Use of the Modified Rayleigh Conjecture method for determining the shape of an acoustically-soft bounded 2D body from the scattered sound field

Abstract

The idea of the Modified Rayleigh Conjecture (MRC) [1], in the inverse scattering context, is to obtain the partial wave amplitudes directly from the scattered field, assumed to be known on a circle completely enclosing the body, and then to obtain the shape of the body by employing the Rayleigh hypothesis ansatz of the scattered field [2] in the boundary condition. This method does not require matrix inversions, contrary to the one exploited in [2]. It is shown that in one of the forms of the MRC, the local radius of the body, for a given polar angle, can be obtained by solving a single non-linear equation, just as in the ICBA method [3]. The MRC method, like the ICBA method, leads to solutions of the inverse problem that are not unique. A technique is suggested for reducing this non-uniqueness.