Equivalence of perturbation theories for sound scattering by rough surfaces

Abstract

Some approaches to rough‐surface perturbation theory employ the Rayleigh hypothesis, but a method based on the extinction theorem avoids this assumption and gives a series which is apparently different. One might expect the latter method to be superior, but Winebrenner and Ishimaru have shown numerically that the two series give equivalent results for scattering from sinusoidal surfaces [D. P. Winebrenner and A. Ishimaru, J. Acoust. Soc. Am. Suppl. 1 75, S73 (1984)]. We have shown that the two series are the same for arbitrary surfaces. This proof depends upon term‐by‐term reciprocity of the perturbation series.