Adaptive ray tracing in freeform gradient-index media using an index directional derivative

Freeform gradient index (F-GRIN) media are increasingly used in optical systems. The existing ray tracing methods for F-GRIN have low calculation efficiency and require manual adjustment of step size, making the design process complex. To address this, we propose an adaptive ray tracing (ART) method for F-GRIN. ART obtains an initial step size based on an index directional derivative and the element's length. During the subsequent transmission process, the step size is adaptively adjusted. The accuracy and speed of ART were verified through multiple comparison tests. ART can reduce manual participation and significantly improve efficiency in the optical design of F-GRIN.