iel6/8/25516/01140429.pdf

Rayleigh scattering

This paper examines the statistical behavior of the phase difference AO between the HH-polarized and VV-polarized backscattered signals recorded by an L-band SAR over an agricultural test site in Illinois. Polarization-phase difference (??) distributions were generated for about 200 agricultural fields for which ground information had been acquired in conjunction with the SAR mission. For the over-whelming majority of cases, the AX distribution is symmetrical and has a single major lobe centered at the mean value of the disstribution ?? Whereas the mean AX was found to be close to zero degrees for bare soil, cut vegetation, alfalfa, soybeans, and clover, a different pattern was observed for the corn fields; the mean ?? increased with increasing incidence angle 0 from about zero at 0 = 150 (near-range of the image) to about 140° at 0 = 35°. The explanation proposed for this variation is that the corn canopy, most of whose mass is contained in its vertical stalks, acts like a uniaxial crystal characterized by different velocities of propogation for waves with horizontal and vertical polarization. Thus, it is hypothesized that the observed backscatter is contributed by a combination of propagation delay, forward scatter by the soil surface, and specular bistatic reflection by the stalks. Model calculations based on this assumption were found to be in general agreement with the phase observations.

Thomas B. A. Senior

Papers

Electromagnetic and acoustic scattering by simple shapes

Approximate boundary conditions in electromagnetics

Impedance boundary conditions for imperfectly conducting surfaces

Rayleigh scattering

Relating Polaization Phase Difference of SAR Signals to Scene Properties