Complete family of functions methods, based on the Rayleigh hypothesis andon the extinction theorem, for inverse acoustic wave scattering problems

This work deals with the inverse problem of finding the object (more specif ically, its shape), submitted to an incident wave, from the measured, simul ated or imposed scattered wave. To do this we propose two complete family o f functions methods; the first is inspired by the Rayleigh hypothesis and t he other arises from the extinction theorem and the use of an approximate G reen's function. The inversion algorithms are outlined for two types of per iodic objects (closed cylinder and grating) and numberical results are give n which demonstrate the feasibility of the proposed methods.