为了加快控制变形镜进行波前整形的随机并行梯度下降(SPGD)算法的收敛速率, 提高实时波前整形能力, 本文利用由12阶Zernike多项式构成的畸变波前和32单元变形镜建立了仿真模型。基于Zernike多项式的单位正交性, 得到了两个常数矩阵, 当斯特列尔比(SR)达到08时, 需要算法迭代660次, 简化了算法的运算过程, 加快了算法运行时间。通过Matlab7.8.0对6种SPGD算法进行仿真对比, 结果显示: 当SR要求不高时, 可使用间接固定双边SPGD算法来提高收敛速度; 当SR要求较高时, 则应当使用间接自动双边SPGD算法。提出的算法为实际的激光整形提供了理论指导。

To speed up the convergence rate of Stochastic Parallel Gradient Descent(SPGD) algorithm that was used to control a deformable mirror for wavefront shaping and to enhance the capability of real-time wave-front shaping, a simulation model was established by using wave-front distortion described by 12 Zernike polynomials and a 32-unit deformable mirror. Two constant matrixes were obtained with the orthogonality of Zernike polynomials in a unit circle, which simplizes computations and speeds up the running time of the algorithm. After 660 iterations, the Strehl ratio is 08. Comparison results of 6 kinds of SPGD algorithms with Matlab7.8.0 show that indirect-fixed-bilateral SPGD algorithm can be used in the conditions of low Strehl ratio, and indirect-varied-bilateral SPGD algorithm can be used in the conditions of high Strehl ratio, which will speed up the convergence rate of SPGD algorithm and provide the theoretical guidance for laser shaping.