For non-Kolmogorov turbulence we develop a differential angle-of-arrival fluctuation coefficient, which is the ratio between the transverse and longitudinal differential angle-of-arrival variances, and a slope structure-correlation coefficient, which is the ratio between the transverse and longitudinal differences of the slope correlation function and the slope structure function, to measure the power-law exponent of a phase power spectrum with a Shack–Hartmann wave-front sensor: The differential arrival-of-angle fluctuation coefficient and the slope structure-correlation coefficient are both related to power-law exponent <i>β</i> and are independent of strength parameter <i>ρ</i><sub>0</sub> of the turbulence. We compare the methods developed and use them to evaluate <i>β</i> in recently completed horizontal atmospheric experiments for 1000-m laser beam propagation.
© 1999 Optical Society of America
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.7060) Atmospheric and oceanic optics : Turbulence
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
Changhui Rao, Wenhan Jiang, and Ning Ling, "Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack Hartmann wave-front sensor," Opt. Lett. 24, 1008-1010 (1999)