Volume 5 Issue 4
Aug.  2012
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WANG Wei-bing, ZHAO Shuai, GUO Jin, WANG Ting-feng. Convergence rate of stochastic parallel gradient descent algorithm based on Zernike mode[J]. Chinese Optics, 2012, 5(4): 407-415. doi: 10.3788/CO.20120504.0407
Citation: WANG Wei-bing, ZHAO Shuai, GUO Jin, WANG Ting-feng. Convergence rate of stochastic parallel gradient descent algorithm based on Zernike mode[J]. Chinese Optics, 2012, 5(4): 407-415. doi: 10.3788/CO.20120504.0407

Convergence rate of stochastic parallel gradient descent algorithm based on Zernike mode

doi: 10.3788/CO.20120504.0407
  • Received Date: 13 Feb 2012
  • Rev Recd Date: 23 May 2012
  • Publish Date: 10 Aug 2012
  • To speed up the convergence rate of Stochastic Parallel Gradient Descent(SPGD) algorithm that was used to control a deformable mirror for wavefront shaping and to enhance the capability of real-time wave-front shaping, a simulation model was established by using wave-front distortion described by 12 Zernike polynomials and a 32-unit deformable mirror. Two constant matrixes were obtained with the orthogonality of Zernike polynomials in a unit circle, which simplizes computations and speeds up the running time of the algorithm. After 660 iterations, the Strehl ratio is 0.8. Comparison results of 6 kinds of SPGD algorithms with Matlab7.8.0 show that indirect-fixed-bilateral SPGD algorithm can be used in the conditions of low Strehl ratio, and indirect-varied-bilateral SPGD algorithm can be used in the conditions of high Strehl ratio, which will speed up the convergence rate of SPGD algorithm and provide the theoretical guidance for laser shaping.

     

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