On the Generation of Distributed Spherical Harmonics Expansions for Inverse Source Solutions

Distributed spherical harmonics expansions are a powerful approach for the efficient solution of inverse source problems. They allow for a relatively accurate representation of the geometric support of the source distribution without the overhead of handling a mesh and mesh-specific basis functions representing the commonly utilized surface current densities. Standard spherical harmonics expansions distributed over a Huygens surface around the source domain are, however, redundant. Therefore, we discuss ways towards the reduction of this redundancy, where we are in particular interested in the construction of spherical harmonics with predominant radiation into the actual solution domain. Several sets of such spherical harmonics are presented and their utilization with measured and synthetic near-field data is demonstrated.