Research On Wave-front Correction Technique Based On The Stochastic Parallel Gradient Descent Algorithm

The stochastic parallel gradient descent (SPGD) algorithm's mathematical basis and evolution process are studied in detail in this paper. The algorithm's iterative formula is presented, and its convergence characteristic, the improvement technique and the application in model-free adaptive optics system are discussed. Theoretical analysis demonstrates that the SPGD algorithm has the merits of computational simplicity, fast speed convergence, etc., so it is suitable for multivariable objective function optimization. On the basis of the analysis above, a numerical testing model is built to validate and analyze the performance of the SPGD algorithm. One concise and practical system performance metric is adopted in the model. Static phase distortions introduced by a deformable mirror itself are corrected by using the SPGD algorithm. Testing results demonstrate that the algorithm can operate efficiently whether for system performance metric maximization or minimization. The optimal value ranges can be obtained by doing a number of data testing for the algorithm's parameters, including iteration length, random perturbations amplitude of control variables and so on. The methods of introducing an additional penalty function and self-optimization of iteration length are taken to further improve the performance of the algorithm. In conclusion, on account of the SPGD algorithm's fast speed convergence and huge improvement potential, the implementation of it in adaptive optics system based on direct system performance metric optimization would enhance real-time response capability of the system significantly.