Modified Beckmann-Kirchhoff scattering model for rough surfaces with large incident and scattering angles

Surface scattering effects are merely diffraction phenomena resulting from random phase variations induced on the reflected wavefront by microtopographic surface features. The Rayleigh-Rice and Beckmann-Kirchhoff theories are commonly used to predict surface scattering behavior. However, the Rayleigh-Rice vector perturbation theory is limited to smooth surfaces, and the classical Beckmann-Kirchhoff theory contains a paraxial assumption that confines its applicability to small incident and scattering angles. The recent development of a linear systems formulation of nonparaxial scalar diffraction phenomena, indicating that diffracted radiance is a fundamental quantity predicted by scalar diffraction theory, has led to a reexamination of the classical Beckmann-Kirchhoff scattering theory. We demonstrate an empirically modified Beckmann-Kirchhoff scattering model that accurately predicts nonintuitive experimental scattering data for rough surfaces at large incident and large scattering angles, yet also agrees with Rayleigh-Rice predictions within their domain of applicability for smooth surfaces.