Complete Family of Functions Methods, Based on the Rayleigh Hypothesis and on the Extinction Theorem, for Inverse Acoustic Wave Scattering Problems

This work deals with the inverse problem of finding the object (more specifically, its shape), submitted to an incident wave, from the measured, simulated or imposed scattered wave. To do this we propose two complete family of functions methods; the first is inspired by the Rayleigh hypothesis and the other arises from the extinction theorem and the use of an approximate Green's function. The inversion algorithms are outlined for two types of periodic objects (closed cylinder and grating) and numberical results are given which demonstrate the feasibility of the proposed methods.