Imaging of a small dielectric sphere buried in a half space

¹ Département de Recherche en Électromagnétisme, Laboratoire des Signaux et Systèmes, UMR 8506 (CNRS-Supélec-Université Paris-Sud 11), Gif-sur-Yvette, France.
² Institut Fresnel, UMR 6133, Marseille, France.

Abstract

A MUSIC-type non-iterative, single-frequency imaging method is investigated, in line with recent works by the authors and colleagues on the subject. A small dielectric sphere is buried within the lower half of a two-half-space medium and illuminated from the upper one by a planar electric dipole array. Data of the imaging, the Multi-Static Response Matrix (MSR) involving the dyadic Green function of the medium and exploited via singular value decomposition, are either exact or asymptotic ones. Exact ones are computed by the Coupled Dipole Method (CDM). Asymptotic ones account for coupling to the interface via a Polarization Tensor (PT) calculated in closed form in the bispherical coordinate system attached to the (two-body) sphere-interface system. Comparisons between field data and between images of the inclusion inferred from them are discussed. Among other items, the capabilities of localization of the imaging procedure are exhibited. Whenever the inclusion is far enough from the interface, simplifying the PT to the one of an inclusion in free space is shown to be reliable. Use of a leading-order approximation of the Green function to speed up the imaging procedure is also investigated.