The Phase Perturbation Technique vs. an Exact Numerical Method for Random Rough Surface Scattering

Abstract

There is a need for a solution to the problem of wave scattering from rough surfaces that is accurate when both the classical field perturbation and Kirchhoff approximations are not. In previous work it was shown numerically that the phase perturbation reflection and backscattering coefficients reduce to those of field perturbation theory and the Kirchhoff approximation in the appropriate limits; however, for cases when the classical solutions did not apply, the accuracy of the phase perturbation results could not be determined. In this paper we examine the validity of the phase perturbation technique for a region in parameter space when the two classical solutions fail. Numerical results for the bistatic scattering cross section are compared with exact numerical results for one-dimensional surfaces having a Gaussian roughness spectrum and satisfying a Dirichlet boundary condition. It is found that in the region considered the phase perturbation results agree with the exact results over all scattered angles, except low grazing angles, for a fixed angle of incidence. Furthermore, in many cases it is found that exchanging incident and scattered angles in the phase perturbation equations gives an alternate phase perturbation solution whose numerical results are in excellent agreement with exact results.