A noise error estimation method for Shack-Hartmann wavefront sensor

In adaptive optics (AO) system, the detector noise is one of the main error sources of Shack-Hartmann wavefront sensor (SH-WFS). Based on the statistical analysis of the noise, a noise error estimation method is presented by using multiframe of the Hartmann spots pattern and the centroid displacements calculated from them. A numerical simulation system for wavefront measuring is built, and used to verify the validity of this method. It shows that the estimation error of this method could be lower than 2%, provided that the signal-noise-ratio (SNR) is sufficient for the WFS working normally. We studied the least frames of data that are required for the method when the SNR of the WFS is at different levels. It indicates that fewer frames are required as the SNR level is higher, and only 2 frames of data are required when the SNR level is high enough. For different types of detector noise, we have analyzed the influence of the accuracy of their prior information on the estimation error. It shows that the influence of the readout noise is strong, and the influence of the photon-noise, the dark-current noise and the sky-background noise is neglectable, since the WFS is usually exposed shortly. The work in this paper can be of certain significance in estimating the point spread function of AO system with the WFS measurements.