Finite source effects in microlensing: A precise, easy to implement, fast and numerical stable formalism

The goal of this paper is to provide a numerically fast and stable description for the microlensing amplification of an extended source (either uniform or limb-darkened) that holds in any amplification regime. We show that our method of evaluating the amplification can be implemented into a light-curve fitting routine using the Levenberg-Marquardt algorithm. We compare the accuracy and computation times to previous methods that either work in the high-amplification regime only, or require special treatments due to the singularity of elliptic integrals. In addition, we also provide the equations including finite lens effects in microlensing light curves. We apply our methods to the MACHO-1995-BLG-30 and the OGLE-2003-BLG-262 events and obtain results consistent to former studies. We derive an upper limit for the OGLE-2003-BLG-262 event lens size. We conclude that our method allows to simultaneously search for point-source and finite-source microlensing events in future large area microlensing surveys in a fast manner.