Quantifying Specular Approximations for Angular Scattering from Perfectly Conducting Random Rough Surfaces

Abstract

Angular scattering predictions for perfectly conducting random rough surfaces are obtained from rigorous electromagnetic scattering solutions and quantitatively compared with predictions from approximate specular solutions. The theoretical formulation of the electromagnetic scattering solution based on the extinction theorem and the Fresnel and Kirchhoff approximations are presented. One-dimensional random rough surface profiles are generated for a broad range of correlation lengths, rms roughness, wavelengths, and incident angles, including grazing incident angles and surfaces which exhibit significant forward and backscattering. An angular criterion, based on a finite angular region surrounding the specular direction, is used to evaluate the accuracy of the approximations. Surface parameter domains for accurate scattering predictions by the Fresnel and Kirchhoff approximations are evaluated on an angular basis. The regions of validity of both approximations are quantified and these regions are beyond those previously reported.