基于K-L模式的SPGD控制算法波前校正  

Wavefront Correction Based on K-L Modes by SPGD Control Algorithm

作　　者：杨慧珍 苏杭 张之光 Yang Huizhen;Su Hang;Zhang Zhiguang(School of Electronic Engineering,Jiangsu Ocean University,Lianyungang 222005,Jiangsu,China;School of Network and Communication Engineering,Jinling Institute of Technology,Nanjing 211169,Jiangsu,China)

机构地区：[1]江苏海洋大学电子工程学院,江苏连云港222005 [2]金陵科技学院网络与通信工程学院,江苏南京211169

出　　处：《中国激光》2023年第14期133-139,共7页Chinese Journal of Lasers

基　　金：国家自然科学基金(U2141255,11573011);江苏省“六大人才高峰”高层次人才项目(KTHY-058)。

摘　　要：随机并行梯度下降(SPGD)算法是无波前探测自适应光学(AO)系统最常用的控制算法,这种方法一般以变形镜的驱动电压作为控制参数。但随着变形镜单元数的增加,以变形镜驱动电压作为控制参数的AO系统的收敛速度将会大大降低,常采用模式法来降低控制参数的维度。对比分析了不同单元数的变形镜对K-L模式和Zernike模式各阶像差的拟合能力,并以大气湍流影响下的光波波前像差作为校正对象,分别考察了K-L模式和Zernike模式系数作为控制参数时的AO系统的收敛速度和校正效果。结果表明:以常规SPGD控制算法(以驱动器电压作为控制参数)的收敛情况作为参考指标时,基于K-L模式的SPGD控制算法和基于Zernike模式的SPGD控制算法的收敛速度相较于常规SPGD控制算法分别提升了47.5%和29.4%。当大气湍流强度分别为10、15、20时,以K-L模式系数作为控制参数时的校正效果和收敛速度均优于以Zernike模式系数作为控制参数时的情况。以上研究结果为基于K-L模式的SPGD控制算法的实际应用提供了参考。Objective The stochastic parallel gradient descent(SPGD) algorithm is one of the most commonly used control algorithms for wavefront sensorless adaptive optics(AO) systems.This method usually uses the driving voltages of deformable mirrors as control parameters,and the number of actuators is equal to the number of dimensions of the control parameters.It is simple and suitable for AO systems that have a small number of actuators and do not have any requirement for the convergence speed.With the increasing applications of AO,the number of actuators required has gradually increased.In wavefront sensorless AO systems,when taking the driving voltages of the deformable mirrors as control parameters,an increase in the number of actuators leads to a greater number of dimensions of the control parameters and a larger optimization space of the algorithm,which will lead to slower convergence of the algorithm.Various modal coefficients are often used as control parameters to reduce the dimensions of control parameters.When the modal coefficients are modeled as control parameters,the optimization space of the algorithm can be reduced,and the convergence speed can be improved.Methods The Zernike polynomial,which was introduced by Zernike to represent the diffraction effects on concave mirrors,is often used to describe optical wavefront aberrations.When using the Zernike mode to calculate the covariance matrix of the amplitude in Kolmogorov turbulence,namely,the Noll matrix,there are nonzero elements outside the diagonal.This inherent modal crosstalk indicates the statistical dependence between modes,which limits the correction ability of AO systems based on these modes.In this study,the Karhunen–Loève(K-L) modal coefficients derived from the Zernike mode are used as the control parameter of a wavefront sensorless AO system.First,the rationality of the K-L mode is analyzed.The aberration-fitting ability of the deformable mirror(DM)to the K-L and Zernike modes is then discussed.Finally,the convergence speed and correction eff

关 键 词：光通信 自适应光学 随机并行梯度下降 变形镜 K-L模式 波前校正 

分 类 号：TP273.2[自动化与计算机技术—检测技术与自动化装置]