A unified perturbation expansion for surface scattering

Abstract

Starting with the extinction theorem, we present a perturbation expansion which, to first and second orders, converges over a wider domain than the small perturbation expansion and the momentum transfer expansion. We show that, in the appropriate limits, both of these theories, as well as the two‐scale expansion, are recovered. There is no adjustable parameter, such as a spectral split, in the theory. We apply this theory to random rough surfaces and derive analytic expressions for the coherent field and the bistatic cross section. Finally, we present a numerical test of the theory against method of moments results for Gaussian random rough surfaces with a power law spectrum. These results show that the expansion is remarkably accurate over a large range of surface heights and slopes for both horizontal and vertical polarization.