Meta-heuristic SPGD algorithm in spatial light wavefront distortion correction

To improve the problem of slow convergence speed and ease of falling into the local extreme value of the traditional stochastic parallel gradient descent (SPGD) algorithm, a meta-heuristic SPGD (MHSPGD) algorithm is proposed. The proposed algorithm combines the exploration and exploitation of the metaheuristic algorithm with the SPGD algorithm. First, the gradient descent search of the SPGD algorithm is used to obtain the local optimal solution, and then the neighborhood search is carried out to obtain the possible optimal solution outside the local optimal region. The new starting point of iteration is determined by comparing the performance indexes of all solutions. With the adaptive expansion of the search range, the algorithm can avoid falling into the local extremum and tends to converge to the global optimum. At the same time, to avoid repeated searches, a memory table is established to save the suboptimal solution generated in the iterative process. The model of the wavefront sensor-less adaptive optics system was established, and the proposed algorithm was used to correct the wavefront distortion under different turbulence intensities. A simulation of distortions under different Zernike orders was also carried out. Under three turbulence intensities, the Strehl ratios (SR) of the MHSPGD algorithm are 0.7621, 0.6554 and 0.3749, which are 0.1%, 2% and 18.6% higher than those of the SPGD algorithm. In addition, when the distortion contains more high-order components, compared with the traditional SPGD algorithm, the number of iterations required for SR convergence to 0.6 is reduced by approximately 47%, and the limit value of SR convergence is increased by approximately 9.4% for the proposed algorithm. The results show that compared with the three main optimization algorithms, MHSPGD can achieve a higher convergence limit under various turbulence intensities while maintaining a faster convergence rate, which means it effectively solves the problem of local convergence.