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.