Statistical properties of laser speckle produced in the diffraction field

Area of Science:

• Optics and Photonics
• Statistical Optics
• Laser Physics

Background:

• Laser speckle patterns arise from the interference of coherent light scattered by a diffuse object.
• Understanding the statistical properties of speckle is crucial for applications in imaging and metrology.
• Previous studies often relied on specific assumptions or limited ranges for speckle analysis.

Purpose of the Study:

• To theoretically and experimentally investigate the statistical properties of laser speckle from weak diffuse objects.
• To derive general formulas for the probability density function and average contrast of speckle.
• To validate these formulas across the entire object surface and diffraction field.

Main Methods:

• Developed theoretical models based on Gaussian statistics for speckle formation.
• Derived general mathematical formulas for probability density function and average contrast.
• Conducted experiments using a weak diffuse object illuminated by a Gaussian laser beam to verify theoretical predictions.

Main Results:

• Introduced general formulas for probability density function and average contrast, encompassing previously studied special cases.
• Evaluated these formulas for a weak diffuse object illuminated by a Gaussian laser beam.
• Experimental results showed good agreement with the derived theoretical formulas.

Conclusions:

• The study provides a comprehensive framework for analyzing laser speckle statistics in the diffraction field.
• The validated general formulas offer improved accuracy and applicability for weak diffuse objects.
• Discussion on speckle circularity and noncircularity provides further insights into statistical properties.