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Large-Scale Turbulence Effects Simulations for Piston Phase Retrieval

Abstract : In the conventional atmospheric turbulence numerical simulation techniques based on the split-operator method, the turbulence-induced refractive index inhomogeneities are represented by a set of infinitely narrow (2D) phase distorting layers (phase screens). These conventional phase screens cannot represent large-scale refractive index inhomogeneities due to limitations imposed by computational grid size. For this reason, this commonly used model cannot be applied for computer analysis of atmospheric optical systems that are affected by the presence of large-scale turbulence eddies. Among these systems are coherent imaging ladars, optical vibrometers and interferometers. In the classical Kolmogorov turbulence theory, the impact of the large-scale turbulence eddies are associated with the turbulence outer scale. Contrary to the conventional approach, in the computer simulation technique introduced here the turbulence-induced refractive index inhomogeneities are represented by a set of large-scale phase distorting screens that account for refractive index inhomogeneities which extend beyond the numerical grid correlation length. The results are applied to the analysis of piston phase fluctuations for the cases when the turbulence outer scale significantly exceeds the receiver aperture size. We also analyze the piston phase fluctuations in deep turbulence conditions in presence of phase singularities (phase cuts and branch points), and show that the conventional definition of piston phase cannot be applied for this case. We introduce a more general definition of piston phase which is useful for analysis in deep turbulence conditions.