Shape Reconstruction of Body of Revolution at Resonant Frequencies

Abstract

The method of obstacle shape reconstruction at its resonant frequencies is extended to the case of body of revolution. The scalar three-dimensional acoustic problem is reduced to a two-dimensional one. Connection between the field on the boundary and far field asymptotic is used for modeling a set of the scattering patterns. Resonant frequencies are defined as the frequencies at which the orthogonal complement function exists. Such a function generates the Herglotz wave function, one of whose zero lines is the boundary contour. The method is tested on several model examples.