Circle modeling with low iteration deviation for freeform lens design

Current freeform lens design methodologies commonly employ tangential plane iteration, wherein the freeform surface geometry is constructed based on vector-defined grid nodes partitioned by energy distribution. However, this approach often suffers from degradation in illumination quality due to discrepancies between the actual surface normal vectors at grid nodes and the target normals, which arise from iterative inaccuracies. To address this limitation, this paper introduces a circular iteration method. By imposing constraints on the outgoing ray directions at successive iteration points, the method ensures that the normal vector at each grid node remains consistent with that derived from Snell’s law. This approach fundamentally mitigates the accumulation of iterative deviations and preserves illumination quality. A design case study demonstrates that the proposed circular iteration method improves illumination uniformity by up to 17.6% compared to traditional tangential plane iteration, without compromising energy utilization efficiency. The method is compatible with a wide range of optical simulation platforms and significantly reduces trial-and-error cycles, thereby accelerating the development process of freeform optical components.