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，实现一种普适且灵活的自由曲面设计方法，能够将零扩展光源的分布调制为任意辐照度分布，是一项重要挑战。现有设计方法通常将问题表述为偏微分方程，并通过复杂的数值方法求解（尤其在离轴场景下）。然而，当前多数方法不适用于直接求解包含多自由曲面或自由曲面与球面混合的设计问题。为应对这些挑战，我们提出基于可微分光线追迹算法的B样条曲面裁剪方法。该方法采用计算高效的B样条模型，结合基于最优传输映射的两步优化策略，能够根据模拟分布与目标分布之间的偏差对曲面形状进行快速迭代调整，同时确保最终曲面光滑。实验表明，所提方法在近轴与离轴场景中均表现优异，并在混合设计案例中展现出卓越的灵活性。