A Statistical Kirchhoff Model for EM Scattering from Gaussion Rough Surface

Abstract

In this paper we propose a statistical Kirchhoff model (SKM) for shadow-corrected EM scattering from a rough surface. It treats the local coordinates and Fresnel reflection coefficients statistically over the orientation distribution of surface unit norm as characterized by the joint probability distribution function of its two directional slopes. In calculating the incoherent scattered power, for a Gaussian rough surface, the joint probability distribution function of surface unit norms at two different surface points is shown to follow a joint Gaussian distribution with zero mean and covariance matrix of special form. Decomposition of such covariance matrix into uncorrelated term and fully correlated terms of different types not only assists a better understanding of the interaction between any pair of points on the surface, but also enables the simplification of calculation of the expectation of the product of Kirchhoff term at one point and the conjugate Kirchhoff term at another point. The validity of SKM is demonstrated through the good agreements between model predictions and method of moment (MoM) simulations for statistically known surfaces. More importantly, all the simulated cases are outside the validity regions of small perturbation model (SPM) and conventional Kirchhoff model (KM), which means that SKM can bridge the gap between SPM and KM.