Generalization of the Principal Component Analysis algorithm for interferometry

Vargas, Javier; Sorzano, Carlos Óscar S.; Estrada, J. C.; Carazo, José-Marı́a

doi:10.1016/j.optcom.2012.09.017

Cited by 67 publications

(39 citation statements)

References 6 publications

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“…The first work on PCA as nPSA was presented as a linear algorithm which could demodulate any set of phase-shifted fringes, almost error-free [33]. Afterwards this was found not to be exact and several attempts have been made to improve plain PCA [35,[38][39][40]. However, the PCA can be combined with AIA, obtaining a PCA-AIA algorithm which eliminate the phase-errors left by plain PCA [35].…”

Section: Pca-npsa Phase Demodulation Formulamentioning

confidence: 99%

“…Afterwards this was found not to be exact and several attempts have been made to improve plain PCA [35,[38][39][40]. However, the PCA can be combined with AIA, obtaining a PCA-AIA algorithm which eliminate the phase-errors left by plain PCA [35]. The PCA providing the first phase estimation making the AIA to converge faster [35].…”

Section: Pca-npsa Phase Demodulation Formulamentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Pca-npsa Phase Demodulation Formulamentioning

confidence: 99%

Section: Pca-npsa Phase Demodulation Formulamentioning

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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show abstract

“…In addition, PCA is inherently resistant to harmonics or/and other issues such as over or under exposure that might arise from image capture. If necessary, the proposed algorithm can be improved using iterative least squares techniques [11][12].…”

Section: Introductionmentioning

confidence: 99%

Application of principal component analysis in phase-shifting photoelasticity

Quiroga¹,

Gómez‐Pedrero

2016

Opt. Express

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Principal Component Analysis Phase Shifting (PCA) is a useful tool for fringe pattern demodulation in phase shifting interferometry. The PCA has no restrictions on background intensity, fringe modulation and it is a self-calibrating Phase Sampling Algorithm (PSA). Moreover, the technique is well suited for analyzing arbitrary sets of phase-shifted interferograms due to its low computational cost. In this work, we have adapted the standard phase shifting algorithm based on the PCA to the particular case of photoelastic fringe patterns. Compared with conventional PSAs used in photoelasticity, the PCA method does not need calibrated phase steps and, given that it can deal with an arbitrary number of images, it presents good noise rejection properties, even for complicated cases such as low order isochromatic photoelastic patterns.

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“…In recent years, many achievements related to PSI have been presented, especially phase retrieval and phase shift extraction [3][4][5][6][7][8][9][10]. In standard PSI, to retrieval the measured phase, a sequence of N-step phase-shifting interferograms (N ≥ 3) with the known phase shift are required.…”

Section: Introductionmentioning

confidence: 99%

A derivative method of phase retrieval based on two interferograms with an unknown phase shift

Wang

et al. 2016

Optik

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Generalization of the Principal Component Analysis algorithm for interferometry

Cited by 67 publications

References 6 publications

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

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

Application of principal component analysis in phase-shifting photoelasticity

A derivative method of phase retrieval based on two interferograms with an unknown phase shift

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