Revealing stellar brightness profiles by means of microlensing fold   caustics
  With a handful of measurements of limb-darkening coefficients, galactic microlensing has already proven to be a powerful technique for studying atmospheres of distant stars. Survey campaigns such as OGLE-III are capable of providing ~ 10 suitable target stars per year that undergo microlensing events involving passages over the caustic created by a binary lens which last from a few hours to a few days and allow to resolve the stellar atmosphere by frequent broadband photometry. For a caustic exit lasting 12 h and a photometric precision of 1.5%, a moderate sampling interval of 30 min (corresponding to ~ 25-30 data points) is sufficient for providing a reliable measurement of the linear limb-darkening coefficient Gamma with an uncertainty of ~ 8% which reduces to ~ 3% for a reduced sampling interval of 6 min for the surroundings of the end of the caustic exit. While some additional points over the remaining parts of the lightcurve are highly valuable, a denser sampling in these regions provides little improvements. Unless a high-precision measurement is desired, limb-darkening coefficients for several filters can be obtained or observing time can be spent on other targets during the same night. The adoption of an inappropriate stellar intensity profile yields characteristic systematics in the model residuals which can be distinguished from those arising from effects causing an acceleration between source and caustic which are however unlikely to affect the lightcurve significantly for most events, although a free acceleration parameter blurs the limb-darkening measurement if the passage duration cannot be accurately determined. 
M. Dominik