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.

翻译：在非成像光学领域，设计一种可以调节零发散源的分布到任意辐照度分布的自由曲面的通用灵活设计方法是一项重大挑战。目前的设计方法通常将问题公式化为偏微分方程，并通过复杂的数值方法求解，特别是在非轴向情况下更是如此。然而，大多数当前的方法不适用于直接解决多自由曲面或混合设计问题，包含自由曲面和球面。为了解决这些挑战，我们提出了基于可微分光线跟踪算法的B样条曲面整形方法。我们的方法具有计算效率高的B样条模型和基于最优输运映射的两步优化策略。这允许基于模拟和目标分布之间的偏差进行快速迭代调整曲面形状，同时确保平滑的结果曲面形状。在实验中，所提出的方法在近轴和非轴向情况下均表现良好，并在应用于混合设计案例时展现出优越的灵活性。