NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
复制标题
计算引力透镜放大图的反多边形映射的新进展：优化计算
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Jiménez
中科院分区：
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作者：
E. Mediavilla;T. Mediavilla;J. A. Muñoz;O. Ariza;P. López;C. González;J. Jiménez
我们推导出一个精确解（级数展开的形式）来计算引力透镜放大率映射。它是基于后向重力透镜映射的一个分区的图像平面在多边形细胞（逆多边形映射，IPM），不包括临界点（除了可能在细胞的边界）。级数展开的零阶项导致Mediavilla等人描述的方法。一阶项用于研究零阶级数截断引起的误差，解释IPM即使在这种低阶近似下也具有高精度。解释的逆射线拍摄（IRS）的IPM方面的方法，我们解释了以前报道的N−3/4依赖的IRS误差与每像素收集的射线数。由临界曲线包围的细胞（临界细胞）转换为具有拓扑病理的非单连通区域，如转换下的边界自动重叠或不保留。为了定义非临界划分，我们使用临界曲线的线性近似将每个临界单元划分为两个非临界子单元。单元尺寸的最佳选择基本上取决于临界曲线的曲率。对于放大图的像素是爱因斯坦半径的一小部分的典型应用，在没有透镜的情况下，单元和像素大小之间的一对一关系保证了方法的一致性和非常高的精度。这个处方很简单，但很保守。我们表明，可以使用大得多的细胞，以获得放大图，节省了大量的计算时间。
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previously reported N−3/4 dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.