RECONSTRUCTION OF THE BRIGHTNESS DISTRIBU TION OVER A STELLAR DISK FROM OBSERVATIONS OF GRAVITATIONAL MICROLENSING

The problem of reconstruction of the brightness distribution over a so urce through analysis of the flux variation curve observed during grav itational microlensing of the source is formulated. If the source has circular symmetry, econstruction of the radial brightness distribution is reduced to solution of the ill-posed inverse problem for a Fredhol m integral equation of the 1st kind. This solution can be found on com pact sets of functions with special structure, including non-negative, concave downward functions and non-negative functions that are non-in creasing with distance from the center of the visible disk of the sour ce. Estimates of the solution accuracy and its stability to the effect of random noise are obtained from the results of numerical experiment s.