为提高随机并行梯度下降(SPGD)算法的波前像差优化校正的收敛速度,从SPGD算法原理出发,分析算法迭代中制约其收敛速度的因素,提出一种基于波前像差梯度平方寻优的随机并行梯度下降算法。通过理论公式推导,分析波前梯度平方和波前随机扰动量的线性关系,并利用远场光斑的归一化二阶矩,近似计算波前像差梯度平方,最终实现波前像差的优化校正。随后采用数值仿真方法对比分析已有的SPGD算法和本文算法的收敛速度和校正效果。最后通过菲涅耳波带片波前像差的无波前传感自适应光学校正实验,进一步验证算法的性能。数值仿真和校正实验结果一致,表明本文算法具有更快的收敛速度,适应性更强。

This study presents a stochastic parallel gradient descent (SPGD) algorithm based on the optimization of square of wavefront aberration gradient to improve the convergence speed of the SPGD algorithm for correcting the wavefront aberrations. Based on the principle of the SPGD algorithm, this study analyzes the constrained factors of the convergence speed in the algorithm iteration. Further, the linear relation between the square of wavefront aberration gradient and disturbances from random aberration is analyzed by deriving the theoretical formula; subsequently, the square of wavefront aberration gradient is approximately calculated by using the far-field spot's normalized second moment, and the optical correction of wavefront aberrations is finally realized. The convergence speed and correction effect of the proposed SPGD algorithm are then analyzed using numeric simulations and compared with those of the previous SPGD algorithms. Finally, a wavefront sensorless adaptive optics correction experiment for Fresnel zone plate wavefront aberrations is performed to validate the performance of the proposed SPGD algorithm. The numeric simulation and results of correction experiments consistently denote that the proposed method has a high convergence speed and a robust corresponding adaptability.