Generalization of differential ray tracing by automatic differentiation of computational graphs

Abstract

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).

dO: A Differentiable Engine for Deep Lens Design of Computational Imaging Systems

“…To partially tackle these challenges, derivative-aware lens design engines [29], [30], [31] were inspired by automatic differentiation (AD) [32], a fundamental technique in deep learning. The main distinction of a derivative-aware engine compared to conventional ones is differentiability: The availability of derivative information relating design parameters and the error metric.…”

“…The main distinction of a derivative-aware engine compared to conventional ones is differentiability: The availability of derivative information relating design parameters and the error metric. Via differential ray tracing [30], design parameters and their gradients are chained to the error metric through a so-called computational graph, on which backpropagation results in how each design parameter should quantitatively change to reduce the error metric. Together with gradient-based optimization, the obtained derivatives provide a searching direction in the hyper-parameter space to locally guide evolution of current design, improving performance in terms of the error metric.…”

“…This memory issue has not been fully addressed in previous derivative-aware ray tracing works [29], [30], [33], [13] due to different application-oriented goals. In [13], the implementation of a differentiable ray tracing scheme enables image rendering, and thus rays are traced backwardly starting from the sensor plane, through the lenses, landing at the scene.…”

An exploration of the freeform two-mirror off-axis solution space

“…Global optimization algorithms are currently unpractical, freeform design being by nature a problem with a large number of degrees of freedom. On the other hand, local optimization algorithms can cope with very large dimensionality, especially when one can do without finite-difference gradients [3], but the final outcome will depend on the suitability of the starting point chosen.…”

Differential method for freeform optics applied to two-mirror off-axis telescope design

“…Global optimization methods are often not practical in freeform optical design because of the large solution space. Nonetheless, methods have been propose recently to mitigate these difficulties with strategies to find smart starting points [1] or analytic differentiation of optical design merit functions [2].…”