微透镜中的有限源效应：精确、易于实现、快速和数值稳定的形式
Finite source effects in microlensing: A precise, easy to implement, fast and numerical stable formalism
摘要：
本文的目标是提供一个数值快速和稳定的描述微透镜放大的扩展源（均匀或肢体变暗），在任何放大制度。我们表明，我们的方法评估放大可以实施到一个光曲线拟合例程使用Levenberg-Marquardt算法。我们比较的准确性和计算时间，以前的方法，无论是在高放大制度，或需要特殊的处理，由于椭圆积分的奇异性。此外，我们还给出了微透镜光变曲线中包含有限透镜效应的方程。我们将我们的方法应用于AMIO-1995-BLG-30和OGLE-2003-BLG-262事件，并获得与以前的研究一致的结果。我们推导出OGLE-2003-BLG-262事件透镜尺寸的上限。我们的结论是，我们的方法可以同时搜索点源和有限源微透镜事件在未来的大面积微透镜调查中以快速的方式。
英文摘要：
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.
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