# Accession Number:

## AD0684120

# Title:

## IRRADIANCE STATISTICS OF AN OPTICAL WAVE IN A TURBULENT MEDIUM,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1969-01-27

# Pagination or Media Count:

## 8.0

# Abstract:

The probability distribution for the intensity fluctuations of an optical wave has received considerable attention in the recent literature. Tatarski has claimed the distribution in I in the far field where geometric optics is not applicable to be log-normal i.e., lnI is normal by applying the central limit theorem to the first order Rytov solution. It has recently been shown that it is necessary to retain the second order Rytov term in order to compute the standard deviation of the intensity fluctuations correct to first order in n1. Hence, Tatarskis derivation of a log-normal distribution function for propagation paths dominated by single scattering cannot be valid. In fact, it can easily be seen that the only first order function proportional to n1, the index of refraction fluctuations, which gives the correct mean and standard deviation for the intensity, is a linear one. Hence, the correct first order statistics are given only by the first order Born approximation, and application of the central limit theorem then yields a normally distributed intensity distribution. This result should be valid for propagation paths small compared to the single scattering length, Lc, but the experimental evidence supports a log-normal rather than a normal distribution. Author

# Descriptors:

# Subject Categories:

- Optics