SCATTERING AND DIFFRACTION OF A PLANE-WAVE BY A RANDOMLY ROUGH HALF-PLANE - EVALUATION OF THE 2ND-ORDER PERTURBATION

This paper deals with the scattering and diffraction of a plane wave b y a randomly rough half-plane by three tools: the small perturbation m ethod, the Wiener-Hopf technique and a group theoretic consideration b ased on the shift-invariance of a homogeneous random surface. For a sl ightly rough case, the scattered wavefield is obtained up to the secon d-order perturbation with respect to the small roughness parameter and represented by a sum of the Fresnel integrals with complex arguments, integrals along the steepest descent path and branch-cut integrals, w hich are evaluated numerically. For a Gaussian roughness spectrum, int ensities of the coherent and incoherent waves are calculated in the re gion near the edge and illustrated in figures, in terms of which sever al characteristics of scattering and diffraction are discussed.