Irradiance Statistics of an Optical Wave in a Turbulent Medium.

A comment on studies of the probability distribution for the intensity fluctuation of an optical wave. Tatarski's derivation of a log-normal distribution function for paths dominated by single scattering cannot be valid, since the only first-order function that gives the correct mean and standard deviation is linear. The correct first-order statistics are given by the Born approximation; application of the central limit theorem then yields a normally distributed intensity curve--but the experimental evidence supports a log-normal rather than a normal distribution. The authors plotted cumulative distributions for I according to each of three models--log-normal, Rayleigh, and exponential, with the single parameters of the last two chosen so that the mean would correspond to the mean intensity in Fried's experimental data. The difference between the distributions is great. At present, the only consistent theoretical treatment of irradiance statistics in the far field is obtained from the Born approximation, which gives a normal distribution. Geometric optics, considered valid only in the near field, do yield a log-normal intensity distribution. A modified geometric optics approach might lead to better understanding. 5 pp. Ref. (MW)