Generalized phase-shifting interferometry by parameter estimation with the least squares method

Juarez-Salazar, Rigoberto; Robledo-Sánchez, Carlos; Meneses-Fabian, Cruz; Guerrero-Sanchez, Fermin; Aguilar, L. M. Arévalo

doi:10.1016/j.optlaseng.2012.12.020

Cited by 52 publications

(14 citation statements)

References 38 publications

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“…Namely, Fourier fringe-normalized analysis [36], and the generalized phase-shifting algorithm for inhomogeneous phase shift and spatiotemporal fringe visibility variation [21,37]. Although this last was devised from the viewpoint of phase shifting, it can be classified into the hybrid carrier category.…”

Section: Wrapped Phase Extractionmentioning

confidence: 99%

“…Additionally, other desirable properties for phase-shifting techniques are a reduced number of necessary fringe patterns, maximum contrast, and the capacity to handle spatiotemporal visibility (i.e., the background and modulation light are functions of both p and k) [37,59,[60][61][62]. For this, a generalized phase-shifting algorithm was proposed [21].…”

Section: Generalized Phase-shifting Algorithm To Inhomogeneous Phamentioning

confidence: 99%

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Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

2015

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Some advances in fringe analysis technology for phase computing are presented. A full scheme for phase evaluation, applicable to automatic applications, is proposed. The proposal consists of: a fringe-pattern normalization method, Fourier fringe-normalized analysis, generalized phase-shifting processing for inhomogeneous nonlinear phase shifts and spatiotemporal visibility, and a phase-unwrapping method by a rounding-least-squares approach. The theoretical principles of each algorithm are given. Numerical examples and an experimental evaluation are presented.

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Section: Wrapped Phase Extractionmentioning

confidence: 99%

Section: Generalized Phase-shifting Algorithm To Inhomogeneous Phamentioning

confidence: 99%

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

2015

Self Cite

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“…The quadratic polynomial is used for the fitting (Copeland, 2012 andJuarez-Salazar et al, 2013) U ¼ spanf1; t; tg; / 0 ðtÞ ¼ 1; / 1 ðtÞ ¼ t; / 2 ðtÞ ¼ t 2 ; 3 5 ) 4a 0 þ 22a 1 þ 166a 2 ¼ 25:44 22a 0 þ 166a 1 þ 1408a 2 ¼ 136:53 166a 0 þ 1408a 1 þ 12568a 2 ¼ 1029:09:…”

Section: The Lowest Acidification Pointmentioning

confidence: 99%

Acid inhibition during anaerobic digestion of biodegradable kitchen waste

Dai

et al. 2015

Journal of Renewable and Sustainable Energy

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The aim of this work was to investigate the acid inhibition during the anaerobic digestion of kitchen waste. Four biodegradable substrates of soybean, fat meat, rice, and celery cane were considered in this paper. A series of anaerobic codigestion tests were performed on the four substrates at the load of 1.0 gVS/(lÁday) and anaerobic granular sludge. The results show that the acid inhibition was occurred at the load of 1.0 gVS/(lÁday) for the soybean and rice; the corresponding pH values at the lowest acidification points were 5.03 and 3.73, respectively. There was no acid inhibition during the whole digestion period for the celery cane substrate. And the results also reveal that the order of the cumulative gas yields for different substrates from highest to lowest is: celery cane > soybean > fat meat > rice; while the order of the average methane (CH 4 ) percentage from highest to lowest is: celery cane > fat meat > soybean > rice. Finally, the method to calculate the lowest acidification points of the four substrates was provided by the least squares method, and it is verified by the measured data, and good agreement is found. V C 2015 AIP Publishing LLC. [http://dx.

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“…Traditionally phase shifting algorithms (PSAs) require precise phase-shifting steps, however, it is not easy to be absolutely sure that an interferometer have a zero-error phase-shifter. Therefore, methods to estimate nonuniform phase-shifting steps and the desired modulating phase from nonlinear phase-shifted data have been investigated [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The Lissajous ellipse fitting technique is one of the earliest phase demodulation methods for dealing with nonuniform phase-stepped images [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Fourier spectra for nonuniform phase-shifting algorithms based on principal component analysis

Servı́n¹,

Padilla²,

Garnica³

et al. 2019

Opt. Express

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We develop an error-free, nonuniform phase-stepping algorithm (nPSA) based on principal component analysis (PCA). PCA-based algorithms typically give phasedemodulation errors when applied to nonuniform phase-shifted interferograms. We present a straightforward way to correct those PCA phase-demodulation errors. We give mathematical formulas to fully analyze PCA-based nPSA (PCA-nPSA). These formulas give a) the PCA-nPSA frequency transfer function (FTF), b) its corrected Lissajous figure, c) the corrected PCA-nPSA formula, d) its harmonic robustness (R H ), and e) its signal-to-noise-ratio (SNR). We show that the PCA-nPSA can be seen as a linear quadrature filter, and as consequence, one can find its FTF. Using the FTF, we show why plain PCA often fails to demodulate nonuniform phase-shifted fringes. Previous works on PCA-nPSA (without FTF), give specific numerical/experimental fringe data to "visually demonstrate" that their new nPSA works better than competitors. This often leads to biased/favorable fringe pattern selections which "visually demonstrate" the superior performance of their new nPSA. This biasing is herein totally avoided because we provide figures-of-merit formulas based on linear systems and stochastic process theories. However, and for illustrative purposes only, we provide specific fringe data phase-demodulation, including comprehensive analysis and comparisons.2019-04-01 Centro de Investigaciones en Optica A. C.

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Generalized phase-shifting interferometry by parameter estimation with the least squares method

Cited by 52 publications

References 38 publications

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

Acid inhibition during anaerobic digestion of biodegradable kitchen waste

Fourier spectra for nonuniform phase-shifting algorithms based on principal component analysis

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