Wave structure function and long-exposure MTF for laser beam propagation through non-Kolmogorov turbulence

• Non-Kolmogorov turbulence has less impact on WSF for power-law values near 3.
• Different power-law values produce varying effects on both WSF and imaging systems.
• Convergent Gaussian-beams degrade the turbulence MTF more than other beams.
• Atmospheric turbulence acts as a low-pass filter in imaging systems.

The degrading effects of atmospheric turbulence on an imaging system can be characterized by the atmospheric modulation transfer function (MTF). In this paper, we derived analytically a new expression for the wave structure function (WSF) of a Gaussian-beam based on the weak fluctuation theory. We assumed the beam-wave is propagating through a horizontal path experiencing isotropic and homogeneous non-Kolmogorov atmospheric turbulence where the power spectrum has a generalized spectral power-law exponent which varies between 3 and 4 instead of the fixed classical Kolmogorov power-law exponent of 11/3. Using the WSF, we derived mathematical expressions for the spatial coherence radius and the long-exposure turbulence MTF of the Gaussian-beam wave. These new expressions were used to analyze the influence of power-law variations and beam sizes on the WSF and quality of imaging systems. The simulation results show that different exponent values produce varying effects on both WSF and imaging systems.