基于拉普拉斯本征函数的Woofer-Tweeter自适应光学系统解耦控制算法  

Decoupling Control Algorithm Based on Laplacian Eigenfunction for Woofer-Tweeter Adaptive Optics System

作　　者：程涛 刘文劲[1,3] 杨康健 文良华 何星[1,3] 董理治[1,3] 杨平[1,3] 许冰[1,3] Cheng Tao1,2,3, Liu Wenjin1,3, Yang Kangjian1,2,3, Wen Lianghua1,2,3, He Xing1,3, Dong Lizhi1,3, Yang Ping1,3, Xu Bing1,3(l.Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China ; 2University of Chinese Academy of Sciences, Beijing 100049, China ; 3 Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China)

机构地区：[1]中国科学院自适应光学重点实验室,四川成都610209 [2]中国科学院大学,北京100049 [3]中国科学院光电技术研究所,四川成都610209

出　　处：《中国激光》2018年第9期289-298,共10页Chinese Journal of Lasers

基　　金：国家自然科学基金(11704382); 中国科学院国防科技创新基金(CXJJ-16M208)

摘　　要：为了实现对Woofer-Tweeter双变形镜自适应光学系统的解耦控制,提出了一种基于拉普拉斯本征函数的解耦控制算法。通过求解不同齐次Neumann边界条件下的拉普拉斯本征方程,获得不同光瞳区域下自身和一阶偏导数均正交的拉普拉斯本征函数。利用不同光瞳区域下的拉普拉斯本征函数,实现了对不同光瞳区域下WooferTweeter双变形镜自适应光学系统的解耦控制。此外,拉普拉斯本征函数的一阶偏导数具备正交性,这使得在构建Tweeter耦合抑制矩阵时无需对Tweeter驱动器响应函数面形进行逐个测量,极大简化了Tweeter耦合抑制矩阵的构造过程。采用Woofer-Tweeter双变形镜自适应光学系统对该算法的有效性进行了实验验证,结果表明:基于拉普拉斯本征函数的解耦控制算法能够实现对Woofer和Tweeter同步控制,并能有效地抑制Woofer和Tweeter之间的耦合误差。In order to realize the decoupling control for the Woofer-Tweeter adaptive optics system,we propose a decoupling control algorithm based on Laplacian eigenfunction.By solving Laplacian eigen equations under different homogeneous Neumann boundary conditions,we can obtain Laplacian eigenfunctions which are orthogonal to themselves and whose first-order partial derivatives are orthogonal under different pupil regions.Using the Laplacian eigenfunctions under different pupil regions,we achieve the decoupling control for the Woofer-Tweeter adaptive optics system in different pupil regions.In addition,the first-order partial derivatives of the Laplacian eigenfunction is orthogonality,so that it is not necessary to measure the response function surface shape of Tweeter actuator to construct a constraint matrix for Tweeter.A Woofer-Tweeter adaptive optics system is used to verify the validity of this algorithm.The experimental results show that the decoupling control algorithm based on Laplacian eigenfunctions can synchronously control Woofer and Tweeter,and effectively suppress the coupling error between Woofer and Tweeter.

关 键 词：自适应光学 双变形镜 解耦控制 拉普拉斯本征函数 

分 类 号：O439[机械工程—光学工程]