Influence of anisotropic turbulence on the long-range imaging system by the MTF model

• Effective anisotropic factor is introduced to the derived MTF model.
• Finite turbulence inner and outer scales are included in the final derived MTF model.
• Increased effective anisotropic factor decreases turbulence’s influence on the imaging system.
• Increased finite turbulence outer scale produces more effects on the imaging system.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, new analytic expressions for the anisotropic non-Kolmogorov turbulence modulation transfer function (MTF) based on Rytov approximation theory have been derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. Compared with the previously published results where the turbulence inner and outer scales were set separately to zero and infinite for calculation convenience, the concept of anisotropy at different turbulence cell scales and finite turbulence inner and outer scales are introduced to study the MTF models. Also, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. To reduce the complexity and calculation time of the analytic results, the asymptotic-fit expressions are also derived and they fit well with the closed-form ones. Calculations are performed to analyze the anisotropic non-Kolmogorov turbulence’s influence on the long-range imaging system.