Differentiable design of freeform illumination optics with robust curvature control based on topological constraint

Recent advances in differentiable design methodologies for freeform illumination optics have attracted considerable research interest in non-imaging optics. These approaches represent the freeform optical surfaces with trainable parameters and refine surface profiles iteratively according to the differentiable ray-tracing simulation. Currently, the B-spline surface model has emerged as the prevalent parametric framework due to its inherent global smoothness and local support property. While the local support characteristic ensures local shape adjustment capabilities, enhancing system performance and optimization efficiency, it can also lead to large curvature regions during the optimization process. Effectively constraining the surface curvature remains a challenging problem. To address this issue, we combine physical priors and directed triangular meshes to implement a topological constraint for the intersection points of sampled rays with the target plane. Design examples demonstrate that the proposed constraint can effectively control the curvature while maintaining the optical performance of the system, with a maximum reduction of the mean curvature by approximately one order of magnitude, significantly improving the manufacturability of the surface.