Statistics 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 the weak and strong turbulence condition. Long-Term PSF is well known and is currently widely used for the estimates of the optical system performance and simulation of the image distortions caused by turbulence. We discuss some peculiarities of the Long-Term PSF that are related to the specifics of the propagation in turbulence, and are often overlooked in the recent literature. Models for the Short-term PSF have been used since mid-1960's, and were the subject of some recent publications. We review the recently published model and present sample calculations of the Short-term PSF. We calculate the variances of the power in the instantaneous PSF and the Strehl ratio at the average PSF center, and correlation between the total power and the Strehl ratio. This information allows modeling the instantaneous PSF with random width and height. Analysis of the calculation results shows that for the most practical situations random Strehl ratio is a product of two uncorrelated random variables - power and axial directivity.