Fractal Algorithm for Multiple-lens Analyses

A microlensing exoplanet search is a unique method for finding planets orbiting distant stars. However, in the past, the method used to analyze microlensing data could not deal with complex lens systems. The number of lenses was limited to three or less. Position calculations of images and their integration suffered from severe round-off errors because of singularities. We developed a new algorithm to calculate the light curves of multiple-lens systems. In this algorithm, fractal-like consecutive self-similar division (SSD) is used to find sparse images. SSD is also useful for integrating images to efficiently obtain magnifications. The new algorithm does not use root finding for the lens equation and is free from caustic singularities. There is no limit on the number of lenses that can be used with this algorithm. Compared to inverse-ray shooting, this method dramatically improves the computing time. The calculation can be adjusted to obtain either a high-precision final result or a high-speed quick result. Although this new algorithm was developed for a microlensing planet search, its application to quasar microlensing is also expected. This paper discusses problems in the modeling of a multiple-lens system and then presents the new algorithm in detail.