The Centroid of Speckle Image and the Wavefront Tilt

The relation between the centroid of speckle image and the wavefront tilt is discussed in this paper.The centroid of speckle image is proved mapping to the global tilt of wavefront.This relation is independent of whether the pupil aperture is larger than the atmospheric coherent length.The conclusion is not strictly limited by the near-field approximation.An important inference is that the Optical Transfer Function(OTF)of the "Shift & Add"according to the centroids of speckle images is just the traditional average short-exposure OTF given by Fried.The inference is very important to the adaptive optics and high resolution image reconstruction techniques, especially to those with the"Shift & Add"technique.