A Survey of Clear Air Turbulence and its Effect on Seeing

An introduction to random ßuctuations in the refractive index of air and their effect on optical images, including the impact on MTF. The aim of these notes is to study, in an introductory way, random ßuctuations in the refractive index of air and their effect on optical images. Image quality is measured by a modulation transfer function (MTF) that characterizes the turbulent viewing, and also by a minimal resolution length. It will be seen that the MTF describing image formation for either “looking up” or “looking down” is describable by a 53 -power exponential falloff with frequency. Also, the ultimate resolution for “looking up” follows a completely different dependence on altitude from “looking down”.In fact, for “looking up” the ultimate resolution increases indeÞnitely with altitude of source, whereas for “looking down” the ultimate resolution length approaches a constant, with altitude, for a source on the ground. The constant length is somewhere between 5 cm and 10 cm in extent. This review will differ from others, cited below, in a few ways. First, it will necessarily be briefer. Cited references should help the interested student Þll out desired sections. Second, we will take a “motivational approach” — e.g., why are “structure functions”, which seem at Þrst such an alien concept, necessary? Third, we will use an intuitive, physical analysis of Lee and Harp (1969) as a basic approach to the problem, instead of the rather forbidding differentialequations approach of the Russian school that is usually taken up. These notes will not consider the important phenomenon of radiative transfer into the atmosphere from the earth or oceans. However, the notes on “Optical Properties of the Oceans” will provide some coverage of this subject. 1 A Synopsis of the Approach First,we introduce the purely mathematical concepts of correlation function and power spectra, relate the two, take up the special cases of shift invariance and isotropy, and relate three-dimensional quantities (which appear in the later