The use of the Principal Components Analysis (PCA) for recovering the modulating phase, given a sequence of Phase-Shifted Interferograms (PSI), is a very important contribution to the field. However, its verbatim translation from statistics to PSI has limited the view to consider only constant background illuminations. Here, we show that the Singular Value Decomposition (SVD), used in PCA, actually separates the background illumination (constant or not) and the phase modulation terms. We show that the modulating phase can be correctly recovered if the phase-shifts sample full periods uniformly, independently of the spatial distribution of the number of fringes.
We model a set of Phase-Shifting Interferogram (PSI) images in a new and versatile way that allows exploring
interesting numerical approaches for the analysis of PSI. We show how this representation can be used to recover
the modulating phase if the phase steps are known, and we also show how it can be used as the baseline for an
iterative algorithm. For the case in which the phase steps are known we compare against the four step algorithm.
For the case of unknown phase steps, we compare against the Principal Component Analysis (PCA) and the
Advanced Iterative Algorithm (AIA).
We report a parametric study of a long-range plasmon waveguide for the modal profiles, effective index and propagation losses as a function of the metal layer thickness and the variations in the refraction index of the upper cladding. Such device can be used as an optical biosensor. All calculations are performed using COMSOL Multiphysics, and the amplitude- and phase- responses of the device are obtained from the changes in the real and imaginary part of the effective index of the plasmon mode, respectively.
In this research an interferometric system was developed that generates four simultaneous interferograms with independent phase shifts using modulated polarization. The proposed system consists of three coupled interferometers: the first system is a polarized Mach-Zehnder interferometer, which generates the pattern, the second and the third interferometer system, function as replicators of the first pattern, so the four patterns are generated. To show the novelty of the developed system, the calculation of optical path difference (OPD) for phase samples are shown.
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