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A method is proposed to optimized the adaptive optics (AO) system based on the stochastic parallel gradient descent (SPGD) algorithm. In order to increase the speed of convergence, we use the power spectrum method. First of all, we analysis the relation between the atmosphere turbulence power spectrum which can be described as Von Karman spectrum and the stochastic perturbation, and then, we optimize the cutoff frequency of the Von Karman spectrum based on the dependency of the two item mentioned before, finally, an AO model based on the SPGD algorithm is set up, and the phase aberration with the Von Karman spectrum is simulated numerically. Results show that, compared with the conventional SPGD algorithm, the method proposed in this paper not only has a great advantage in increasing the convergence speed, but also can improve the performance index. Experiment proves the correction of the theory and the feasibility of the method. The method proposed in this paper will give a great instruction to the real time AO system.

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