Beyond the Kirchhoff approximation

The three most successful models for describing scattering from random rough surfaces are the Kirchhoff approximation (KA), the small perturbation method (SPM) and the two‐scale roughness (or composite roughness) surface scattering (TSR) models. In this paper it will be shown how these three models can be derived rigorously from one perturbation expansion based on the extinction theorem for scalar waves scattering from perfectly rigid surfaces. It will also be shown how corrections to the Kirchhoff approximation proportional to the surface curvature and higher order derivatives may be obtained. Using these results, the scattering cross section will be derived for various surface models.