Source Reconstruction as an Inverse Problem

Abstract

Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically subject to some bias, they can invert data without requiring one to assume a particular model for the source. The Backus-Gilbert method in particular concentrates on the tradeoff between resolution and stability, and allows one to select an optimal compromise between them. We use these tools to analyse the problem of reconstructing features of the source star in a microlensing event, show that it should be possible to obtain useful information about the star with reasonably obtainable data, and note that the quality of the reconstruction is more sensitive to the number of data points than to the quality of individual ones.