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

In this work, we report on the analysis of speckle patterns produced by illuminating different rough surfaces with an optical vortex, a first-order (l=1) Laguerre-Gaussian beam. The generated speckle patterns were observed in the normal direction exploring four different planes: the diffraction plane, image plane, focal plane, and exact Fourier transform plane. The digital speckle patterns were analyzed using the Hurst exponent of digital images, an interesting tool used to study surface roughness. We show a proof of principle that the Hurst exponent of a digital speckle pattern is more sensitive with respect to the surface roughness when the speckle pattern is produced by an optical vortex and observed at a focal plane. We also show that Hurst exponents are not so sensitive with respect to the topological charge l. These results open news possibilities of investigation into speckle metrology once we have several techniques that use speckle patterns for different applications.