Generalization of differential ray tracing by automatic differentiation of computational graphs

Optical design relies on ray tracing to evaluate and optimize the performance of optical systems. Differential ray tracing, in which the ray properties are calculated together with their derivatives, has been shown to be of interest to improve the accuracy and speed of common optical design tasks. We present in this paper an algorithm capable of performing differential ray tracing in the general case. This algorithm is not constrained by a specific optical system geometry such as rotational symmetry or restricted to a set of surface definitions (e.g., conics, polynomial aspheres).