Surface Current Source Reconstruction for Given Radiated Electromagnetic Fields

A general analytic approach is presented for reconstructing: 1) the minimum energy source enclosed by a sphere, and 2) the surface current distribution on a sphere from the knowledge of the radiated fields. The surface current source is derived by adding proper non-radiating sources to the minimum energy source. In contrast to the minimum energy volumetric distribution, the surface current derived in this paper is practically realizable. Finally, we present a closed form formula for the reconstructed spherical surface current source. We will show that this spherical surface current is indeed the unique solution of the inverse source problem for square-integrable surface electric current on a sphere in a homogenous medium.