Statistics of spatially integrated speckle intensity difference.

Area of Science:

• Optics and Photonics
• Statistical Optics
• Electromagnetic Wave Propagation

Background:

• Speckle patterns arise from coherent light scattering.
• Statistical properties of speckle are crucial for applications like imaging and remote sensing.
• Understanding intensity differences between separated apertures is key to characterizing optical fields.

Purpose of the Study:

• To derive closed-form analytic solutions for the statistics of spatially integrated speckle intensity differences.
• To investigate the impact of aperture size and optical field coherence on speckle statistics.
• To provide a theoretical framework for analyzing speckle phenomena in optical systems.

Main Methods:

• Consideration of spatially integrated speckle intensity differences from two separated finite collecting apertures.
• Derivation of probability density function (PDF) and cumulative distribution function (CDF) for fully developed speckle.
• Development of closed-form expressions for the nth statistical moments.

Main Results:

• Closed-form analytic solutions for PDF and CDF were successfully derived.
• Solutions are valid for arbitrary mean number of speckles and degree of coherence.
• Closed-form expressions for nth statistical moments were also obtained.

Conclusions:

• The study provides a comprehensive theoretical treatment of speckle intensity difference statistics.
• The derived solutions offer valuable tools for analyzing optical fields and speckle phenomena.
• This work advances the understanding of speckle statistics in optical systems with finite apertures.