Abstract

The distribution of the sum of log-normal variates is shown for most cases of interest to be very accurately represented by a log-normal distribution instead of a normal or Rayleigh distribution that might be expected from the central-limit theorem. As a result, observation of the log-normal distribution for the fluctuations of flux received after propagation through a random medium can be readily explained, regardless of the size of the receiving aperture.

In every case, the log-normal distribution is a better representation than the normal for the distribution of the sum of log-normal variates. However, in some cases not even the log-normal distribution is very accurate. The questions of convergence and accuracy are examined in detail.

© 1968 Optical Society of America

Are Strong Irradiance Fluctuations Log Normal or Rayleigh Distributed?*

David A. de Wolf
J. Opt. Soc. Am. 59(11) 1455-1460 (1969)

Perturbed log-normal distribution of irradiance fluctuations*

Ting-i Wang and John W. Strohbehn
J. Opt. Soc. Am. 64(7) 994-999 (1974)

Log-normal paradox in atmospheric scintillations*

Ting-i Wang and John W. Strohbehn
J. Opt. Soc. Am. 64(5) 583-591 (1974)

Measurements of three-parameter log-normally distributed optical-field irradiance fluctuations in a turbulent medium*

F. Davidson and A. Gonzalez-del-Valle
J. Opt. Soc. Am. 65(6) 655-663 (1975)

Photon-Count Distributions and Irradiance Fluctuations of a Log-Normally Distributed Light Field*

Van Bluemel, Lorenzo M. Narducci, and Richard A. Tuft
J. Opt. Soc. Am. 62(11) 1309-1314 (1972)