Scattering of a diffusive wave by a subsurface object

Abstract

We present a theoretical and numerical study of the scattering of a diffusive wave by an object embedded in a semi-infinite substrate. We derive exact integral equations for the scattered wave, using Green’s theorem and appropriate Green’s functions. We show that two methods can be used, leading either to a purely surface-integral formalism or to a formalism involving a volume integral and a surface term. In the first case, we derive an extinction theorem for diffusive waves and present an efficient numerical procedure to solve exactly the scattering problem. In the second formalism, physically more explicit, we apply an improved Born approximation, and study its range of validity by comparison with rigorous numerical results. Our approach also suggests a simple way to determine the depth of the object. In this article, we focus on thermal waves. Yet the formalism can be applied to photon-density waves.