which can be analytically solved to yield Gaussian intensity Distribution. The time-average intensity distribution at the receptor for a Gaussian-profile transmitted beam is (46) where PT is the transmitted optical power, r)r is the atmospheric transmission efficiency and a, the beam radius at the 1/e-intensity points, is where the parameter (i is used to characterize the beam quality of the optical transmitter in terms of its far-field or focused beam radius being a specified number (/3) times the diffraction limited radius. The quantities a0 and / are the 1/e beam radius at the transmitter and the optical system focal length, respectively. Setting / equal to infinity corresponds to a collimated beam, while setting / equal to R corresponds to best focus at the receptor. The latter condition applies here, so Eq. (13) reduces to where the turbulence coherence length, is given by Fried and Mevers (47) for propagation down through the atmosphere as
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