The factorization method for the acoustic transmission problem

Abstract

In this work, the shape reconstruction problem of acoustically penetrable bodies from the far-field data corresponding to time-harmonic plane wave incidence is investigated within the framework of the factorization method. Although the latter technique has received considerable attention in inverse scattering problems dealing with impenetrable scatterers and it has not been elaborated for inverse transmission problems with the only exception being a work by the first two authors and co-workers. We aim to bridge this gap in the field of acoustic scattering; the paper on one hand focuses on establishing rigorously the necessary theoretical framework for the application of the factorization method to the inverse acoustic transmission problem. The main outcome of the investigation undertaken is the derivation of an explicit formula for the scatterer's characteristic function, which depends solely on the far-field data feeding the inverse scattering scheme. Extended numerical examples in three dimensions are also presented, where a variety of different surfaces are successfully reconstructed by the factorization method, thus, complementing the method's validation from the computational point of view.