本文首先介绍了基于Zernike模式的SPGD算法对大气湍流畸变波前的整形原理, 通过推导得到了关于性能指标的简明表达式, 使SPGD算法收敛速率得到明显提升。然后建立了自适应光学随机并行梯度下降算法波前整形系统模型, 主要对SPGD算法收敛速率、整形能力和整形效果随波前畸变量和变形镜模型的变化规律作了较为详细的仿真研究, 整体定性结果表明: 三者的变化规律有一定的相似性, 同时利用最小二乘法得到了关于整形能力和整形效果变化规律的定量表达式, 若从自适应光学波前整形系统的实时性和简单性考虑, 在保证一定整形效果的情况下, 选择37单元变形镜对畸变波前的3~27(25)阶Zernike像差进行整形即可。

Firstly, we introduce the principle of wave-front shaping with stochastic parallel gradient descent(SPGD) algorithm based on Zernike mode for adaptive optics in atmospheric turbulence, and achieve brief expression about Strehl ratio that makes convergence rate of SPGD algorithm be accelerated obviously. Then we construct wave-front shaping system with SPGD algorithm of specific parameters, and mainly make detailed simulations on the laws of convergence rate, shaping capability and shaping effect about distortion wave-front, Zernike order and actuator number of deformable mirror. The qualitative results show that three change laws are similar, and quantitative expressions of shaping capability and shaping effect are achieved by the least square method. And it can be found from discussion that it's better to select 37-unit deformable mirror to shape 3~27(25) order Zernike aberrations of distortion wave-front at the conditions of some shaping effect considering the nature of real-time and simplification of system.