用于激光光束整形的连续自由曲面的设计

庄雯; 张宁; 徐熙平; 尹鹏; 陈琦; 李清瑶

光学技术, 2019, 45 (1): 21, 网络出版: 2019-04-16

用于激光光束整形的连续自由曲面的设计

Design of continuous freeform surfaces used for laser beam shaping

论文大纲

庄雯 ^*张宁徐熙平尹鹏陈琦李清瑶

作者单位

长春理工大学光电工程学院，　吉林长春　130022

连续自由曲面光线映射最优运输线性平流方程逐线积分 continuous freeform surfaces ray mapping optimal mass transport linear advection Eq. line-by-line integration

摘要

设计一个有效的连续自由曲面，将给定的准直激光光束映射成任意模式的目标照明，仍然是一个具有挑战性的问题。提出一种基于光线映射来构造连续自由曲面的方法，通过计算光源与目标区域两者辐照度分布之间的光线映射关系，构造出光滑连续的自由曲面。对于准直输入光束，采用最优运输法计算光源与目标之间的光线映射; 根据折反射定律和可积条件，推导出用于求解可积映射关系和连续自由曲面的一般条件; 证明在小角度近似的情况下，基于最优运输法得到的光线映射关系可以满足可积条件; 通过逐线积分法求解出满足一定边界条件的线性平流方程，从而完成连续自由曲面的构造。实验表明，利用逐线积分法求解标准积分方程构造出的连续自由曲面能实现任意模式的目标照明，能量利用率达98.95%。结果表明，基于最优运输法得到的光线映射关系在自由曲面和目标平面之间的距离较大时近似可积，提供了一种有效的构造连续自由曲面的方法。

Abstract

Currently, designing an effective continuous freeform surface to map a given light source to an arbitrary target illumination pattern is still a challenging problem for collimated input beams. A method is proposed for constructing continuous freeform surfaces based on ray-mapping. The method requires the calculation of a ray mapping between the source and the irradiance distribution on the target plane. The challenging aspect of this approach is to find an integrable mapping ensuring a continuous surface. A ray mapping between the source and the irradiance distribution on the target plane is calculated via optimal mass transport(OMT) for a collimated input beam; According to the law of reflection / refraction and an integrability condition, a general condition for the surface and ray mapping is derived. It is shown that in a small-angle approximation the mapping calculated via optimal mass transport can satisfy the integrability conditions and the surface can be constructed by solving a linear advection Eq. with appropriate boundary conditions. Experimental results indicate the continuous freeform surface constructed by the line-by-line integration method can realize an arbitrary target illumination pattern. The energy utilization is up to 98.95%.The results show that the optimal mass transport mapping is approximately integrable over a wide range of distances between the freeform and the target plane. An efficient way is proposed to construct the surface.

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庄雯, 张宁, 徐熙平, 尹鹏, 陈琦, 李清瑶. 用于激光光束整形的连续自由曲面的设计[J]. 光学技术, 2019, 45(1): 21. ZHUANG Wen, ZHANG Ning, XU Xiping, YIN Peng, CHEN Qi, LI Qingyao. Design of continuous freeform surfaces used for laser beam shaping[J]. Optical Technique, 2019, 45(1): 21.

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