We address the inverse problem of designing two-dimensional reflectors that transform light from a finite, extended source into a prescribed far-field distribution. The reflector height is represented by a neural network and optimized with two objective functions: a direct change-of-variables loss based on the closed-form inverse ray map, and a mesh-based loss that maps target cells back to the source and remains usable for discontinuous sources. Gradients are computed by automatic differentiation and minimized with a robust quasi-Newton method. As a baseline, we adapt a deconvolution pipeline built on a simplified finite-source approximation: a one-dimensional monotone map is recovered from flux balance, converted to a reflector by an integrating-factor ODE solve, and embedded in a modified Van Cittert iteration with nonnegativity clipping and ray-traced feedback. Across four benchmarks, covering continuous and discontinuous sources and minimum-height constraints, accuracy is measured by ray-traced normalized mean absolute error. On the two main benchmarks, the neural method reaches errors of about 2e-5 and 5e-5 within a few seconds on one NVIDIA RTX 4090 GPU, compared with 4e-3 and 5e-2 for the deconvolution baseline after several hundred seconds. The results show that the neural formulation is both more accurate and substantially faster, while still supporting practical height constraints. We also discuss extensions to rotationally symmetric and full three-dimensional reflector design through iterative correction schemes.

翻译：我们研究了将有限扩展光源的光变换为指定远场分布的二维反射器逆设计问题。反射器高度由神经网络表示，并通过两个目标函数进行优化：基于闭式逆光线映射的直接变量替换损失，以及将目标单元映射回光源并适用于不连续光源的网格基损失。梯度通过自动微分计算，并由稳健的拟牛顿法最小化。作为基准方法，我们构建了基于简化有限光源近似的反卷积管道：通过通量平衡恢复一维单调映射，利用积分因子ODE求解转换为反射器，并嵌入含非负性裁剪和光线追踪反馈的改进型Van Cittert迭代。在涵盖连续/不连续光源及最小高度约束的四个基准测试中，我们使用光线追踪归一化平均绝对误差衡量精度。在两项主要基准测试中，神经网络方法在单块NVIDIA RTX 4090 GPU上于数秒内达到约2e-5和5e-5的误差，而反卷积基线方法在数百秒后仍为4e-3和5e-2。结果表明神经公式既更精确又显著更快，同时仍支持实际高度约束。我们还讨论了通过迭代校正方案向旋转对称和全三维反射器设计的扩展。