Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes

Abstract

In this work, we introduce an alternativemethod of analysis in vortexmetrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortexmetrology for uniformin-plane displacement determination. On the basis of two recorded intensity speckled distributions, corresponding to two states of a diffuser coherently illuminated, we numerically generate an analytical signal fromeach recorded intensity pattern by using a version of the Riesz integral transform. Then, fromeach analytical signal, a two-dimensional pseudophase map is generated in which the vortices are located and characterized in terms of their topological charges and their core’s structural properties. The second part of the procedure allows obtaining Young’s interference fringes when Fourier transforming the light passing through a diffracting mask with multiple apertures at the locations of the homologous vortices. In fact, we use the Fourier transformas amathematical operation to compute the far-field diffraction intensity pattern corresponding to themultiaperture set. Each aperture fromthe set is associatedwith a rectangular hole that coincides both in shape and size with a pixel from recorded images.We show that the fringe analysis can be conducted as in speckle photography in an extended range of displacement measurements. Effects related with speckled decorrelation are also considered. Our experimental results agree with those of speckle photography in the range in which both techniques are applicable. © 2012 Optical Society of America OCIS codes: 050.4865, 030.6140.