Roulettes：一个弱透镜形式主义的强透镜- II。推导与分析
Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysis
摘要：
我们提出了一个新的扩展弱透镜形式主义能够描述强透镜图像。本文附有论文I，arXiv：1603.04698，其中我们提供了该方法的简要概述，并说明了它是如何工作的。在这里，我们给出了所有必要的细节，以及一些更明确的例子。我们解决了非线性测地偏差方程的订单订单，保持领先的衍生工具的光学潮汐矩阵，从而产生一系列的地图，形成一个完整的强透镜图像。通过分离每个映射的迹和无迹部分来分解映射族。每个无迹张量代表一个独立的旋转模式，它将圆扭曲成屏幕空间中的各种轮盘。它示出如何总结这一系列的扩展，使我们能够创建大的强透镜图像的收敛，剪切和屈曲是不够的。本文件是对第一份文件的详细阐述，第一份文件在更广泛的范围内介绍了这一主题的主要内容。
英文摘要：
We present a new extension of the weak lensing formalism capable of describing strongly lensed images. This paper accompanies Paper I, arXiv:1603.04698 where we provided a condensed overview of the approach and illustrated how it works. Here we give all the necessary details, together with some more explicit examples. We solve the non-linear geodesic deviation equation order-by-order, keeping the leading derivatives of the optical tidal matrix, giving rise to a series of maps from which a complete strongly lensed image is formed. The family of maps are decomposed by separating the trace and trace-free parts of each map. Each trace-free tensor represents an independent spin mode, which distort circles into a variety of roulettes in the screen-space. It is shown how summing this series expansion allows us to create large strongly lensed images in regions where convergence, shear and flexion are not sufficient. This paper is a detailed exposition of Paper I which presents the key elements of the subject matter in a wider context.
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