Use of a Shack–Hartmann wave-front sensor to measure deviations from a Kolmogorov phase spectrum

Experimental results indicate that the statistics of phase measured across a telescope aperture do not always obey the power laws associated with the Kolmogorov model of atmospheric turbulence. We show that the statistical relations between a wave front and its aperture-averaged first derivative previously derived for a Kolmogorov spectrum can be easily generalized for any power law. We also show that a Shack–Hartmann sensor can be used to measure the form of the structure function of phase fluctuations, and experimental data are presented.