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 stochastic 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,convergences come forth after about 58 times,197 times,133 times of iterations,respectively,but the evolution curve of spot radius oscillates seriously.Encircled energy ratios increase from 0.200 5,0.127 7,0.200 5 before shaping to0.669 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 shaping 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.