Speckle patterns produced by an optical vortex and its application to surface roughness measurements.

Area of Science:

• Optics and Photonics
• Surface Metrology

Background:

• Speckle patterns are generated by coherent light scattering from rough surfaces.
• Optical vortices, such as Laguerre-Gaussian beams, offer unique light field properties.
• Hurst exponent analysis is a quantitative method for characterizing surface roughness.

Purpose of the Study:

• To analyze speckle patterns generated by an optical vortex (first-order Laguerre-Gaussian beam) interacting with rough surfaces.
• To investigate the sensitivity of Hurst exponent analysis to surface roughness under different observation planes.
• To determine the optimal conditions for using Hurst exponent to measure surface roughness with optical vortex illumination.

Main Methods:

• Illumination of various rough surfaces with a first-order (l=1) optical vortex beam.
• Observation and digital capture of generated speckle patterns in four distinct planes: diffraction, image, focal, and Fourier transform planes.
• Quantitative analysis of digital speckle patterns using the Hurst exponent to assess surface roughness.

Main Results:

• The Hurst exponent of digital speckle patterns demonstrates increased sensitivity to surface roughness when the speckle is generated by an optical vortex and observed at the focal plane.
• Speckle pattern analysis at the focal plane using the Hurst exponent provides a more effective measure of surface roughness compared to other observed planes.
• The study found that Hurst exponents are relatively insensitive to variations in the topological charge (l) of the optical vortex.

Conclusions:

• The focal plane is identified as the optimal observation plane for enhanced surface roughness sensitivity when analyzing speckle patterns produced by optical vortices.
• Hurst exponent analysis of optical vortex-induced speckle patterns offers a promising advancement in speckle metrology for surface characterization.
• The findings suggest new avenues for developing advanced speckle-based techniques for diverse metrological applications.