Differential piston phase variance in non-Kolmogorov atmospheres

Area of Science:

• Wave Propagation and Optics
• Atmospheric Turbulence Modeling

Background:

• Understanding atmospheric turbulence is crucial for optical systems.
• Existing models often rely on Kolmogorov turbulence assumptions, which may not always apply.
• Non-Kolmogorov turbulence models are needed for greater accuracy in diverse atmospheric conditions.

Purpose of the Study:

• To derive a generalized expression for differential piston phase variance.
• To analyze this variance in non-Kolmogorov turbulence characterized by a power-law medium.
• To investigate the influence of medium exponent and aperture size on phase variance.

Main Methods:

• Developed a generalized expression for differential piston phase variance.
• Utilized Mellin-transform techniques for the derivation.
• Maintained Kolmogorov assumptions of homogeneity and isotropy.

Main Results:

• The differential piston phase variance exhibits power-law behavior proportional to the medium's power-law exponent.
• Phase variance decreases as aperture size increases.
• For a power-law exponent approaching unity, the variance becomes independent of aperture size.

Conclusions:

• The derived analytical expression provides a new tool for analyzing optical wave propagation in non-Kolmogorov turbulence.
• The findings highlight the significant impact of turbulence characteristics and system parameters on phase variance.
• This work contributes to more accurate modeling of atmospheric effects on optical signals.