The Performance of wavefront aberration detection and recovery, is limited by the spatial resolution in subaperture, especially for the high-order aberration. To improve the accuracy of wavefront reconstruction, our paper focuses more on the phase retrieval using the stochastic parallel gradient descent (SPGD) algorithm with lower subaperture. In this paper, the theoretical that Shack-Hartmann wavefront sensor can get a single subaperture high spatial frequency components, which are four-dimensional spatial position and spatial frequency information of the two-dimensional light field is researched.Numerical simulations show that compared with conventional methods, the SPGD algorithm can effectively improve the phase retrieval precision of higher-order aberrations, and decrease the influence of the spatial resolution in subaperture. At the same time, by selecting the appropriate algorithm iterative initial value can effectively enhance the speed of wave front reconstruction.
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