Uniqueness of the inverse source problem for quasi-homogeneous, partially coherent sources

Abstract

The inverse source problem for quasi-homogeneous, partially coherent sources is investigated. Comparisons are made between the formulations for two-dimensional and three-dimensional source distributions. A unified approach is presented herein by considering the two-dimensional source distribution as a three-dimensional distribution with delta-function support in one dimension. It is shown that measurements of the cross-spectral density of the field on a surface enclosing the source are sufficient to reconstruct the unknown source cross-spectral density for two-dimensional sources, while the measurements are insufficient for three-dimensional sources. The use of a priori information and its effect on the uniqueness of the three-dimensional inverse source problem is discussed. In particular, a set of supplemental data and associated inversion algorithm is described that guarantees uniqueness of the three-dimensional inverse and that is less restrictive than the data previously identified. Finally, practical considerations for making the required measurements are discussed.