Shape Reconstruction of Three-Dimensional Body at Resonant Frequencies

In this paper the method that reconstructs the body shape at resonant frequencies of its inner domain is extended to the case of three dimensions. A scalar acoustic problem of scattering on three-dimensional body is considered. The “measured” scattered patterns, that is, far-field asymptotics, are calculated by an arbitrarily chosen but linear independent set of fields on the body boundary. Body resonant frequencies are determined from the existence condition of the orthogonal complement function. By this function, the Herglotz wave function can be calculated having the sought body boundary among its zero surfaces. The method is tested on model examples and the results are presented.