Abstract
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.
Highlights
In many fields of optics the modulated patterns have being used along the time for numerous purposes; this is because of the information that can be and selectively retrieved from intensity recordings [1]
The inclusion of high frequency components given by fringe systems superposition lead to the generation of plenty unstable phase singularities when using Riesz transform to obtain the complex signal from intensity distribution, and, on the other hand, the properties of the modulation are diminished by Laguerre-Gauss transform band-pass filter. For this reason we propose a novel transform to preserve the high frequency components from modulated distributions without the generation of unstable phase singularities in the pseudo-phase retrieval from complex-valued signal representation
The first row depicts the intensity from the interference pattern, and the second row the respective phase modulo 2π
Summary
In many fields of optics the modulated patterns have being used along the time for numerous purposes; this is because of the information that can be and selectively retrieved from intensity recordings [1]. In the recent years a particular interest in the singular optics field has been rising This field of optics uses the modulation to retrieve information that is not available otherwise; in particular, in some proposals, the optical singularities from N-pinhole interferometer are characterized and employed to measure the angular momentum from astrophysical light [7, 8]. This N-pinhole system is used in the generation of high-order optical vortices when pinholes are arranged in a spiral line around the origin [9]. These applications rely on ad hoc phase modulo 2π from fields, and this information is not always available or easy to obtain
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