## Abstract

Laser-beam propagation through atmospheric turbulence is analyzed theoretically and compared with measurements at λ = 0.63 and 10.6 *μ*m. 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 *μ*m are nearly diffraction limited, whereas corresponding data for 0.63 *μ*m are strongly influenced by variations of the refractive-index structure constant *C** _{n}*. 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

*μ*m support this conclusion.

© 1973 Optical Society of America

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