Unwrapped-phase distribution model for speckle and turbulence

Area of Science:

• Optics and Photonics
• Atmospheric Physics
• Signal Processing

Background:

• Speckle fields are sensitive to atmospheric turbulence.
• Accurate modeling of phase fluctuations is crucial for optical remote sensing and imaging.
• Existing models may not fully capture the probability density function (PDF) of unwrapped phase in clear air turbulence.

Purpose of the Study:

• To propose a novel model for the unwrapped phase of a speckle field propagating through clear air turbulence.
• To develop a formulation for the probability density function (PDF) of this unwrapped phase.
• To provide a method for deriving model parameters from physical system and environmental characteristics.

Main Methods:

• Development of a mathematical model for speckle field unwrapped phase.
• Formulation of the probability density function (PDF) for the unwrapped phase.
• Experimental validation using CO2 laser measurements at an atmospheric test site.

Main Results:

• A model for the unwrapped phase of a speckle field in clear air turbulence was successfully proposed.
• A PDF formulation for the unwrapped phase was developed.
• Parameters for the unwrapped phase PDF were shown to be obtainable from target, laser, and atmospheric conditions.

Conclusions:

• The proposed model accurately represents the unwrapped phase of speckle fields in clear air turbulence.
• The developed PDF formulation provides a robust statistical description of phase behavior.
• Experimental results confirm the model's validity and its ability to incorporate system and environmental parameters.