Identification of objects in an acoustic wave guide inversion II: Robin–Dirichlet conditions

Abstract

SUMMARY 9In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for 11 solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body 13 radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of 15 arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct 17 solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown object using a least-squares matching of computed, acoustic ÿeld against the measured, scattered ÿeld. 19

An image method for a sphere in an acoustic waveguide

“…Gilbert, Scotti, Wirgin and Xu [19,20] extended these ideas to consider the ICBA in a waveguide; however, they used a cylinder as the canonical body which led to inaccuracies on the upper-most and lower-most portions of the body. See also the works using ICBA by Buchanan et al [1][2][3][4][5]7] and the current author's two recent works [24,25].…”