Inversion of polarimetric data from eclipsing binaries

We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the Backus-Gilbert method to control the resolution and stability of the recovered solution, and to make quantitative estimates of the maximum accuracy possible. Using this method we confirm that the limb polarization can indeed be recovered, and demonstrate this with simulated data, thus determining the level of observational accuracy required to achieve a given accuracy of reconstruction. This allows us to set out an optimal observational strategy , and to critcally assess the claimed detection of limb polarization in the Algol system. The use of polarization in stars has been proposed as a diagnostic tool in microlensing surveys by Simmons et al. (1995), and we discuss the extension of this work to the case of microlensing of extended sources.