Laser-beam propagation through atmospheric turbulence is analyzed theoretically and compared with measurements at λ=0.63 and 10.6 µm. Calculations based either on irradiance statistics or mutual coherence function (MCF) are analyzed; a general expression for long-term-average beam spread based on the turbulence MCF is obtained. The spread of a laser beam focused over moderate distances can be separated into short- and long-term averages that differ by beam wander, which has been found to be essentially independent of wavelength and adequately described by geometric optics. However, a significant wavelength dependence of short-term-average beam spread is found experimentally. Measurements at 10.6 µm are nearly diffraction limited, whereas corresponding data for 0.63 µm are strongly influenced by variations of the refractive-index structure constant Cn. An empirical formula for long-term-average beam spread is at variance with the wave-number-dependent functional form predicted by MCF calculations. Both the irradiance and MCF approaches go over into the same asymptotic functional dependence for visible wavelengths and long ranges. Angular-beam-spread measurements at 0.63 µm support this conclusion.
James A. Dowling and Peter M. Livingston, "Behavior of focused beams in atmospheric turbulence: Measurements and comments on the theory," J. Opt. Soc. Am. 63, 846-858 (1973)