Reconstruction of thin electromagnetic inhomogeneity without diagonal elements of a multi-static response matrix

Abstract

This paper aims to shape the identification of thin inhomogeneities with different dielectric/magnetic properties from a two-dimensional homogeneous background. The shapes are identified through subspace migration without requiring the diagonal elements of the collected multi-static response matrix. To understand why subspace migration without diagonal elements can retrieve the shape of a thin inhomogeneity, we carefully investigate the relations between the imaging function and Bessel functions of orders 0 and 1. This analysis exploits the fact that when a thin homogeneity exists, the measured far-field pattern can be represented as an asymptotic expansion formula. The investigated relation is supported in numerical experiments with noisy data.