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

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.