On the Probability Distribution of Irradiance in a Turbulent Medium

Abstract

Probability distributions of irradiance recently proposed by several authors are compared with experimental results of both high-order irradiance moments and log-amplitude variance that are obtained by a simultaneous measurement. In spite of the fact that almost all the distributions show a reasonable agreement with the experimental results of irradiance moments (measured up to the fifth order) within the saturation region at least, the distributions that can give a good fit also to the results of log-amplitude variance are very limited when they are assessed over the range of irradiance variances so far measured. A fundamental reason of this disagreement is discussed. In Appendix, expressions of the moments of both irradiance and log-amplitude truncated at a given level are shown along with a general theory of probability distribution functions with no finite cutoff value.