Multistatic Response Matrix of Spherical Scatterers and the Back-Propagation of Singular Fields

In view of the development of multiple signal classification-type, non-iterative imaging procedures based on the singular value decomposition of the multistatic response (MSR) matrix of a collection of inclusions, the full 3-D electromagnetic case with arbitrary contrasts of permeability and permittivity (including perfectly electric conducting or perfectly magnetic conducting limit cases) is studied. The structure of the MSR matrix of a single inclusion (or a set of well-separated ones) is analyzed. Emphasis is on a far-field situation, in which one considers an electric dipole array operated in the transmit/receive mode at a single frequency. Back-propagated electric and magnetic fields associated to the singular vectors of the MSR matrix for a single spherical inclusion (or again for well-separated ones) are given in closed form and their leading-order values are exhibited. Numerical illustrations (cross-sectional maps of back-propagated fields computed from a singular value decomposition of the MSR matrix) are presented, for one and two inclusions, to illustrate this behavior as a function of the geometric and electromagnetic parameters of the configuration in a possibly noisy case.