自由曲面光束调控Monge-Ampère方法研究进展  

Research Progress on Monge-Ampère Equation Method for Designing Freeform Beam-Shaping Optics

作　　者：沈凡琪 杨琳[1] 吴仍茂[1] 郑臻荣[1] 李海峰[1] 刘旭[1] Shen Fanqi;Yang Lin;Wu Rengmao;Zheng Zhenrong;Li Haifeng;Liu Xu(College of Optical Science and Engineering,Zhejiang University,Hangzhou 310027,Zhejiang,China)

机构地区：[1]浙江大学光电科学与工程学院,浙江杭州310027

出　　处：《光学学报》2023年第8期172-185,共14页Acta Optica Sinica

基　　金：国家自然科学基金(62022071,12074338);国家重点研发计划(2021YFB2802200)。

摘　　要：自由曲面具有灵活的面形结构,用于光束调控可获得高性能、轻小型的系统,可创造新的结构形式和实现新的光束调控功能。自由曲面光束调控是一个根据输入和目标反求光学自由曲面的逆问题。Monge-Ampère(MA)方法基于理想光源近似,将自由曲面光束调控逆问题转化成一个带有非线性边界条件的MA方程。MA方法无需预先给定光线落点位置,而是通过控制曲面的高斯曲率分布来实现对光传输的高效灵活调控,被认为是当前最有效的可自动满足曲面连续性可积条件的自由曲面设计方法。对MA方法的研究进展进行了概述,详细介绍了自由曲面光束强度调控模型,以及自由曲面光束强度和波前同时调控模型的构建过程与求解方法,并通过三个设计实例充分展示了各类光束调控模型的有效性和MA方法的优势。Significance Freeform surfaces are optical surfaces without linear or rotational symmetry.Their flexible surface geometry offers high degrees of freedom,which can be employed to avoid restrictions on surface geometry and create compact yet efficient designs with better performance.Therefore,freeform surfaces can endow beam shaping with more new functions and satisfy the ever-growing demand for advanced beam-shaping systems.The design of freeform beam-shaping optics can be formulated as follows.Given an input(a light source)and an output(a prescribed irradiance/intensity distribution),one or multiple freeform surfaces are to be designed so that the light rays emitted from the source are redirected to produce the prescribed irradiance/intensity distribution.According to theétendue of the light source,the design of freeform beam-shaping optics can be divided into two groups,i.e.,zero-étendue algorithms based on ideal source assumption and design algorithms for extended light sources.The zero-étendue algorithms assume that the spatial or angular extent of the light source is zero,which means that only one single ray passes through each ray-piercing point on the optical surface.However,the situation becomes different when theétendue of the light source is non-zero.There are an infinite number of light rays passing through each ray-piercing point on the optical surface.When the influence of the spatial or angular extent of a light source on the performance of the beam-shaping system can be ignored,the light source can be considered as an ideal source(a point source or a parallel beam).Then,the design of freeform beam-shaping optics can be greatly simplified by zero-étendue algorithms.Additionally,as the extended light source can be considered to be composed of an infinite number of ideal light sources,most of the current designs of freeform beam-shaping optics are involved in zero-étendue algorithms.The zero-étendue algorithms include three typical methods including the ray mapping method,the support quadratic m

关 键 词：光学设计 光束调控 自由曲面 Monge-Ampère方程方法 逆问题 

分 类 号：O436[机械工程—光学工程]