Person:
Quiroga Mellado, Juan Antonio

First Name

Juan Antonio

Last Name

Quiroga Mellado

URI

https://hdl.handle.net/20.500.14352/75019

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Físicas

Department

Óptica

Area

Optica

Identifiers

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Search Results

Now showing 1 - 9 of 9

Noise in phase shifting interferometry
(Optics Express, 2009) Quiroga Mellado, Juan Antonio; Estrada, Julio César; Servín Guirado, Manuel; Mosiño, Juan Francisco; Cywiak Garbarcewics, Moisés
We present a theoretical analysis to estimate the amount of phase noise due to noisy interferograms in Phase Shifting Interferometry (PSI). We also analyze the fact that linear filtering transforms corrupting multiplicative noise in Electronic Speckle Pattern Interferometry (ESPI) into fringes corrupted by additive gaussian noise. This fact allow us to obtain a formula to estimate the standard deviation of the noisy demodulated phase as a function of the spectral response of the preprocessing spatial filtering combined with the PSI algorithm used. This phase noise power formula is the main result of this contribution.
Spectral analysis of phase shifting algorithms
(Optics Express, 2009) Quiroga Mellado, Juan Antonio; Estrada, Julio César; Servín Guirado, Manuel
Systematic spectral analysis of Phase Shifting Interferometry (PSI) algorithms was first proposed in 1990 by Freischlad and Koliopoulos (F&K). This analysis was proposed with the intention that "in a glance" the main properties of the PSI algorithms would be highlighted. However a major drawback of the F&K spectral analysis is that it changes when the PSI algorithm is rotated or its reference signal is time-shifted. In other words, the F&K spectral plot is different when the PSI algorithm is rotated or its reference is time-shifted. However, it is well known that these simple operations do not alter the basic phase demodulation properties of PSI algorithms, except for an unimportant piston. Here we propose a new way to analyze the spectra of PSI algorithms which is invariant to rotation and/or reference time-shift among other advantages over the nowadays standard PSI spectral analysis by F&K.
The general theory of phase shifting algorithms
(Optics Express, 2009) Quiroga Mellado, Juan Antonio; Estrada, Julio César; Servín Guirado, Manuel
We have been reporting several new techniques of analysis and synthesis applied to Phase Shifting Interferometry (PSI). These works are based upon the Frequency Transfer Function (FTF) and how this new tool of analysis and synthesis in PSI may be applied to obtain very general results, among them; rotational invariant spectrum; complex PSI algorithms synthesis based on simpler first and second order quadrature filters; more accurate formulae for estimating the detuning error; output-power phase noise estimation. We have made our cases exposing these aspects of PSI separately. Now in the light of a better understanding provided by our past works we present and expand in a more coherent and holistic way the general theory of PSI algorithms. We are also providing herein new material not reported before. These new results are on; a well defined way to combine PSI algorithms and recursive linear PSI algorithms to obtain resonant quadrature filters.
Phasorial analysis of detuning error in temporal phase shifting algorithms
(Optics Express, 2009) Quiroga Mellado, Juan Antonio; Mosiño, Juan Francisco; Servín Guirado, Manuel; Estrada, Julio César
Phase error analysis in Temporal Phase Shifting (TPS) algorithms due to frequency detuning has been to date only performed numerically. In this paper, we show an exact analytical expression to obtain this phase error due to detuning using the spectral TPS response. The new proposed method is based on the phasorial representation of the output of the TPS quadrature filter. Doing this, the detuning problem is reduced to a ratio of two symmetrical spectral responses of the quadrature filter at the detuned frequency. Finally, some popular cases of TPS algorithms are analyzed to show the usefulness of the proposed method.
Single fringe pattern with closed fringes demodulation using row by row scanners
(Interferometry XIII: Techniques and Analysis, 2006) Quiroga Mellado, Juan Antonio; Estrada, Julio César; Servín Guirado, Manuel; Marroquín Zaleta, José Luis
Sequential methods like the regularized phase tracker (RPT) are commonly used for fringe pattern demodulation with closed fringes. The only drawback of the RPT method is the necessity to implement a two-dimensional (2D) fringe following scanning in order to obtain the expected modulated phase. In this article we present a new method to demodulate single fringe patterns with closed fringes which use a simple 2D row by row scanning strategy. This is an important contribution because the 2D row by row scanning is extremely fast and easy to implement unlike the fringe following scanning. We have called this method the phase curvature tracker (PCT) because it uses the frequency curvature as regularizer to obtain the expected phase as a C^2 function with continuous curvature.
Easy and straightforward construction of wideband phase-shifting algorithms for interferometry
(Optics Letters, 2009) Quiroga Mellado, Juan Antonio; Servín Guirado, Manuel; Estrada, Julio César
We show a practical way for building wideband phase-shifting algorithms for interferometry. The idea presented combines first- and second-order quadrature filters to obtain wideband phase-shifting algorithms. These first- and second-order quadrature filters are analogous to the first- and second-order filters commonly used in communications engineering, named building blocks. We present a systematic way to develop phase-shifting algorithms with large detuning robustness or large bandwidth. In general, the approach presented here gives a powerful frequency analysis and design tool for phase-shifting algorithms robust to detuning for interferometry.
Path independent demodulation method for single image interferograms with closed fringes within the function space C^2
(Optics Express, 2006) Quiroga Mellado, Juan Antonio; Estrada, Julio César; Servín Guirado, Manuel; Marroquín Zaleta, José Luis
In the last few years, works have been published about demodulating Single Fringe Pattern Images (SFPI) with closed fringes. The two best known methods are the regularized phase tracker (RPT), and the two-dimensional Hilbert Transform method (2D-HT). In both cases, the demodulation success depends strongly on the path followed to obtain the expected estimation. Therefore, both RPT and 2D-HT are path dependent methods. In this paper, we show a novel method to demodulate SFPI with closed fringes which follow arbitrary sequential paths. Through the work presented here, we introduce a new technique to demodulate SFPI with estimations within the function space C ; in other words, estimations where the phase curvature is continuous. The technique developed here, uses a frequency estimator which searches into a frequency discrete set. It uses a second order potential regularizer to force the demodulation system to look into the function space C^2. The obtained estimator is a fast demodulator system for normalized SFPI with closed fringes. Some tests to demodulate SFPI with closed fringes using this technique following arbitrary paths are presented. The results are compared to those from RPT technique. Finally, an experimental normalized interferogram is demodulated with the herein suggested technique.
Steerable spatial phase shifting applied to single-image closed-fringe interferograms
(Applied Optics, 2009) Quiroga Mellado, Juan Antonio; Servín Guirado, Manuel; Estrada, Julio César; Gómez Pedrero, José Antonio
It is well known that spatial phase shifting interferometry (SPSI) may be used to demodulate two-dimensional (2D) spatial-carrier-interfrograms. In these crises the application of SPSI is straightforward because the modulating phase is a monotonic increasing function of space. However, this is not true when we apply SPSI to demodulate a single-image interferogram containing closed fringes. This is because using these algorithms, one would obtain a wrongly demodulated monotonic phase all over the 2D space. We present a technique to overcome this drawback and to allow any SPSI algorithm to be used as a single-image fringe pattern demodulator containing closed fringes. We make use of the 2D spatial orientation direction of the fringes to steer (orient) the one-dimensional SPSI algorithm in order to correctly demodulate the nonmonotonic 2D phase all over the interferogram.
Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry
(Optics Express, 2008) Quiroga Mellado, Juan Antonio; Servín Guirado, Manuel; Cywiak Garbarcewics, Moisés; Malacara Hernández, Daniel; Estrada, Julio César
It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to have more possibilities to phase demodulate them; even further, it would be even better to apply a quadrature filter having a spatial spread given by a real number to these 3 interferograms. In this paper we propose to do just that; namely we show how to demodulate a set of M-steps phase shifting images with a quadrature filter having a real-number as spatial spread. The interesting thing in this paper is to use a higher than M spread quadrature filter to demodulate our interferograms; in traditional PS interferometry one is stuck to the use of M step phase shifting formula to obtain the searched phase. Using a less than M PS formula is not interesting at all given that we would not use all the available information. The main idea behind the "squeezing" phase shifting method is to re-arrange the information of the M phase shifted fringe patterns in such a way to obtain a single carrier frequency interferogram (a spatio-temporal fringe image) and use any two dimensional quadrature filter to demodulate it. In particular we propose the use of Gabor quadrature filters with a spread given by real-numbers along the spatial coordinates. The Gabor filter may be designed in such way that we may squeeze the frequency response of the filter along any desired spatio-temporal dimension, and obtain better signal to noise demodulation ratio, and better harmonic rejection on the estimated phase.