Based on the representation of the solution of the stochastic Helmholtz wave equation in the form of a path integral (Samelsohn G., Mazar R., Phys. Rev. E. 1996. V. 54, N 5), an expression for the spatial coherence function of a spherical wave propagating in a turbulent atmosphere is derived. The calculations are carried out using the Kolmogorov model of the fluctuation spectrum of dielectric permittivity under the assumption that the geometrical optics approximation is valid for a random wave phase increment in the path integral. Estimates of the corrections to this approximation on the order of magnitude are found. The derived formula has no limitations on the wavelength and the angular separation between the observation points, which arise when using the parabolic and Markov approximations. The error in estimating the radius of spatial coherence in the parabolic approximation, which is due to wave front sphericity upon 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 several times.
Banakh et al. (Sun,) studied this question.