Experiments indicate that the variance of irradiance fluctuations of a wave propagating through a turbulent atmosphere saturates with increasing path length or turbulence strength. In addition, many experimental data indicate that the saturation value depends on the path length. In this paper we calculate the variance of the irradiance fluctuations by a method originally proposed by Keller, but we view it in a conceptually different manner. The reason that this method is reconsidered is that it leads to solutions whose validity is essentially independent of distance for the coherent field and average energy flux. Our calculations yield a saturation curve that agrees with the experimental data, with a saturation value that depends on both the wavelength and the length of the propagation path. It also leads to a saturation curve with a pronounced maximum for the case of constant turbulence conditions and variable path length. Finally, the amplitude fluctuations are found to be Rayleigh distributed in the limit of infinite path length.
M. I. SANCER and A. D. VARVATSIS, "Saturation Calculation for Light Propagation in the Turbulent Atmosphere," J. Opt. Soc. Am. 60, 654-659 (1970)