Scattering From Layered Rough Surfaces: Analytical and Numerical Investigations

The first-order perturbative solution of scattering from layered rough surfaces is investigated numerically and analytically. The analytical solution is obtained using a small perturbation approach based on the extended boundary conditions (EBCs). Recently, the first-order scattering solution of a two-rough-surface structure with inhomogeneous dielectric profiles was derived using an EBC-based small perturbation method. In this paper, using those solutions and utilizing the Bragg scattering nature of the first-order perturbative solutions, the problem of scattering from a multi-rough-surface structure is solved straightforwardly. The derived first-order elements of the scattering matrix are simplified and rewritten explicitly in terms of the generalized reflection and transmission coefficients. Due to the simple form of the final solutions, they are easily interpreted in terms of simple scattering mechanisms. Then, the solutions are numerically evaluated for three-layer rough surfaces with different subsurface parameters. It is observed that the difference normalized radar cross sections follow definite simple patterns as the subsurface characteristics are changed. Finally, these variation patterns, which could be of interest in inverse scattering problems, are analytically explained using the derived theoretical solutions. Indeed, the solutions are expressed in forms in which the terms responsible for the observed patterns are explicitly distinguished.