Rough-surface effects on incoherent scattering from random volumetric scatterers: Approximate analytic series solution

Abstract

An approximate analytic series solution is obtained for the effects of randomly rough surfaces on the time-dependent ultrasonic backscatter that are due to beam-microstructure interactions. The transmission of sound through the rough surface is modeled by scalar waves by use of the phase-screen and Fresnel approximations, whereas the transducer is assumed to produce a focused normally oriented Gaussian beam. The beam–microstructure interaction is described by a simple, generic model that attributes backscattering to inhomogeneities in the elastic constants of the sample; density variations are ignored. Key predictions of the approximate series solution are that (a) acoustic backscatter is relatively insensitive to surface roughness for unfocused probes, (b) roughness can dramatically reduce the backscatter noise seen by focused probes, (c) backscatter is increased at early times because of weak localization, and (d) backscatter is reduced at late times because of increased diffraction. The predictions of the series solution are briefly compared with available experiment.