Single Scattering and Diffusive Limits of the Ultrasonic Radiative Transfer Equation

Abstract

Microstructural characterization of polycrystalline metals is often performed using ultrasonic backscatter techniques [1,2,3]. The backscattered diffuse or incoherent signals, also called grain noise, contain microstructural information about grain size, orientation, and composition which is useful for materials characterization. The grain noise can also interfere with flaw detection. Understanding the scattering mechanism is thus important. When the time and/or length scales of a backscatter experiment are long compared with the time and length scales of the random scattering events occurring within the medium, multiple scattering effects become important. The multiple scattering problem has two limits. In the limit of early times or weakly scattering materials, and for experiments involving focussed transducers, a single scattering approximation has been successful for modeling grain noise [1,2,3]. This assumption implies that the incident wave strikes, on average, a single scatterer before being detected. In the opposite limit, at late times after the energy has scattered many times, the behavior is governed by a diffusion equation [4,5]. The intermediate multiple scattering regime has not, however, been fully utilized for microstructural characterization possibly because of the lack of an adequate theory with which to describe corresponding experiments.