A UNIFIED PERTURBATION EXPANSION FOR SURFACE SCATTERING

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.