In this work, we introduce an alternative method of analysis in vortex metrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortex metrology for uniform in-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 from each recorded intensity pattern by using a version of the Riesz integral transform. Then, from each 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 transform as a mathematical operation to compute the far-field diffraction intensity pattern corresponding to the multiaperture set. Each aperture from the set is associated with 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.

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Recently we proposed an alternative method of displacement analysis in vortex metrology, based on the application of the Fourier optics techniques, that is suitable for an intermediate range of displacement measurements ranging below the resolution of speckle photography and above that of the conventional vortex metrology. However, for smaller displacements, we introduce an approach to perform the Fourier analysis from vortex networks. In this work, we present an enhanced method for measuring uniform in-plane displacements, taking advantage of the capability of determining the subpixel locations of vortices and having the ability to track the homologous vortices onto a plane. It is shown that high-quality fringe systems can be synthesized and analyzed to accurately measure in an extended range of displacements and for highly decorrelated speckle patterns. Experimental results supporting the validity of the method are presented and discussed.

A novel vortex-transform is proposed. This transform allows for generating complex-valued functions from modulated intensity patterns, including high frequency components from modulation, without the generation of unstable phase singularities. From these complex-valued functions it is possible to obtain intensity and pseudo-phase maps to analyze the intensity recordings without the necessity of phase retrieval techniques. The intensity and pseudo-phase maps obtained by using this transform preserve the modulation structure onto the intensity and phase modulo 2π maps, including stable phase singularities.