Efficient Calculation of the Kirchhoff Integral for Predicting the Bistatic Normalized Radar Cross Section of Ocean-Like Surfaces

Methods for improving efficiency in computing bistatic scattering from ocean-like surfaces are presented. The methods focus on approximations for the Kirchhoff integral required in evaluating the predictions of multiple theories of bistatic scattering from the ocean surface including the physical optics (PO) and small slope approximation (SSA) approaches. A representation of the integral in terms of the probability density function (pdf) of a symmetric alpha stable random variable is examined for near-specular scattering as has been proposed previously in the literature. Methods for evaluating this form are presented for azimuthally varying surfaces having a general spectrum model as well as a fully analytical expression for surfaces described by an isotropic Pierson–Moskowitz spectrum. The resulting forms are also compared and contrasted with the standard geometrical optics (GO) theory of surface scattering to provide insight into the cutoff wavenumber used in the standard GO method. Additional two-scale and small roughness approximations to the integral are also investigated for the prediction of scattered fields outside the near-specular region.