B-spline freeform surface tailoring for prescribed irradiance based on differentiable ray-tracing

A universal and flexible design method for freeform surface that can modulate the distribution of an zero-\'etendue source to an arbitrary irradiance distribution is a significant challenge in the field of non-imaging optics. Current design methods typically formulate the problem as a partial differential equation and solve it through sophisticated numerical methods, especially for off-axis situations. However, most of the current methods are unsuitable for directly solving multi-freeform surface or hybrid design problems that contains both freeform and spherical surfaces. To address these challenges, we propose the B-spline surface tailoring method, based on a differentiable ray-tracing algorithm. Our method features a computationally efficient B-spline model and a two-step optimization strategy based on optimal transport mapping. This allows for rapid, iterative adjustments to the surface shape based on deviations between the simulated and target distributions while ensuring a smooth resulting surface shape. In experiments, the proposed approach performs well in both paraxial and off-axis situations, and exhibits superior flexibility when applied to hybrid design case.