Abstract

This paper is concerned with the amplitude or irradiance scintillations of a wave propagating in a clear turbulent atmosphere. Experimentally, it is known that the variance of the log-irradiance fluctuations saturate and even decrease with increasing path length or turbulence. This effect is not predicted by the classical theory. Previous attempts at explaining the saturation effect have not been successful. Presently, the best formulations for this problem are in terms of partial differential equations involving derivatives with respect to nine variables in the general case and five variables for a plane wave. A related question is the form of the probability distribution of the irradiance scintillations. Experimentally, the results appear to be in agreement with the log-normal probability distribution. Again, theoretically there is no conclusive agreement among different authors. In this paper we take a different approach that should help to clarify some of the issues involved. We assume that the statistics of the wave are log-normal. Given this assumption, the partial differential equation for the variance and covariance function of the log-irradiance functions reduces to an equation with derivatives with respect to five variables in the general case and to two for a plane wave. The solution of this equation should lead to one of the following two conclusions. First, if the predictions of the simplified equation agree with experiment, then the log-normal distribution has further justification, and simpler equations may be used in studying propagation effects. Second, if the theoretical predictions of the simplified equations do not agree with experiment, then there is a disagreement between theory and experiment that implies that both areas need more careful investigation.

© 1972 Optical Society of America

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Equations (96)

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