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The theory of optical propagation through atmospheric turbulence demonstrates the sensitivity of such quantities as log-amplitude variance and covariance to strength of refractive turbulence and transverse wind. We exploit this sensitivity by using a crossed-path technique to derive path profiles of these quantities. The results are insensitive to changes in the spatial spectrum of the refractive-index variations. The path resolution is easily varied by changing the receiver and transmitter separations and is ultimately limited by signal-to-noise considerations. The experimental results for horizontal paths, described here, will ultimately be used to indicate the feasibility of profiling on vertical paths with passive sources.

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.

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.