Generalized phase shifting interferometry based on Lissajous calibration technology

Liu, Fengwei; Wu, Yirong; Wu, Fan; Song, Weihong

doi:10.1016/j.optlaseng.2016.03.003

Cited by 19 publications

(13 citation statements)

References 31 publications

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“…The CFI will be demodulated pixel by pixel, thereby permitting variations in background/modulation and local phase shift to be fully considered and well compensated. It also differs considerably from our previous LEF-based methods (ETC 27 , ETCI 9 ) the pixel-level Lissajous figure here is created using nonuniform illumination points. The background/modulation and even the local phase shift at each pixel can be simultaneously demodulated.…”

Section: Introductionmentioning

confidence: 96%

“…A well-calibrated phase shifter and stable environment are crucial factors to TPS due to equal steps conventionally used in phase-shifting algorithms (PSA) 3 , 4 . Though various kinds of generalized PSI have been put forward in recent years as a means of coping with random phase shift error caused by vibration 5 – 9 , it remains difficult to achieve real time phase demodulation in dynamic measurement operations since at least three interferograms are usually required in order to record and process data. Dynamic measurement is an attractive option not only in optical shop testing, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In our previously published works 9 , 27 , the Lissajous figure and ellipse-fitting (LEF) was shown to be effective in the correction of phase extraction errors in TPS and was successfully extended to a generalized PSA by combining with AIA. This differs from the PCA or other temporal PSA-based SCPS methods, which simply transfer the temporal PSA into SCPS to perform demodulation.…”

Section: Introductionmentioning

confidence: 99%

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Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

Liu

et al. 2018

Sci Rep

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Phase demodulation from a single carrier-frequency fringe pattern is becoming increasingly important particularly in areas of optical metrology such as dynamic interferometry, deflectometry and profilometry. The Fourier transform (FT) method and the spatial-carrier phase-shifting technique (SCPS) are two popular and well-established approaches to demodulation. However FT has the drawback of significant edge errors because of the Gibbs effect, whilst detuning errors for the local phase shift occur when SCPS is applied. A novel demodulation method based on pixel-level Lissajous figure and ellipse fitting (PLEF) is presented in this paper. Local demodulation in the spatial domain makes PLEF more flexible than the FT method, without spectral leakage. Based on a more adaptable approach, account is taken of variations in illumination and phase distribution over a few neighboring pixels. The mathematic demodulation model is of interest and has been demonstrated via simulation. Theoretical phase extraction error is as low as 10 −4 rad. Experiments further corroborate the effectiveness of the proposed method. In conclusion, various influencing factors, e.g. variations of background/modulation, phase amplitude, carrier frequency, additive noise that may affect the precision of PLEF are discussed in detail.Interferometry, deflectometry and profilometry are diagnostic tools frequently used in optical metrology to achieve highly accurate, non-contact and full-field measurements. Since the relevant physical information is usually encoded in the fringe phase, phase demodulation always plays a very critical role in fringe analysis. Temporal phase shifting (TPS) is a phase demodulation method, which has been used extensively in optical metrology since its introduction 1 .Phase shifting interferometry (PSI), for example, has already become a standard configuration of a modern high accuracy interferometer 2 . A well-calibrated phase shifter and stable environment are crucial factors to TPS due to equal steps conventionally used in phase-shifting algorithms (PSA) 3,4 . Though various kinds of generalized PSI have been put forward in recent years as a means of coping with random phase shift error caused by vibration 5-9 , it remains difficult to achieve real time phase demodulation in dynamic measurement operations since at least three interferograms are usually required in order to record and process data. Dynamic measurement is an attractive option not only in optical shop testing, e.g. high-aperture and long-distance primary mirror testing 10 but also in many other phase-demodulation operations, e.g. visual monitoring of cell culture in the biomedical domain 11 . With the exception of simultaneous phase shifting interferometry (SPSI) 12 , which is not our concern in this contribution, demodulation of a single shot fringe pattern is an attractive option. The spatial carrier-frequency (SCF) method is a good choice since implementation of spatial carrier-frequency interferometry (SCFI) is relatively easily accomplished on most advan...

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

Liu

et al. 2018

Sci Rep

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“…Equation ( 12) constitutes the corrected PCA-nPSA formula. The Lissajous ellipses are then transformed into circles without explicitly knowing the nonuniform phase-steps 0 1 { ,..., } N    [27][28][29][30][31].…”

Section: Correcting the Lissajous Ellipse Of The Pca-npsa Analytic Si...mentioning

confidence: 99%

“…For erroneous phase demodulation, the Lissajous figure of the analytic signal is not a circle, it is an ellipse. The ellipse fitting method convert the Lissajous ellipse into a Lissajous circle, and the phase demodulation error is eliminated [27][28][29][30][31][32]. The Lissajous technique is a powerful technique to correct phase demodulation errors; it is currently based on least squares fitting of a rotated and origin-shifted ellipse; this has however its own difficulties which are sometimes not trivially solved [27][28][29][30][31][32].…”

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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A novel algorithm based on sub-fringe integration method for direct two-dimensional unwrapping phase reconstruction from the intensity of one-shot two-beam interference fringes

El‐Morsy

2019

Appl. Phys. B

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Generalized phase shifting interferometry based on Lissajous calibration technology

Cited by 19 publications

References 31 publications

Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

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

A novel algorithm based on sub-fringe integration method for direct two-dimensional unwrapping phase reconstruction from the intensity of one-shot two-beam interference fringes

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