The point source method in acoustic scattering: Numerical reconstruction of the scattered field from far field measurements of inhomogeneous media

A fundamental problem in scattering theory is to reconstruct the scattered field on a given region from knowledge of the wave on a surface in the far field. A recent methodology which we call point source methods has been developed and applied to the reconstruction of impenetrable obstacles. In this work we present the application of point source methods to the reconstruction of the scattered acoustic field from far field measurements of an unknown penetrable inhomogeneous medium illuminated by a single plane wave.