The dependence of the complex optical transfer function of an image-forming system on range through the atmosphere has been investigated experimentally. The simple case of a horizontal line of sight over flat terrain has been studied and empirical equations have been obtained which relate the transfer function to range and to the atmospheric temperature structure function. These equations agree with a general theory of wave propagation in a turbulent medium and are therefore applicable to a wide range of situations, provided that the distribution of the temperature structure function along the line of sight can be obtained. The experimental results also furnish evidence that the Kolmogorov expression for the temperature structure function (“the two-thirds law”) is applicable to scale sizes of about a centimeter or so.
C. E. COULMAN, "Dependence of Image Quality on Horizontal Range in a Turbulent Atmosphere," J. Opt. Soc. Am. 56, 1232-1238 (1966)