Irradiance Statistics of an Optical Wave in a Turbulent Medium.

by R. F. Lutomirski, Harold T. Yura

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback5 pages $20.00 $16.00 20% Web Discount

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)

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.