Probability Density Function Measurements Of Optical Scintillations In The Atmosphere

Abstract

We have made measurements of the probability density function of irradiance for a laser propagating through atmospheric turbulence. For each measurement, a diverged laser beam was used as the source. The beams were propagated horizontally over flat grassland at a height of 1 to 2 meters. Several path lengths of up to 2.4 km were used. At the receiver, a time series of the irradiance was digitized and recorded for later processing. During each experiment, the cross-path wind velocity, the refractive turbulence structure parameter Cn2, and the inner scale of turbulence 10 were measured optically. These data were recorded along with the irradiance data. To obtain an estimate of the probability density function, we normalized each time series by its mean value and sorted the result into a histogram. At the same time, the second and third moments were calculated. These were used to obtain the parameters of the theoretical density functions that were considered. Two phenomenological density functions have been proposed to describe irradiance fluctuations in the atmosphere. These are the I-K and the lognormally modulated Rician. Each requires two parameters that depend on atmospheric conditions and each can be used under any atmospheric conditions. Both reduce to the widely accepted negative exponential density function in very strong integrated turbulence. Both are numerically tractable. We compare each of these density functions with our measured histograms under a variety of atmospheric conditions.