Statistical modeling of the point spread function for imaging through turbulence

Abstract

We use a rigorous Markov approximation-based propagation model to calculate statistical properties of the instantaneous turbulent point spread function (PSF) for weak and strong turbulence conditions. Long-exposure PSF is well-known, and is currently widely used for estimates of optical system performance and simulation of the image distortions caused by turbulence. We discuss some peculiarities of the long-exposure PSF that are related to specifics of propagation in turbulence, which are often overlooked in the literature. Models for the short-exposure PSF have been used since the mid-1960s, and were the subject of some recent publications. We review a recently published model, and present sample calculations of the short-exposure PSF. Based on the available results of the optical propagation theory, we calculate variances of power fluctuations in the instantaneous PSF and the Strehl ratio, and covariance of the total power and the Strehl ratio. Analysis of the calculation results shows that for the most practical situations, the random Strehl ratio is a product of two uncorrelated, random variables-power and axial directivity. This information enables modeling of the instantaneous PSF with random width and height.