arXiv:2604.02184cs.LG2026-04被引 1

用神经网络快速设计高精度二维反光镜,支持复杂光源

Neural-network methods for two-dimensional finite-source reflector design

论文配图:Neural-network methods for two-dimensional finite-source reflector design
图 1 · 摘自论文原文
  • 用神经网络参数化反光镜高度,结合变分与网格损失优化
  • 误差低至5e-5,速度比传统方法快上百倍
  • 适合需要高精度与快速设计的光学系统开发

我们解决二维反光镜逆问题:将有限扩展光源转换为指定远场分布。反光镜高度由神经网络表示,通过两种目标函数优化:基于闭式逆射线映射的变分损失,以及适用于不连续光源的网格损失。梯度通过自动微分计算,使用鲁棒拟牛顿法最小化。作为基线,采用基于简化有限源近似的去卷积流程:从通量平衡恢复一维单调映射,通过积分因子常微分方程求解转换为反光镜,并嵌入改进的Van Cittert迭代,含非负性截断和光线追踪反馈。在四个基准测试中(涵盖连续与不连续光源及最小高度约束),准确率以光线追踪归一化平均绝对误差衡量。在两个主要基准上,神经方法在单张NVIDIA RTX 4090 GPU上数秒内达到约2e-5和5e-5误差,而基线方法耗时数百秒,误差分别为4e-3和5e-2。结果表明,神经方法在精度与速度上均显著优于基线,同时仍支持实际高度约束。还讨论了通过迭代修正方案拓展至旋转对称及全三维反光镜设计。

原文摘要 · Abstract (English)

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.

反光镜设计神经网络光学逆问题光线追踪

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