The brightness distribution over a stellar disk derived from observations of microlensing by a binary system

Using a model-independent technique, we have reconstructed a one-dimensional strip distribution of the brightness over a stellar disk from observations of microlensing of a Galactic bulge star by a caustic of the binary gravitational lens OGLE-1999-BUL-23, obtained by the international PLANET group. The ill-posed inverse problem was solved using a regularization method taking into account the non-negativity of the brightness distribution. The radial brightness distribution was searched for on a compact set of convex-upward, monotonically non-increasing, non-negative functions, assuming that the source is circularly symmetrical. The reconstructed brightness distribution is compared with the results of model fitting and limb-darkening calculations based on models of stellar atmospheres.