给定光分布问题自由曲面光学的简化构建机制与方法

The prescribed irradiance problem involves producing a desired irradiance distribution from a light source in a high efficiency manner. The desired irradiance problem has gained more and more attention as the increase of the energy crisis and light pollution. Freeform optics is an effective way for solving the prescribed irradiance problem. However, it is a very complicated inverse problem to construct the freeform optics for the prescribed irradiance distribution. There is a rigorous mathematical model only under the condition of point light source approximation, but the derivation process is very complicated and the equation is tediously long. It is more difficult to solve the prescribed irradiance problem when considering the size of the light source, and a direct solution cannot be imagined. The existing freeform optical construction methods either have a high complexity, slow speed, or have large errors, and their ability becomes increasingly limited when dealing with multiple freeform surfaces and more complicated light distributions. We aim to establish a new freeform optical construction mechanism and develop an elegant, efficient and precise construction method for point light source and extended source respectively. This method can construct a variety of freeform optical structures flexibly and achieve excellent lighting effects which are difficult to be achieved by the conventional methods. This project can provide a powerful theoretical and technical support for the rapid development of LED lighting, emerging laser lighting and laser beam shaping.

给定光分布问题关注如何将光源发光高效的转化为人类所需要的光分布形式。随着能源危机和光污染的加剧，给定光分布问题越来越受到重视。自由曲面光学是解决给定光分布问题的有效途径。然而，实现给定光分布的自由曲面光学构建是非常复杂的逆问题，目前仅在点光源近似下有严格的数学模型，但推导过程异常繁琐，方程十分复杂。当考虑光源的扩展性时，处理起来更加困难，直接求解不可想象。现有的自由曲面光学构建方法要么数值求解复杂性高、速度很慢，要么存在较大误差，特别是当处理多个自由曲面和更复杂的光分布时，能力愈发有限。本课题分别针对点光源与扩展光源的给定光分布问题，建立新型的自由曲面光学简化构建机制，研究简洁、高效、准确的自由曲面光学构建方法，灵活构建多种自由曲面光学结构，实现常规方法难以实现的优异照明效果。本课题可为快速发展的LED照明、新兴的激光照明以及激光光束整形提供有力的理论与技术支持。

本项目以给定光分布问题为主线，以半导体照明及激光光束整形应用为背景，分别针对点光源近似与扩展光源情形下的自由曲面光学构建难题，确立了新型的自由曲面光学简化构建机制与方法。面向点光源近似情形，提出了以迭代波前裁剪(IWT)法、中间照度搬运(IIT)法为代表的简化构建途径，将自由曲面光学构建问题转化为间接求解一系列紧邻待求自由曲面的出射波前或相位的蒙日-安培方程，结合Newto-Krylov求解算法及多尺度求解策略，使问题求解难度大大降低。面向扩展光源情形，基于多尺度高斯径向基函数的曲面表达，将自由曲面光学构建问题转化为由粗到细的多层高斯径向基函数项权重优化问题。这些方法简洁、有效、通用性强，可实现平面或曲面目标上的复杂光分布调控。本项目还研究了如何利用自由曲面透镜作为激光分束器以生成具有任意能量比的离散光斑阵列以及面向LED道路照明应用时兼顾照明质量与照明效率的非对称光分布双自由曲面透镜构建。本项目的研究结果除可直接应用于半导体照明、激光加工外，还有望应用于激光雷达、结构光三维成像等领域。