The turbulence of the atmosphere places an upper limit on the quality of an image of ground objects obtained by long-exposure photography from high altitudes in the atmosphere or in space. (By making the imaging optics good enough, the film resolution fine enough, and the platform stable enough, this limit could be approached but not exceeded.) A useful quantity for indicating the magnitude of this limit is the integral of the MTF associated with the turbulence. Treating the integral as a two-dimensional bandwidth, one-half the inverse of its square root can be associated with a resolution length, or angle, in the same manner that an electrical engineer associates a rise time with one-half the inverse of the bandwidth of an <i>R</i>—<i>C</i> filter. Based on published data for typical strength of atmospheric turbulence, the integral of the MTF was calculated as a function of altitude and the corresponding resolution computed. This resolution is shown to correspond to a length of about 4.6 cm on the ground. It is shown that as an observer goes deeper into space, this limiting ground resolution remains constant, but the diameter of the optics needed to approach the limit goes up. Graphs of achievable ground resolution at any altitude and of the diameter of the optics needed to approach this limit are presented.
D. L. FRIED, "Limiting Resolution Looking Down Through the Atmosphere," J. Opt. Soc. Am. 56, 1380-1384 (1966)