Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack Hartmann wave-front...

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 beta and are independent of strength parameter rho(0) of the turbulence. We compare the methods developed and use them to evaluate beta in recently completed horizontal atmospheric experiments for 1000-m laser beam propagation.