Shape reconstruction of acoustic obstacles from the modulus of the far field pattern

Abstract

We consider the inverse problem of time-harmonic acoustic wave scattering where the shape of an obstacle is reconstructed from a given incident field and the modulus of the far field pattern of the scattered field. Our approach is based on a pair of nonlinear and ill-posed integral equations to be solved for the shape of the unknown boundary. This approach is an extension of the method suggested by Kress and Rundell [5] for an inverse boundary value problem for the Laplace equation. Since the modulus of far field pattern is invariant under translations [4] we can reconstruct the shape of the obstacle but not the location.   &nbspThe numerical implementation of the method is described and it is illustrated by numerical examples that the method yields satisfactory reconstructions both for sound-soft and sound-hard obstacles, also in the case when the modulus is given in a limited aperture.