Log-normal paradox in atmospheric scintillations*

Abstract

In a previous paper, we have derived a simplified equation for the irradiance scintillations of an optical wave propagating in the turbulent atmosphere, based on the assumption that the amplitude fluctuations follow a log-normal probability distribution. We have now solved this equation numerically and find that the equation does not correctly predict the experimental results, or even give consistent answers. These solutions definitely prove that either the probability distribution cannot be log-normal or that some other approximation used in deriving the equations must be inappropriate. After a careful investigation of the latter possibility, we are convinced that the theory predicts the probability distribution cannot be exactly log-normal. This presents the interesting paradox that the measurements of most workers appear to be in agreement with a log-normal probability distribution, even in the saturation region, whereas the theory appears to show that this cannot be completely correct. This result poses some rather interesting questions for both the theoreticians and the experimentalists.