Study of the Phase Perturbation Technique for Scattering of Waves by Rough Surfaces at Intermediate and Large Values of the Roughness Parameter

Abstract

The phase perturbation technique is numerically examined in the case of scalar waves scattered by one-dimensional normally distributed random rough surfaces, on which Dirichlet boundary conditions hold. Particular attention is devoted to surfaces for which the Rayleigh parameter has intermediate or large values. It is shown that the considered method is not limited to either small roughness or gentle undulations. It is demonstrated that the phase perturbation technique smoothly interpolates between the two classical approximations, namely the perturbation approach and the Kirchhoff method. The cases in which the phase perturbation theory converges to physical optics are characterized by large values of the Lynch parameter. A conclusion is drawn that the phase perturbation technique is amenable to surfaces whose roughness spectra are wide. Asymptotic expansions, simplifying the evaluation of the phase perturbation backscattering cross-section in the high roughness limit are derived.