M. B. Bogdanov* and A. M. Cherepashchuk**
*Research Institute of Mechanics and Physics, Saratov State University, ul. Universitetskaya 42, Saratov, 410601 Russia
**Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119899 Russia
Received November 20, 1995
Abstract—The problem of reconstructing the brightness distribution over a source through an analysis of the
flux variation curve observed during gravitational microlensing of the source is formulated. If the source has
circular symmetry, the reconstruction of the radial brightness distribution is reduced to a solution of the ill-
posed inverse problem for a Fredholm integral equation of the first kind. This solution can be found on com-
pact sets of functions with special structure, including nonnegative, concave downward functions and non-
negative functions that are nonincreasing with distance from the center of the visible disk of the source.
Estimates of the solution accuracy and its stability to the effect of random noise are obtained from the
results of numerical experiments.
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