Scattering of Scalar Waves by a Convex Transparent Object with Statistical Surface Irregularities

Abstract

The scattering of time‐harmonic spherical scalar waves by a large, convex, transparent, dense, and three‐dimensional object with statistically corrugated surface is considered. The maximum deviation of the corrugated surface from the smooth one is assumed to be small, and hence the boundary‐perturbation technique is utilized in this study. First, the scattering of scalar waves by a large, transparent, and dense sphere with statistical surface irregularities is treated as a canonical problem in the general discussion. After the perturbation solution is expanded asymptotically for large ka, it is found that the higher‐order solutions can be obtained from the zeroth‐order solution in a simple and straightforward manner. Then this relationship is generalized to scattering by a large, convex, transparent, and dense object with statistical surface irregularities; a general recipe is given. Finally, the asymptotic expressions of mean values of the scattered wavefunction and the scattered intensity are given for the general problem.