Study on Centroid-of-Correlation-Function Approach for Estimating Sub-Image Shifts in Extended Scene Shack-Hartmann Wavefront Sensor

The calculation of the shifts between sub-images in extended scene Shack-Hartmann wavefront sensor is one of the key factors affecting the accuracy of wavefront sensing, which is commonly achieved by correlation algorithm and it can attain sub-pixel precision through methods such as parabolic interpolation algorithm. The calculation can also be achieved by using the centroid of the correlation function. The main step is first calculating the correlation function between two sub-images and then calculating the centroid of the correlation function, which achieves sub-pixel precision. Based on simulation, the measurement accuracy of this method is related to the size of the sub-image, the window size of the correlation function in the calculation of the centroid and threshold of the correlation function. Besides, the signal-to-noise ratio of the image also effects the accuracy of the calculation. Studies show that, when the signal-to-noise ratio of the image is less than 1, the error of the centroid algorithm is relatively large. When the signal-to-noise ratio of the image is larger than 2, the error of the centroid-of-correlation-function approach is only half of that of the parabolic interpolation. The experimental results are in good agreement with the simulation results.