A Statistical Integral Equation Model for Shadow-Corrected EM Scattering From a Gaussian Rough Surface

We propose a statistical model in conjunction with the integral equation formalism for electromagnetic scattering from Gaussian rough surfaces with small to moderate heights and Gaussian power spectra where we include the statistical features of the surface slopes and the effect of shadowing. In evaluating the Kirchhoff incoherent power, for the correlated term due to correlation between the normal vectors of two neighboring points on the surface, an approximation scheme based on the decomposition of the covariance matrix is proposed. For the cross and complementary incoherent powers, due to their subdominant nature, the cross correlations between the surface slopes at different points on the surface are neglected to reduce the computational complexity. The validity of the proposed statistical integral equation model is demonstrated through agreement between its theoretical predictions and method of moment simulations. Moreover, all the simulated cases are outside the regions of validity of the small perturbation method and the conventional Kirchhoff model, which indicates that the statistical model holds the potential of bridging the gap between these two traditional models.