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Measurement error analysis of a cross correlation algorithm with a threshold centroiding method

The measurement error of a cross correlation algorithm with a threshold centroiding method, which is not only related to the background noise variance, the image spatial variance, the size of the reference image, and the image sensor parameters, but also concerned with the half width at half maximum and the threshold value of the cross correlation function, is derived theoretically in detail. Our general calculation formula of the measurement error of the cross correlation algorithm with the optimal normalized threshold value of 0.6035 is fit for the arbitrary sampling condition and extended target. Furthermore, the experimental results of the measurement error of the cross correlation algorithm using different sunspots taken by the correlating Shack-Hartmann wave-front sensor are compared with the theoretical measurement error. The experiment results agree well with the theoretical results.