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Perturbed log-normal distribution of irradiance fluctuations

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Abstract

In this paper, we try to clarify some of the issues involved in the log-normal paradox for irradiance scintillations of an optical wave propagating through the turbulent atmosphere. Quite arbitrarily, a perturbation has been introduced in the log-normal distribution of the irradiance fluctuations. The results show that the log-irradiance variance and covariance functions are extremely sensitive to the log-normal assumption. We find that the deviation from the log-normal distribution, in the saturation region, may be detectable experimentally. This appears to be confirmed by recent Russian experimental results. We also show that our results lend insight into other distributions as well. In particular, there are certain regions where the Rice–Nakagami probability distribution cannot exist.

© 1974 Optical Society of America

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