Implementation of the higher order small slope approximation for scattering from a Gaussian rough surface

Computation of the higher-order small slope approximation (SSA) for electromagnetic scattering from a penetrable randomly rough surface is discussed, under the assumption of a Gaussian random process with an isotropic Gaussian correlation function. A simplified form for the first correction to the lowest order SSA theory is presented, and sample results illustrated to investigate the parameter space under which the first correction is appreciable. Reduction of the higher-order SSA to the physical optics approximation limit is also discussed for both perfectly-conducting and dielectric surfaces.