随机并行梯度下降算法在激光束整形中的应用

为了满足高光束质量要求，校正激光束在传输过程中产生的波前畸变，改善激光位相分布，进而提高聚焦光斑的能量集中度，基于79单元微机械薄膜变形镜（MMDM）搭建了一套激光束整形实验系统。利用随机并行梯度下降（SPGD）算法，分别选择聚焦光斑半径、形心为中心的环围能量比和质心为中心的环围能量比作为算法性能指标，开展了激光束整形实验研究。3种情况下，分别经过58次、197次、133次迭代趋于收敛，但光斑半径作为性能指标时振荡严重；环围能量比从整形前的0.200 5、0.127 7、0.200 5分别增加到整形后的0.669 9、0.733 9、0.864 0。实验结果表明：MMDM用于激光束整形具有良好的效果，光斑半径作为性能指标整形速度最快，其次为质心环围能量比，形心环围能量比最慢；质心环围能量比作为性能指标整形效果最好，其次为形心环围能量比，光斑半径最差。综合比较，质心环围能量比作为性能指标时综合效果最好。

Application of stochastic parallel gradient descent algorithm in laser beam shaping

In the field of laser applications, in order to meet the need of high laser beam quality, correct the wave-front aberration generated during the transmission of laser beam and improve the laser phase distribution, thereby increase the energy concentration of the beam focusing spot, a set of laser beam shaping experimental system is built based on a 79-channel micromachine membrane deformable mirror（MMDM）. By using stochas- tic parallel gradient descent（SPGD） algorithm, the laser beam shaping experiment is carried out respectively with three performance indexes：radius of the focused spot, encircled energy ratio with geometric center as the center, and encircled energy ratio with centroid as the center. In the three cases, convergenees come forth af- ter about 58 times, 197 times, 133 times of iterations, respectively, but the evolution curve of spot radius os- cillates seriously. Encircled energy ratios increase from 0. 200 5, 0. 127 7, 0. 200 5 before shaping to 0. 669 9, 0. 733 9, 0. 864 0 after shaping, respectively. The results of experiments show that MMDM can be used for laser beam shaping with well results. The shaping speed is fastest with spot radius as the performance index, followed by encircled energy ratio of centroid and encircled energy ratio of geometric center. The sha- ping effect is best with encircled energy ratio of centroid, followed by the encircled energy ratio of geometric center and spot radius. After synthetical comparison, it is best to choose encircled energy ratio of centroid as the performance index.