Tomographic Reconstruction for Impenetrable Objects

Abstract

A practical technique is presented for finding the shape of a smooth, reflecting, convex object from its scattered field. The method assumes the field on the surface of the object satisfies Dirichlet boundary conditions. A surface identifier is computed from the T-matrix of the scatterer, which in turn, is found from data recorded on a surface surrounding the object. We restrict ourselves to two dimensional objects and the scalar wave equation, but the methods will readily extend, for example, to three dimensions or electromagnetic waves.