Solution of Inverse Source Problems with Distributed Spherical Harmonics Expansions

Inverse source solutions for field transformations and diagnostics are mostly working with surface current densities on appropriately defined Huygens surfaces around the test object. This gives excellent modeling flexibility, but the handling of the discretized surface current representation requires also substantial computational effort. Distributed spherical harmonics expansions of low order, for example based on a solution space partitioning as used in the multilevel fast multipole method, have somewhat reduced modeling flexibility, but they can save considerable computational effort, and they are, thus, an excellent choice of expansion functions for many practical inverse source problems. We discuss different forms of distributed spherical harmonics expansions comprising purely scalar spherical modes and vector spherical modes. Moreover, we discuss how the different surface source expansions consisting of electric and magnetic surface currents with Love condition or without, or consisting of directive Huygens radiators can be related to corresponding distributed spherical harmonics expansions.