Statistics and generation of non-Markov phase screens

Abstract

Statistics of the random phase screens used for the modeling of beam propagation and imaging through the turbulent atmosphere is currently based on the Markov Approximation (MA) for wave propagation. This includes the phase structure functions of individual screens and the use of the statistically-independent screens for the multi-screen splitstep simulation of wave propagation. As the propagation modeling progresses to address the deep turbulence conditions, the increased number of phase screens is required to accurately describe the multiple scattering. This makes the MA a critical limitation, both because phase statistic of the thin turbulent layer does not follow MA, and because the closely space screens cannot be considered as statistically and functionally independent. A recently introduced Sparse-Spectrum (SS) model of statistically homogeneous random fields makes it possible to generate 3-D samples of refractive-index fluctuations with prescribed spectral density at a very reasonable computational cost. This leads to generation of samples of the phase screen sets that are free from the limitations of the MA. We investigated statistics of the individual phase screens and cross-correlations between the pairs of phase screens and found that the thickness Δz of the turbulent layer replaced by the phase screen is a new parameter defining the phase statistics in the non-Markov case. SS-based numerical algorithms for generation of the 3-D samples of the turbulent refractive index, and for the phase screen sets are presented. We also compare the split-step simulation results for the traditional MA and non-Markov screens.