Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes

Abstract

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.

In-plane displacement measurement in vortex metrology by synthetic network correlation fringes

“…In Section 2, the theoretical approach sustaining this proposal is elaborated, and in Section 3, some results are presented and analyzed. This analysis includes a comparison of the accuracy and the application range of our results in relation with those first introduced by Wang et al in [9,10] and those presented in our previous work [7]. This provides an idea about the improvement proposed in this paper.…”

“…It should be noted that there is a contribution for any pair of apertures, no matter whether the pair of apertures corresponds to two homologous vortices or not. Nevertheless, because of the redundancy in the distance and relative orientation of the homologous vortex pairs, also in this case, a system of correlation fringes can be observed onto the diffraction plane whose spatial frequency is related with the displacement between the speckled images [7].…”

“…To allow a comparison of the accuracy and the range of application of the method and also to bring an idea about the value of the improvement proposed in this paper, we present a series of measurements analyzed by using both the present method, those methods presented in [7], and those by Wang et al in [9,10]. We used the setup of Fig.…”

“…Also, a significant reduction in the certainty of measurements is of concern in the decorrelated speckle case. Motivated by these facts, in [7] a method based on the application of the Fourier techniques in vortex metrology that allows measuring of relative displacements by using decorrelated speckle distributions was presented. This method is able to measure in a range where both optical vortex metrology and speckle photography are prone to failure.…”

“…As a consequence, a lack of resolution is of concern. Moreover, although the correlation fringes obtained by using this method [7] allow for studying the in-plane displacements, it is apparent that the speckle noise deteriorates the fringes quality, and their visibilities do not reach the optimum, even if a smoothing filter was applied. This obviously lowers the measurement accuracy by incrementing the respective variances.…”