The aim of this paper is to determine exactly the optical transfer function corresponding to the time-averaged image-degrading effects of atmospheric turbulence. First the average transfer function is shown to be related to the spatial coherence function for the light entering the imaging system. Next an exact closed solution is found for the coherence propagation equation. This yields the desired coherence function in terms of the statistics of the random fluctuations of the atmospheric index of refraction. Published meteorological data are analyzed to determine empirical values for the required index statistics. Of particular interest is the variation of turbulent index fluctuations with altitude. Finally, quantitative predictions of image degradation are made and shown to agree with observed data.
R. E. HUFNAGEL and N. R. STANLEY, "Modulation Transfer Function Associated with Image Transmission through Turbulent Media," J. Opt. Soc. Am. 54, 52-60 (1964)