The scintillation (power fluctuations due to causes other than beam wandering) of laser beams directed upward through the atmosphere is analyzed as a function of turbulence profile, zenith angle, beam waist at the transmitter, and wave-front curvature at the transmitter. Turbulence at the tropopause significantly reduces transmitter- aperture-averaging effects for collimated beams, Defocused beams have greater scintillation (measured by<i>C</i><i><sub>l</sub></i>, the log-amplitude variance) than collimated beams, for the same beam waist at the transmitter, and over certain ranges of defocusing may scintillate more than a point source. The analysis also shows that focused beams may have significantly less scintillation than collimated beams with the same initial beam waist. Because this occurs only for focusing at or above the tropopause, all of the scintillation may be considered as averaged at the focal region, so that far-field receivers receive flux that has been averaged over all of the turbulence.
P. J. Titterton, "Scintillation and transmitter-aperture averaging over vertical paths," J. Opt. Soc. Am. 63, 439-444 (1973)