Abstract

A novel multi-frequency fringe projection profilometry is presented in this paper. Fringe patterns with multiple frequencies are projected onto an object by a digital micro-mirror device projector. The approach involves an improved Fourier transform profilometry method with an additional π phase shifting stage and hence the acquisition of two source images. A peak searching algorithm is then employed to obtain the real height profile of the object together with a mathematical proof of this algorithm. In our method, the height of each point on the object is measured independently and the phase unwrapping procedure is avoided, enabling the measurement of objects with large depth discontinuities, where the phase unwrapping is difficult. The measurement result is given to validate the method in the paper. Our technique has great potential in industrial applications where the measurement of objects with complex shape and large discontinuities is needed.

© 2014 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
    [Crossref]
  2. E. Li, X. Peng, J. Xi, J. Chicharo, J. Yao, and D. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry,” Opt. Express 13(5), 1561–1569 (2005).
    [Crossref] [PubMed]
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    [PubMed]
  4. X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
    [Crossref]
  5. H. Zhang, M. J. Lalor, and D. R. Burton, “Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry,” Appl. Opt. 38(16), 3534–3541 (1999).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. X. Y. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
    [Crossref]
  8. 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]
  9. X. Y. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
    [Crossref]
  10. L. D. Xiong and S. H. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett. 34(15), 2363–2365 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. J. M. Huntley and H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14(12), 3188–3196 (1997).
    [Crossref]
  14. J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36(1), 277–280 (1997).
    [Crossref] [PubMed]
  15. Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19(6), 5149–5155 (2011).
    [Crossref] [PubMed]
  16. E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express 17(10), 7818–7830 (2009).
    [Crossref] [PubMed]
  17. C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244 (1997).
    [Crossref]
  18. 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]
  19. J. Li J, X. Y. Su, and L. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).

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]

2011 (1)

2009 (2)

2005 (1)

2004 (1)

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

2001 (1)

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

2000 (1)

F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

1999 (1)

1997 (5)

1993 (1)

1992 (1)

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

1990 (1)

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

1983 (2)

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]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Burton, D. R.

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

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]

Chicharo, J.

Guo, L.

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

Hahn, J.

Halioua, M.

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]

Huntley, J. M.

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]

L. D. Xiong and S. H. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett. 34(15), 2363–2365 (2009).
[Crossref] [PubMed]

Kim, E. H.

Kim, H.

Lalor, M. J.

Lee, B.

Li, E.

Li, J. L.

Li J, J.

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

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]

Liu, H. C.

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]

Mutoh, K.

Peng, X.

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244 (1997).
[Crossref]

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244 (1997).
[Crossref]

Saldner, H. O.

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Su, H. J.

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. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36(1), 277–280 (1997).
[Crossref] [PubMed]

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

Su, X.-Y.

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Takeda, M.

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244 (1997).
[Crossref]

von Bally, G.

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Vrinivasan, S.

Vukicevic, D.

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Wang, Y.

Xi, J.

Xiong, L. D.

Xu, 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]

Yang, J.

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]

Yao, J.

Zhang, D.

Zhang, H.

Zhang, S.

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]

Zhou, W.-S.

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

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]

X.-Y. Su, W.-S. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Opt. Eng. (2)

F. Chen, G. M. Brown, and M. Song, “Overview of the three-dimensional shape measurement using optical method,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

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

Opt. Express (3)

Opt. Lasers Eng. (3)

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

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]

Opt. Lett. (1)

Proc. SPIE (1)

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244 (1997).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 System layout of fringe projection profilometry.

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Fig. 2
Fig. 2 The optical geometry of fringe projection profilometry.

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Fig. 3
Fig. 3 Spatial frequency spectra of deformed grating pattern.

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Fig. 4
Fig. 4 The simulated curve of Eq. (14) by Matlab.

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Fig. 5
Fig. 5 The object used in the experiment.

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Fig. 6
Fig. 6 (a) Image without background intensity and higher spectrum, (b) Wrapped phase map calculated by Fourier Transform.

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Fig. 7
Fig. 7 The curve of Eq. (14) for point (120,120) in the experiment.

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Fig. 8
Fig. 8 The reconstructed 3D shape of the object.

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Equations (24)

Equations on this page are rendered with MathJax. Learn more.

O(x,y)=a(x,y)+b(x,y)cos[ 2π f 0 x+ φ O (x,y) ]
I(x,y)=a(x,y)+b(x,y)cos[ 2π f 0 x+ φ I (x,y) ]
O 1 (x,y)=a(x,y)+b(x,y)cos[ 2π f 0 x+ φ O (x,y) ]
O 2 (x,y)=a(x,y)+b(x,y)cos[ 2π f 0 x+ φ O (x,y)+π ]
O 0 (x,y)= O 1 (x,y)- O 2 (x,y)=2b(x,y)cos[ 2π f 0 x+ φ O (x,y) ]
I 0 (x,y)= I 1 (x,y)- I 2 (x,y)=2b(x,y)cos[ 2π f 0 x+ φ I (x,y) ]
O 0 ~ (x,y)=2b(x,y)exp[ i2π f 0 x+i φ O (x,y) ]
I 0 ~ (x,y)=2b(x,y)exp[ i2π f 0 x+i φ I (x,y) ]
Δφ(x,y)= φ O (x,y)- φ I (x,y)=arctan Im[ O 0 ~ (x,y) I 0 * ~ (x,y) ] Re[ O 0 ~ (x,y) I 0 * ~ (x,y) ]
H(x,y)= l 0 Δφ(x,y) [ Δφ(x,y)-2π f 0 d ]
H(x,y)= l 0 Δφ(x,y) 2π f 0 d
S(h)= 1 K ∑ k=1 K cos[ C k h-Δφ(x,y) ]
S(h)= 1 K ∑ k=1 K cos[ 2π f k d l 0 h-Δφ(x,y) ]
S(h)= 1 K | ∑ k=1 K exp{ [ 2π f k d l 0 h-Δφ(x,y) ]·i } |
S(h)= 1 K | ∑ k=1 K exp{ [ 2π f k d l 0 ( h-H ) ]·i } |
g(h)= ∑ k=1 K exp{ [ 2π f k d l 0 ( h-H ) ]·i }
f k = f k-1 +m
g(h)= exp[ 2π f 1 d l 0 (h-H)·i ]·{ 1-exp[ 2πKmd l 0 (h-H)·i ] } 1-exp[ 2πmd l 0 (h-H)·i ]
g(h)=exp[ 2π f 1 d l 0 (h-H)·i ]× exp[ 2πd l 0 × Km 2 (h−H)·i ] exp[ 2πd l 0 × m 2 (h−H)·i ]                            × exp[ 2πd l 0 ×( − Km 2 )(h−H)·i ]−exp[ 2πd l 0 × Km 2 (h−H)·i ] exp[ 2πd l 0 ×( − m 2 )(h−H)·i ]−exp[ 2πd l 0 × m 2 (h−H)·i ]
α= 2πd l 0 × m 2 (h-H)
g(h)= exp( iKα ) exp(iα) × sin( Kα ) sin( α ) ×exp( 2α f 1 m ·i )= sin( Kα ) sin( α ) ×exp[ ( K-1 )α+ 2α f 1 m ]·i
S(h)= 1 K | g(h) |= 1 K g(h)× g * (h) = 1 K × sin( Kα ) sin( α )
FreeHeight= l 0 dm
Resolution= l 0 dKm = l 0 d( f k - f 1 )

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