Simulating the phase fluctuations produced by many stars in the weak atmospheric turbulence limit

We propose a method allowing for a simulation of cross-correlated turbulence-induced phase fluctuations produced by many stars is proposed. It turns out that for weak-turbulence conditions which are important for many applications, it is possible to suggest a relatively simple and fast simulation procedure. Both the variation of $C_n^2 $ along a propagation path and an effect of finite outer scale of the turbulence are considered. The validity of the simulation is verified by comparing theoretical and simulated results, and it is shown that there is good agreement takes place even for big separations between the observation points. Adaptive optics, guide stars, speckle interferometry, long-base interferometry, imaging through the turbulence, as well as simulations of the image distortions of extended objects are among the possible applications of this method.