Reconstructing spatially incoherent random sources in the nearfield: Exact inversion formulas for circular and spherical arrays

Abstract

We consider the inverse problem for a two-dimensional, spatially incoherent random source. Under these assumptions, we show that an exact inversion formula can be derived for recovering the source spectral intensity, as a function of position, from nearfield measurements of the emitted radiation recorded on the circumference of a circle enclosing the source region. Although solutions to the inverse random source problem have been reported in the past, these results have almost always employed farfield approximations. After deriving the inversion formula in two dimensions, we discuss an efficient method for numerically evaluating this formula using the fast Fourier transform algorithm. Finally, a generalization of the inverse problem to a three-dimensional source enclosed by a spherical recording surface is given.