Frequency spectrum of fluctuations of the difference between amplitudes of optical beams traveling at different angles in the atmosphere

The approximate method of smooth perturbations is used to obtain an integral representation of the frequency spectrum of fluctuations of the difference between amplitudes of optical beams traveling at different angles in the atmosphere. A numerical analysis of the expression obtained is made for a "longitudinal" wind and this is done as a function of the diffraction size of the beams and angles between the beam axes. It is shown that low frequencies make the dominant contribution to fluctuations of narrow (in the diffraction sense) beams. Asymptotic expressions are obtained for the low- and high-frequency spectral densities.