The asymptotic theory of displacements of spatially limited light beams propagating through the turbulent atmosphere is developed as a Markovian process approximation. The asymptotic representations for variance of beam displacements corresponding to small and large values of the structure function of phase fluctuations of a spherical wave calculated for the transmitter diameter are obtained. (Phase structure function characterizes the intensity of turbulent pulsations of a medium dielectric constant along the path.) The dependence of the displacement variance on the path length is investigated. The final dimensions of the outer scale of atmospheric turbulence are taken into account. In contrast to previous papers, for the second moment of intensity the expression is used which is obtained using the Huygens-Fresnel principle for smooth inhomogeneous media. This procedure enables one to determine more accurately the field of applicability of the results previously obtained and to explain the observed disagreement of experimental data with that obtained theoretically. The saturation effect of variance of angular displacements with the path length increase was observed.
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