Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window

Groot, Peter J. de

doi:10.1364/ao.34.004723

Cited by 221 publications

(93 citation statements)

References 9 publications

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“…Figures 15-17 show the estimated phase errors of N=0.03. To compare these results with Fig.8 of the 7-frame algorithm which is reported as a vibration and noise-immune algorithm 7) , the vertical distribution widths of the phase errors due to the noisy signals are all nearly the same. Therefore, this algorithm is thought to have noise-immunity.…”

Section: Discussion and Considerationsmentioning

confidence: 89%

“…They are 4-frame Carre 4) , simple 4-frame 5) , 5-frame Hariharan 6) , 7-frame Groot 7) , 5-frame in Schmit 8) , and 6-frame in Hibino 9) algorithms. There are many other algorithms and still others may be in development 12) , but they are not identified here, because of restricted space in the paper.…”

Section: Error Estimations Of Representative Algorithms For White -Limentioning

confidence: 99%

“…The estimated algorithms are of 4-frame Carre 4) , simple 4-frame 5) , 5-frame Hariharan 6) , 7-frame Groot 7) , 5-frame in Schmit 8) , and 6-frame in Hibino 9) . Among the algorithms the one satisfying the former requirement is found to be the 7-frame Groot algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

Adachi

2008

OPT REV

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White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements.To find an algorithm which will satisfy the requirements, I extract individual terms (I j m I k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I j is light intensity just after the j-th phase shift. Using computer simulations, I 1 search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.

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Section: Discussion and Considerationsmentioning

confidence: 89%

Section: Error Estimations Of Representative Algorithms For White -Limentioning

confidence: 99%

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Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

Adachi

2008

OPT REV

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“…Fringe projection techniques [1][2][3][4] are exploiting and parallelizing this triangulation principle to eventually give access to the surface topology of an object. The most widespread technique to retrieve unambiguously this surface height information requires at least three frames with corresponding phase-shifted fringe patterns and uses one of the numerous available phase-shifting algorithms [5][6][7][8][9]. Though acknowledged to be the soundest technique in terms of spatial resolution and measurement accuracy, it necessitates the capture of several images at different instants.…”

Section: Introductionmentioning

confidence: 99%

Snap-shot profilometry with the Empirical Mode Decomposition and a 3-layer color sensor

2011

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Remote sensing finds more and more applications, from industrial control, to face recognition, not forgetting terrain surveying. This trend is well exemplified by fringe projection techniques, which enjoyed a considerable development in the recent years. In addition of high requirement in terms of measurement accuracy and spatial resolution, the end-users of full-field techniques show a growing interest for dynamic regimes. We report here what we believe to be the use for the first time of a CMOS 3-layer color sensor (Foveon X3) as the key element of a RGB fringe projection system, together with the processing specifically elaborated for this sensor. The 3-layer architecture allows the simultaneous recording of three phase-shifted fringe patterns and features the precious asset of an unambiguous relationship between the physical sensor pixel and the picture pixel and this for each color layer, on the contrary of common color sensor arrays (Bayer mosaic and tri-CCD). Due to the overlapping of the spectral responses of the layers, color transformation is mandatory to achieve the separation of the three phase-shifted RGB projected fringe patterns. In addition, we propose the use of the Empirical Mode Decomposition to equalize the non-uniform responses of the three layers. Although the conversion of the phase into a height is of primary importance in an actual measurement, it is not treated here, the literature being profuse on the central projection model. 6. P. Groot, "Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window," Appl. Opt. 34(22), 4723-4730 (1995). 7. D. W. Phillion, "General methods for generating phase-shifting interferometry algorithms," Appl. Opt. 36(31), 8098-8115 (1997). 8. Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35(1), 51-60 (1996). 9. J. Novak, P. Novak, and A. Miks, "Multi-step phase-shifting algorithms insensitive to linear phase shift errors," ©2011 Optical Society of AmericaOpt. Commun. 281(21), 5302-5309 (2008). 10. X. Colonna de Lega, and P. Jacquot, "Deformation measurement with object-induced dynamic phase shifting," Appl. Opt. 35(25), 5115-5121 (1996). 11. C. Wust, and D. W. Capson, "Surface profile measurement using color fringe projection," Mach. Vis. Appl. 4(3), 193-203 (1991 550-558 (2010). 22. S. Equis, and P. Jacquot, "The empirical mode decomposition: a must-have tool in speckle interferometry?" Opt.Express 17(2), 611-623 (2009). 23. H. A. Aebischer, and S. Waldner, "Simple and effective method for filtering speckle interferometric phase fringe patterns," Opt. Commun. 162(4-6), 205-210 (1999).

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“…Nowadays, spectral analysis is the gold-standard reference to compare among several PSAs. Most people uses this spectra to visualize and gauge among several promising PSAs, and choose the best one for their needs [4][5][6][7][8]11,12].…”

Section: Introductionmentioning

confidence: 99%

Design of phase-shifting algorithms by fine-tuning spectral shaping

Gonzalez¹,

Servı́n²,

Estrada³

et al. 2011

Opt. Express

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Abstract:To estimate the modulating wavefront of an interferogram in Phase Shifting Interferometry (PSI) one frequently uses a Phase Shifting Algorithm (PSA). All PSAs take as input N phase-shifted interferometric measures, and give an estimation of their modulating phase. The first and best known PSA designed explicitly to reduce a systematic error source (detuning) was the 5-steps, Schwider-Hariharan (SH-PSA) PSA. Since then, dozens of PSAs have been published, designed to reduce specific data error sources on the demodulated phase. In Electrical Engineering the Frequency Transfer Function (FTF) of their linear filters is their standard design tool. Recently the FTF is also being used to design PSAs. In this paper we propose a technique for designing PSAs by fine-tuning the few spectral zeroes of a PSA to approximate a template FTF spectrum. The PSA's spectral zeroes are moved (tuned) while gauging the plot changes on the resulting FTF's magnitude.

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Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window

Cited by 221 publications

References 9 publications

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

Snap-shot profilometry with the Empirical Mode Decomposition and a 3-layer color sensor

Design of phase-shifting algorithms by fine-tuning spectral shaping

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