Mathematical modelling for high precision ray tracing in optical design

Optical systems have conventionally been evaluated by means of ray-tracing techniques, which can extract performance parameters such as aberration and spot size. However, current ray tracing methods in the field of optical design lack satisfactory methods for error analysis and improving its accuracy. Additionally, numerical calculations of large-scale, lengthy, and multi-scale ray tracing often result in inaccurate and even invalid outcomes due to round-off errors. In response to this challenge, we adopt the floating arithmetic theory to analyze the accumulative impact of round-off errors during the ray tracing process and develop a numerical error model for ray tracing. Using this model, we introduce compensation measures to achieve higher precision and then implemented a high-precision ray tracing algorithm. Finally, we conduct numerical experiments to validate our error model and high-precision algorithm, demonstrating their superior precision in comparison to the state-of-the-art authoritative optical design software, Zemax and CODE V.