Comparison of correlation algorithms with correlating Shack-Hartmann wave-front images

Correlating Shack-Hartmann wavefront sensor is widely used in solar adaptive optics in which the relative shift between different subapertures by correlation algorithm is computed, and then the control voltage by wavefront reconstruction can be estimated to use for correcting the wavefront distortion induced by atmospheric turbulence. In this paper, several different correlation algorithms including Cross-Correlation Coefficient, Absolute Difference Function, Absolute Difference Function-Squared and Square Difference Function are used to estimate relative shift in correlating Shack-Hartmann wave-front sensor with the different observed solar structure such as sunspot, solar pore and solar granulation. The measurement noise RMS error is computed to compare the performance of the correlation algorithms. The results show the correlation algorithm precision is directly related to the solar structure. The measurement noise is relatively small with the relatively high contrast target, and vice versa. At the same time, the size of reference image also could influence the measurement noise, the larger size of the reference image, the smaller the measurement noise is.