Null field approach to scalar diffraction III. Inverse methods

Abstract

We show how our null field methods might be adapted to provide a sharp numerical test for the radius at which a series expansion of a scattered field starts to diverge. On the basis of our spherical and cylindrical physical optics approximations we develop an inversion procedure, similar to conventional procedures based on planar physical optics and like them needing scattering data over a wide range of frequencies, suitable for totally reflecting bodies. We introduce another method, also based on spherical and circular physical optics, whereby the shapes of certain bodies of revolution and cylindrical bodies can be reconstructed from scattered fields observed for only two closely spaced frequencies. We present computational examples which confirm the potential usefulness of the latter method.