A new method to compute the target photometric variables of non-imaging optical systems is presented. The method is based on the phase space representation of each surface that forms the optical system. All surfaces can be modeled as detectors of the incident light and emitters of the reflected light. Moreover, we assume that the source can only emit light and the target can only receive light. Therefore, one phase space is taken into account for the source and one for the target. For the other surfaces both the source and target phase spaces are considered. The output intensity is computed from the rays that leave the source and hit the target. We implement the method for two-dimensional optical systems, and we compare the new method with Monte Carlo (MC) ray tracing. This paper is a proof of principle. Therefore, we present the results for systems formed by straight lines which are all located in the same medium. Numerical results show that the intensity found with the ray mapping method equals the exact intensity. Accuracy and speed advantages of several orders are observed with the new method.

中文翻译：

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二维反射光学系统在相空间中的逆射线映射

提出了一种计算非成像光学系统目标光度变量的新方法。该方法基于形成光学系统的每个表面的相空间表示。可以将所有表面建模为入射光的检测器和反射光的发射器。此外，我们假设光源只能发射光，而目标只能接收光。因此，对于源，考虑一个相空间，对于目标，考虑一个相空间。对于其他表面，源相空间和目标相空间均被考虑。输出强度是根据离开光源并撞击目标的光线计算得出的。我们将这种方法用于二维光学系统，并将新方法与蒙特卡洛（MC）光线跟踪进行比较。本文是原理证明。因此，我们介绍了由位于同一介质中的直线形成的系统的结果。数值结果表明，使用射线映射方法发现的强度等于精确强度。新方法可以观察到几个订单的准确性和速度优势。