Statistical Properties of Phase Fluctuations of Optical Radiation Propagating through Atmospheric Turbulence

With the adaptive correction of turbulent distortions of optical radiation, measurements obtained by the Shack-Hartman wavefront sensor have correlation properties. The spatio-temporal correlation dependence on the phase fluctuations of optical radiation contains the coordinates of the focal spots on the hartmanograms, which were recorded by a video camera during a certain time. On the other hand, the coordinates of the centroids are calculated by the centering algorithms. To estimate the coordinates of the centroids from the image of focal spots, one should use the correlation approach, which relies on the comparison of the same phase fluctuations. The results of numerical experiments are presented.