Function of spatial coherence of a spherical wave in a turbulent atmosphere. Analysis based on the wave equation
V.A. Banakh, E.D. Zaloznaya, I.V. Zaloznaya, A.V. Falits
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: spherical wave, coherence, turbulent atmosphere, path integral
Abstract
Based on the representation of the solution of the stochastic Helmholtz equation in the form of a path integral (Samelsohn G., Mazar R. Phys. Rev. E. 1996. V. 54, N 5) for the Kolmogorov model of the turbulence spectrum, an expression for the spatial coherence function of a spherical wave propagating in a turbulent atmosphere is derived under the assumption that the geometric-optical approximation is valid for a random phase incursion in the path integral. Estimates of the corrections to this approximation by order of magnitude are found. The obtained formula has no restrictions on the wavelength and the angle between the observation points that arise when using the parabolic and Markov approximations. The error in estimating the radius of spatial coherence in the parabolic approximation, arising from the sphericity of the wave front with an increase in the angular separation of the observation points, is calculated. It is shown that the error increases with the wavelength, and for millimeter and longer waves it can lead to an overestimation of the scale of spatial coherence of a spherical wave by few times.
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