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Diffraction corrections to the Kirchhoff approximation in the problem of rough surface scattering

Diffraction corrections to geometrical optics (GO) values of currents induced by a plane incident wave at a perfectly conducting rough surface were derived by two iterations of a corresponding integral equation. These diffraction corrections were obtained with an accuracy of ~1/k², where k is the wave number of the incidence radiation. Based on these corrections to the surface currents, the backscattering cross sections at normal incidence from a statistically rough Gaussian surface were derived. In an explicit form they depend on the second and fourth moments of the roughness spatial power spectrum. It was found that for gentle roughness, diffraction results in effective “smoothing” of roughness and an increase in the co-polarized backscattering cross sections. The cross-polarized backscattering, which is absent in the GO limit, is caused exclusively by diffraction at the surface curvature.