Localization and Derivation of an Optimal Sphere for 3d pErfectly Conducting Objects

Abstract

This paper deals with the localization and the approximation by an optimal sphere of 3D objects. These objects are assumed to be perfectly conducting and immersed in a homogeneous lossy medium, the antennas are in a crosswell configuration. This work is performed as a two stage process. In the first step, we determine the parameters of a sphere which serves as an initial guess using a combination of two methods: the position of the object is found with the help of the polarization properties of the scattered field, while the radius is determined from a low frequency approximation of the scattered field. In the second step, this initial guess is refined by optimizing a cost function with the help of a conjugate gradient method. This process is first tested against a spherical object, and the convergence of the algorithm is checked in this case. The procedure is subsequently applied to prolate or oblate ellipsoids.