K-distributed phase differences in turbulent random phase screens

Abstract

Optical path-length fluctuations across a plume of heated air are investigated by various interferometric techniques. Real-time data processing yields spatial and temporal structure functions as well as histograms of optical phase differences. Histograms obtained over a large range of beam separations and beam heights above the heater show an excellent agreement with the class of one-dimensional K distributions. The dependence of the distribution parameters on the probe-beam separation agrees well with a simple empirical model based on four parameters: mean number and mean strength of turbulent eddies and inner and outer eddy scales. The model permits a correct prediction of the averaged intensity in the far field of the screen. Some characteristics of higher-intensity moments can be reproduced by a facet model based on K-distributed phase gradients.