Acoustical imaging of spheres above a reflecting surface

Abstract

An analytical study using the MUSIC method of subspace imaging is presented for the case of spheres above a reflecting boundary. The field scattered from the spheres and the reflecting boundary is calculated analytically, neglecting interactions between spheres. The singular value decomposition of the response matrix is calculated and the singular vectors divided into signal and noise subspaces. Images showing the estimated sphere locations are obtained by backpropagating the noise vectors using either the free space Green’s function or the Green’s function that incorporates reflections from the boundary. We show that the latter Green’s function improves imaging performance after applying a normalization that compensates for the interference between direct and reflected fields. We also show that the best images are attained in some cases when the number of singular vectors in the signal subspace exceeds the number of spheres. This is consistent with previous analysis showing multiple eigenvalues of the time reversal operator for spherical scatterers [Chambers and Gautesen, J. Acoust. Soc. Am. 109 (2001)]. [Work performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]