Tatarski has found the frequency spectra for the amplitude, phase, and phase-difference fluctuations of an infinite plane wave propagating through turbulence. Many practical optical beams, used in atmospheric studies, closely resemble point sources, for which the spherical-wave theory is more applicable. The same spectra, calculated for spherical waves, reveal contributions at higher frequencies for amplitude scintillations, nearly identical phase results, and a phase-difference spectrum with no nulls, in contrast with the plane-wave results. Comparison with recent data is shown.
S. F. CLIFFORD, "Temporal-Frequency Spectra for a Spherical Wave Propagating through Atmospheric Turbulence," J. Opt. Soc. Am. 61, 1285-1292 (1971)