A Statistical Integral Equation Model for Shadow-Corrected EM Scattering from Rough Surface

In this paper we propose a statistical integral equation model (SIEM) 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 density function of its two directional slopes. In addition, it incorporates rigorously the shadow function in the Kirchhoff and complementary fields through a careful treatment of the Poggio & Miller equation. In calculating the incoherent scattered Kirchhoff power, for a Gaussian rough surface, the joint probability density function of surface unit norms at two different surface points is rigorously applied, and decomposition of its covariance matrix into uncorrelated term and fully correlated terms of different types enables the drastic simplification of calculation. For the cross and complementary terms, due to their subdominance nature, a less rigorous treatment is adopted here, namely, to assume the surface norms at different surface points are mutually independent. Such formulation enables SIEM to preserve the conventional definition of scattering coefficient for surface scattering. It can be shown that both IEM and the small slope approximation (SSA) of 0 order are special cases of SIEM. The validity of SIEM is demonstrated through the good agreements between model predictions and method of moment (MoM) simulations for statistically known surfaces.