空间光波前畸变校正中SPGD方法的自适应优化

为了提高传统随机并行梯度下降 (Stochastic Parallel Gradient Descent, SPGD) 算法校正波前畸变的性能，提出了一种基于AdaBelief优化器的新型SPGD优化算法。该算法将深度学习中AdaBelief优化器的一阶动量和二阶动量集成到SPGD算法中以提高算法的收敛速度，并使得算法能够自适应地调整增益系数。 此外，对实际增益系数进行自适应动态裁剪以避免因实际增益系数出现极端值而造成的震荡。仿真结果表明:在37单元变形镜 (Deformable Mirror, DM)下，新型SPGD优化算法能够对不同湍流强度下的波前畸变实现有效校正，不同波前畸变经过校正后的斯特列尔比(Strehl ratio, SR)分别提升至0.83、0.47和0.31。此外，该算法在不同湍流强度下的SR仅仅需要149、229和230次迭代达到阈值，与传统SPGD算法及其他优化算法相比有更快的收敛速度，且在稳定性和参数调节方面也具有一定的优越性。

Adaptive optimization of SPGD method in wavefront distortion correction of space light

In order to improve the performance of traditional stochastic parallel gradient descent (SPGD) algorithm for wavefront distortion correction, a novel SPGD optimization algorithm based on AdaBelief optimizer was proposed. The algorithm integrated the first-order momentum and second-order momentum of the AdaBelief optimizer in deep learning into the SPGD algorithm to improve the convergence speed of the algorithm and enable the algorithm to adaptively adjust the gain coefficient adaptively. In addition, adaptive dynamic clipping of the actual gain coefficient was carried out to avoid the oscillation caused by the extreme value of the actual gain coefficient. Simulation results show that under the 37-element deformable mirror (DM), the novel SPGD optimization algorithm can effectively correct wavefront distortion under different turbulence intensities, and the Strehl ratio (SR) of different wavefront distortions after correction is improved to 0.83, 0.47 and 0.31, respectively. In addition, the SR of the proposed algorithm only needs 149, 229 and 230 iterations to reach the threshold under different turbulence intensities. Compared with the traditional SPGD algorithm and other optimization algorithms, the proposed algorithm has a faster convergence speed, and has certain advantages in stability and parameter adjustment.