Iterative critical ray tracing for local tolerance analysis of freeform imaging systems

Abstract

Tolerance analysis of the freeform surfaces serves as a critical bridge between design and manufacturing, offering essential guidance for the desensitization design of optical systems and playing a crucial role in the development of advanced imaging systems. Recently, Deng et al. proposed a direct method [Deng et al. Optica 9, 1039 (2022)] for solving tolerances of freeform surfaces, which reveals the local characteristics of the tolerances of freeform surfaces. However, the method requires dense sampling of the fields of view (FOVs) and the entrance pupil (EP) to cover as many optical surface points as possible, thereby achieving more accurate tolerance envelope solutions. Here, we propose an iterative algorithm called "critical ray tracing" to calculate the critical rays at points on the optical surface and utilize this information for surface tolerance analysis. This method involves fitting the coordinate space of the optical system into a 4D polynomial and employing numerical iteration to determine the rays closest to the preset wave aberration boundary at each surface point. Converting the FOVs and EP sampling into optical surface sampling significantly reduces the number of samples required, achieving computational efficiency without compromising accuracy in determining tolerable surface errors. We demonstrate the effectiveness of our method through tolerance analysis of two different freeform imaging systems. Furthermore, a tolerance analysis example of a complete off-axis three-mirror optical system demonstrates the universality of the process.