Abstract

Based on wavelet transforms (WTs), an alternative multi-frequency fringe projection profilometry is described. Fringe patterns with multiple frequencies are projected onto an object and the reflected patterns are recorded digitally. Phase information for every pattern is calculated by identifying the ridge that appears in WT results. Distinct from the phase unwrapping process, a peak searching algorithm is applied to obtain object height from the phases of the different frequency for a single point on the object. Thus, objects with large discontinuities can be profiled. In comparing methods, the height profiles obtained from the WTs have lower noise and higher measurement accuracy. Although measuring times are similar, the proposed method offers greater reliability.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. Y. Xu, S. Jia, Q. Bao, H. Chen, and J. Yang, “Recovery of absolute height from wrapped phase maps for fringe projection profilometry,” Opt. Express 22(14), 16819–16828 (2014).
    [Crossref] [PubMed]
  16. X. Zhou and H. Zhao, “Three-dimensional profilometry based on mexican hat wavelet transform,” Acta Opt. Sin. 29(1), 197–202 (2009).
    [Crossref]

2014 (1)

2013 (1)

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

2010 (1)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

2009 (2)

2005 (1)

2004 (3)

J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43(26), 4993–4998 (2004).
[Crossref] [PubMed]

A. Durson, S. Ozder, and N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
[Crossref]

X. Y. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

2003 (1)

D. Ganotra, J. Joseph, and K. Singh, “Second- and first-order phase-locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion,” Opt. Commun. 217(1-6), 85–96 (2003).
[Crossref]

2001 (3)

2000 (1)

F. Chen, G. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–222 (2000).
[Crossref]

1997 (1)

C. A. Hobson, H. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27(4), 355–368 (1997).
[Crossref]

1990 (1)

J. Li, X. Y. Su, and L. Y. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Atkinson, H. T.

C. A. Hobson, H. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27(4), 355–368 (1997).
[Crossref]

Bao, Q.

Borghesi, M.

Brown, G.

F. Chen, G. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–222 (2000).
[Crossref]

Chen, F.

F. Chen, G. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–222 (2000).
[Crossref]

Chen, H.

Chen, W.

X. Y. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

X. Y. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Durson, A.

A. Durson, S. Ozder, and N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
[Crossref]

Ecevit, N.

A. Durson, S. Ozder, and N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
[Crossref]

Galimberti, M.

Ganotra, D.

D. Ganotra, J. Joseph, and K. Singh, “Second- and first-order phase-locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion,” Opt. Commun. 217(1-6), 85–96 (2003).
[Crossref]

Giulietti, A.

Giulietti, D.

Gizzi, L. A.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guo, L. Y.

J. Li, X. Y. Su, and L. Y. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Hobson, C. A.

C. A. Hobson, H. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27(4), 355–368 (1997).
[Crossref]

Jia, S.

Jia, S. H.

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

Joseph, J.

D. Ganotra, J. Joseph, and K. Singh, “Second- and first-order phase-locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion,” Opt. Commun. 217(1-6), 85–96 (2003).
[Crossref]

Li, J.

J. Li, X. Y. Su, and L. Y. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Lilley, F.

C. A. Hobson, H. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27(4), 355–368 (1997).
[Crossref]

Luo, X.

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

Ozder, S.

A. Durson, S. Ozder, and N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
[Crossref]

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Singh, K.

D. Ganotra, J. Joseph, and K. Singh, “Second- and first-order phase-locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion,” Opt. Commun. 217(1-6), 85–96 (2003).
[Crossref]

Song, M.

F. Chen, G. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–222 (2000).
[Crossref]

Su, X. Y.

X. Y. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

X. Y. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

J. Li, X. Y. Su, and L. Y. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Tomassini, P.

Weng, J.

Willi, O.

Xiong, L.

Xu, Y.

Y. Xu, S. Jia, Q. Bao, H. Chen, and J. Yang, “Recovery of absolute height from wrapped phase maps for fringe projection profilometry,” Opt. Express 22(14), 16819–16828 (2014).
[Crossref] [PubMed]

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

Yang, J.

Y. Xu, S. Jia, Q. Bao, H. Chen, and J. Yang, “Recovery of absolute height from wrapped phase maps for fringe projection profilometry,” Opt. Express 22(14), 16819–16828 (2014).
[Crossref] [PubMed]

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

Zhang, Y.

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

J. Zhong and Y. Zhang, “Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry,” Appl. Opt. 40(4), 492–500 (2001).
[Crossref] [PubMed]

Zhao, H.

X. Zhou and H. Zhao, “Three-dimensional profilometry based on mexican hat wavelet transform,” Acta Opt. Sin. 29(1), 197–202 (2009).
[Crossref]

Zhong, J.

Zhou, X.

X. Zhou and H. Zhao, “Three-dimensional profilometry based on mexican hat wavelet transform,” Acta Opt. Sin. 29(1), 197–202 (2009).
[Crossref]

Acta Opt. Sin. (1)

X. Zhou and H. Zhao, “Three-dimensional profilometry based on mexican hat wavelet transform,” Acta Opt. Sin. 29(1), 197–202 (2009).
[Crossref]

Appl. Opt. (3)

Meas. Sci. Technol. (1)

A. Durson, S. Ozder, and N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
[Crossref]

Opt. Commun. (2)

Y. Xu, S. H. Jia, X. Luo, J. Yang, and Y. Zhang, “Multi-frequency projected fringe profilometry for measuring objects with large depth discontinuities,” Opt. Commun. 288, 27–30 (2013).
[Crossref]

D. Ganotra, J. Joseph, and K. Singh, “Second- and first-order phase-locked loops in fringe profilometry and application of neural networks for phase-to-depth conversion,” Opt. Commun. 217(1-6), 85–96 (2003).
[Crossref]

Opt. Eng. (2)

F. Chen, G. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–222 (2000).
[Crossref]

J. Li, X. Y. Su, and L. Y. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (4)

C. A. Hobson, H. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27(4), 355–368 (1997).
[Crossref]

X. Y. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

X. Y. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Opt. Lett. (2)

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Figures (9)

Fig. 1
Fig. 1 System layout of multi-frequency fringe projection profilometry on WT.
Fig. 2
Fig. 2 The optical geometry of the fringe projection profilometry.
Fig. 3
Fig. 3 (a) The semi sphere simulated in MATLAB. (b) The simulated reflected fringe pattern. (c) The relationship between the intensity and pixel position in column 200. (d) Time and frequency information of the sinusoidal fringe in column 200. (e) The phase result of the sinusoidal fringe in column 200 by using Eq. (6). (f) The phase map of the fringe pattern using complex Morlet 1D CWT.
Fig. 4
Fig. 4 Illustrative curve of the peak signal S(h) of Eq. (14).
Fig. 5
Fig. 5 Work piece profiled in the experiment.
Fig. 6
Fig. 6 (a) Image of the reflected fringe pattern with a certain frequency. (b) Wrapped phase map of the object calculated using the complex Morlet 1D CWT.
Fig. 7
Fig. 7 (a) Gray-scale image of the object measured. (b) Reconstructed 3D shape of the work piece measured.
Fig. 8
Fig. 8 (a) Reconstructed 3D shape of the work piece calculated using the 5-step phase shifting method. (b) Reconstructed 3D shape of the work piece calculated using the FTP method. (c) Reconstructed 3D shape of the work piece calculated using the Mexican hat 1D CWT. (d) Reconstructed 3D shape of the work piece calculated using the complex Morlet 1D CWT.
Fig. 9
Fig. 9 (a) Comparison profiles of a work piece calculated using four distinct methods at low noise area. (b) Comparison profiles of a work piece calculated using four distinct methods at high noise area.

Tables (1)

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Table 1 The error statistics of the reconstructed results using FTP, Mexh and Cmor

Equations (17)

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I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + φ I ( x , y ) ]
O ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + φ O ( x , y ) ] .
ψ ( x ) = π 1 / 4 exp ( i c x ) exp ( x 2 / 2 ) .
ψ b , x ( x ) = 1 s ψ ( x b s ) ,
W ( s , b ) = ψ * b , x ( x ) I ( x ) d x .
φ ( s , b ) = tan 1 [ i m a g ( W ( s , b ) ) r e a l ( W ( s , b ) ) ] ,
d φ ( x , y ) = φ O ( x , y ) φ I ( x , y ) ,
d φ ( x , y ) = 2 π f 0 d × H ( x , y ) / l 0 .
S ( h ) = 1 K k = 1 K cos [ C k h d φ ( x , y ) ] ,
C k = 2 π f k d / l 0 ,
S ( h ) = 1 K k = 1 K cos [ 2 π f k d l 0 h d φ ( x , y ) ] .
S ( h ) = 1 K | k = 1 K exp { [ 2 π f k d l 0 ( h H ) ] × i } | .
f k = f k 1 + m ,
S ( h ) = 1 K × sin ( K α ) sin ( α ) ,
α = 2 π d l 0 × m 2 ( h H ) .
F r e e H e i g h t = l 0 d m .
r e s o l u t i o n = ϕ × l 0 2 π f 0 × d ,

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