Abstract

The aim in this work is the development of an image analysis technique for 3D shape acquisition, based on luminous fringe projections. In more detail, the method is based on the simultaneous use of several projectors, which is desirable whenever the surface under inspection has a complex geometry, with undercuts or shadow areas. In these cases, the usual fringe projection technique needs to perform several acquisitions, each time moving the projector or using several projectors alternately. Besides the procedure of fringe projection and phase calculation, an unwrap algorithm has been developed in order to obtain continuous phase maps needed in following calculations for shape extraction. With the technique of simultaneous projections, oriented in such a way to cover all of the surface, it is possible to increase the speed of the acquisition process and avoid the postprocessing problems related to the matching of different point clouds.

© 2009 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, “Overview of three dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
    [CrossRef]
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    [CrossRef]
  3. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier1993).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. S. Xianyu and C. Wenjing, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
    [CrossRef]
  9. L. Su, X. Su, W. Li, and L. Xiang, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153-1158 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. X. Cheng, X. Su, and L. Guo, “Automated measurement method for 360° profilometry of 3-D diffuse objects,” Appl. Opt. 30, 1274-1278 (1991).
    [CrossRef] [PubMed]
  12. A. Asundi and Z. Wensen, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38, 3556-3561 (1999).
    [CrossRef]
  13. G. Häusler and D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. 32, 7164-7169(1993).
    [CrossRef] [PubMed]
  14. Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
    [CrossRef]
  15. W. S. Zhou and X. X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89-93 (1994).
    [CrossRef]
  16. J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
    [CrossRef]
  17. X. Liang and X. Su, “Computer simulation of a 3-D sensing system with structured illumination,” Opt. Lasers Eng. 27, 379-393 (1997).
    [CrossRef]
  18. 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, 3534-3541 (1999).
    [CrossRef]
  19. C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
    [CrossRef]
  20. W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 143-149 (2000).
    [CrossRef]
  21. M. J. Tsai and C. C. Hung, “Development of a high precision surface metrology system using structured light projection,” Measurement 38, 236-247 (2005).
    [CrossRef]
  22. T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199-239 (1994).
    [CrossRef]
  23. H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497-4500 (1994).
    [CrossRef] [PubMed]
  24. H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770-2775 (1997).
    [CrossRef] [PubMed]
  25. J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986-992 (1997).
    [CrossRef]
  26. G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38, 6565-6573 (1999).
    [CrossRef]
  27. C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
    [CrossRef]
  28. J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
    [CrossRef]
  29. B. S. Gilbert and J. H. Blatt, “Enhanced three-dimensional reconstruction of surfaces using multicolor gratings,” Opt. Eng. 39, 52-60 (2000).
    [CrossRef]
  30. Z. Zhang, “A flexible new technique for camera calibration,” Technical Report MSR-TR-98-71 (Microsoft Research, 1998).
  31. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Rob. Autom. 3, 323-344 (1987).
    [CrossRef]

2008 (2)

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
[CrossRef]

J. A. N. Buytaert and J. J. J. Dirckx, “Moiré profilometry using liquid crystals for projection and demodulation,” Opt. Express 16, 179-193 (2008).
[CrossRef] [PubMed]

2005 (2)

M. J. Tsai and C. C. Hung, “Development of a high precision surface metrology system using structured light projection,” Measurement 38, 236-247 (2005).
[CrossRef]

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring with projection moiré,” Opt. Eng. 44, 093605 (2005).
[CrossRef]

2004 (1)

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231-240 (2004).
[CrossRef]

2001 (1)

S. Xianyu and C. Wenjing, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

2000 (5)

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

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

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

B. S. Gilbert and J. H. Blatt, “Enhanced three-dimensional reconstruction of surfaces using multicolor gratings,” Opt. Eng. 39, 52-60 (2000).
[CrossRef]

1999 (4)

1998 (1)

J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
[CrossRef]

1997 (3)

X. Liang and X. Su, “Computer simulation of a 3-D sensing system with structured illumination,” Opt. Lasers Eng. 27, 379-393 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

1994 (3)

H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497-4500 (1994).
[CrossRef] [PubMed]

W. S. Zhou and X. X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89-93 (1994).
[CrossRef]

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

1993 (1)

1991 (1)

1987 (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Rob. Autom. 3, 323-344 (1987).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

Asundi, A.

Blais, F.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231-240 (2004).
[CrossRef]

Blatt, J. H.

B. S. Gilbert and J. H. Blatt, “Enhanced three-dimensional reconstruction of surfaces using multicolor gratings,” Opt. Eng. 39, 52-60 (2000).
[CrossRef]

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Brown, G. M.

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

Bryanston-Cross, P. J.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

Burton, D. R.

Buytaert, J. A. N.

Carocci, M.

Chen, F.

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

Chen, W.

Cheng, X.

Dirckx, J. J. J.

Gilbert, B. S.

B. S. Gilbert and J. H. Blatt, “Enhanced three-dimensional reconstruction of surfaces using multicolor gratings,” Opt. Eng. 39, 52-60 (2000).
[CrossRef]

Guo, L.

Häusler, G.

Heinze, M.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Hung, C. C.

M. J. Tsai and C. C. Hung, “Development of a high precision surface metrology system using structured light projection,” Measurement 38, 236-247 (2005).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

Huntley, J. M.

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

Ina, H.

Iwaasa, Y.

Judge, T. R.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

Kobayashi, S.

Kühmstedt, P.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Lalor, M. J.

Lamberti, L.

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring with projection moiré,” Opt. Eng. 44, 093605 (2005).
[CrossRef]

Li, J. L.

J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
[CrossRef]

Li, W.

Liang, X.

X. Liang and X. Su, “Computer simulation of a 3-D sensing system with structured illumination,” Opt. Lasers Eng. 27, 379-393 (1997).
[CrossRef]

Lin, L.

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

Munkelt, C.

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Mutoh, K.

Notni, G.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Park, B. G.

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

Patorski, K.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier1993).

Peng, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
[CrossRef]

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Ritter, D.

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Rodella, R.

Saldner, H. O.

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

Sansoni, G.

Schreiber, W.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

Sciammarella, C. A.

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring with projection moiré,” Opt. Eng. 44, 093605 (2005).
[CrossRef]

Sciammarella, F. M.

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring with projection moiré,” Opt. Eng. 44, 093605 (2005).
[CrossRef]

Shang, H. M.

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

Song, M.

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

Su, H. J.

J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
[CrossRef]

Su, L.

Su, X.

L. Su, X. Su, W. Li, and L. Xiang, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153-1158 (1999).
[CrossRef]

J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
[CrossRef]

X. Liang and X. Su, “Computer simulation of a 3-D sensing system with structured illumination,” Opt. Lasers Eng. 27, 379-393 (1997).
[CrossRef]

X. Cheng, X. Su, and L. Guo, “Automated measurement method for 360° profilometry of 3-D diffuse objects,” Appl. Opt. 30, 1274-1278 (1991).
[CrossRef] [PubMed]

Su, X. X.

W. S. Zhou and X. X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89-93 (1994).
[CrossRef]

Takeda, M.

Tan, Y.

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Tian, J.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
[CrossRef]

Toyooka, S.

Tsai, M. J.

M. J. Tsai and C. C. Hung, “Development of a high precision surface metrology system using structured light projection,” Measurement 38, 236-247 (2005).
[CrossRef]

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Rob. Autom. 3, 323-344 (1987).
[CrossRef]

Wenjing, C.

S. Xianyu and C. Wenjing, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Wensen, Z.

Xiang, L.

Xianyu, S.

S. Xianyu and C. Wenjing, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Zhang, H.

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” Technical Report MSR-TR-98-71 (Microsoft Research, 1998).

Zhao, H.

Zhao, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
[CrossRef]

Zhou, W. S.

W. S. Zhou and X. X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89-93 (1994).
[CrossRef]

Appl. Opt. (10)

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977-3982 (1983).
[CrossRef] [PubMed]

S. Toyooka and Y. Iwaasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 1630-1633 (1986).
[CrossRef] [PubMed]

H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497-4500 (1994).
[CrossRef] [PubMed]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

L. Su, X. Su, W. Li, and L. Xiang, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153-1158 (1999).
[CrossRef]

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, 3534-3541 (1999).
[CrossRef]

A. Asundi and Z. Wensen, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38, 3556-3561 (1999).
[CrossRef]

G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38, 6565-6573 (1999).
[CrossRef]

G. Häusler and D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. 32, 7164-7169(1993).
[CrossRef] [PubMed]

X. Cheng, X. Su, and L. Guo, “Automated measurement method for 360° profilometry of 3-D diffuse objects,” Appl. Opt. 30, 1274-1278 (1991).
[CrossRef] [PubMed]

IEEE J. Rob. Autom. (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV camera and lenses,” IEEE J. Rob. Autom. 3, 323-344 (1987).
[CrossRef]

J. Electron. Imaging (1)

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231-240 (2004).
[CrossRef]

J. Mod. Opt. (1)

W. S. Zhou and X. X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89-93 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

Measurement (1)

M. J. Tsai and C. C. Hung, “Development of a high precision surface metrology system using structured light projection,” Measurement 38, 236-247 (2005).
[CrossRef]

Opt. Eng. (6)

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

B. S. Gilbert and J. H. Blatt, “Enhanced three-dimensional reconstruction of surfaces using multicolor gratings,” Opt. Eng. 39, 52-60 (2000).
[CrossRef]

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

Y. Y. Hung, L. Lin, H. M. Shang, and B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143-149 (2000).
[CrossRef]

C. A. Sciammarella, L. Lamberti, and F. M. Sciammarella, “High accuracy contouring with projection moiré,” Opt. Eng. 44, 093605 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (5)

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336-342 (2008).
[CrossRef]

S. Xianyu and C. Wenjing, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

J. L. Li, X. Su, and H. J. Su, “Removal of carrier frequency in phase-shifting techniques,” Opt. Lasers Eng. 30, 107-115(1998).
[CrossRef]

X. Liang and X. Su, “Computer simulation of a 3-D sensing system with structured illumination,” Opt. Lasers Eng. 27, 379-393 (1997).
[CrossRef]

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

Other (3)

C. Bräuer-Burchardt, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Phase unwrapping in fringe projection systems using epipolar geometry,” in Advanced Concepts for Intelligent Vision Systems (Springer, 2008), pp. 422-432.
[CrossRef]

Z. Zhang, “A flexible new technique for camera calibration,” Technical Report MSR-TR-98-71 (Microsoft Research, 1998).

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier1993).

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Figures (12)

Fig. 1
Fig. 1

(a) Fringe pattern on the surface. (b) Phase map after phase shifting. (c) Phase map after unwrapping.

Fig. 2
Fig. 2

Acquisition system layout.

Fig. 3
Fig. 3

Superimposition of fringes.

Fig. 4
Fig. 4

Different patterns during step 1 (left), step 2 (middle), step 3 (right).

Fig. 5
Fig. 5

Signal of light intensity in a pixel belonging to (a) a zone with one projection, (b) a zone with superimposition of two projections, (c) a zone with superimposition of three projections.

Fig. 6
Fig. 6

Phase maps of each projector for each acquisition step.

Fig. 7
Fig. 7

Principle of the multispectral phase unwrap.

Fig. 8
Fig. 8

Phase map after unwrapping of each projector.

Fig. 9
Fig. 9

Plot of phase difference between the classical and the proposed technique against occurrences (total number of pixels is 1280 × 1024 ).

Fig. 10
Fig. 10

Fringe pattern on the surface of a cylinder.

Fig. 11
Fig. 11

Unwrapped phase maps of a cylinder.

Fig. 12
Fig. 12

Point clouds of the surface of a cylinder.

Tables (1)

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Table 1 Bullets Indicate which Projector Lights Up Each Subarea

Equations (27)

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φ UNW ( u , v ) = φ ( u , v ) + n 2 π .
Z = φ φ 0 φ Z ¯ φ 0 Z ¯ .
l.c.m. ( P 0 , P 1 , P 2 ) > 1024.
x k = i = 0 2 x k i , k = 0 , 1 , , P 2 1.
f q = 1 P 2 k = 0 P 2 1 x k exp ( j 2 π P 2 k q ) , q = 0 , 1 , , P 2 1.
x k i = A i sin ( 2 π P i k + φ i ) = A i [ sin ( 2 π P i k ) cos φ i + cos ( 2 π P i k ) sin φ i ] .
a i = A i cos φ i , b i = A i sin φ i ,
x k i = a i sin ( 2 π P i k ) + b i cos ( 2 π P i k ) ,
x k = i = 0 2 [ a i sin ( 2 π P i k ) + b i cos ( 2 π P i k ) ] .
f q = 1 P 2 i = 0 2 [ a i k = 0 P 2 1 sin ( 2 π P i k ) exp ( j 2 π P 2 k q ) + b i k = 0 P 2 1 cos ( 2 π P i k ) exp ( j 2 π P 2 k q ) ] .
S q i = 1 P 2 k = 0 P 2 1 sin ( 2 π P i k ) exp ( j 2 π P 2 k q ) , C q i = 1 P 2 k = 0 P 2 1 cos ( 2 π P i k ) exp ( j 2 π P 2 k q ) , q = 0 , 1 , , P 2 1 ,
f q = i = 0 2 ( a i S q i + b i C q i ) .
[ f 0 f 1 f P 2 1 ] = [ S 0 0 C 0 0 S 0 1 C 0 1 S 0 2 C 0 2 S 1 0 C 1 0 S 1 1 C 1 1 S 1 2 C 1 2 S P 2 1 0 C P 2 1 0 S P 2 1 1 C P 2 1 1 S P 2 1 2 C P 2 1 2 ] · [ a 0 b 0 a 1 b 1 a 2 b 2 ] ,
f = [ D ] · c .
c = [ D T D ] 1 D T · f ,
A i = a i 2 + b i 2 ,
φ i = tan 1 ( b i / a i ) .
φ i u = φ i + 2 π n i i = 0 , 1 , 2.
φ 0 u = φ 1 u P 1 P 0 , φ 1 u = φ 2 u P 2 P 1 , φ 0 u = φ 2 u P 2 P 0 .
φ 0 + 2 π n 0 = ( φ 1 + 2 π n 1 ) P 1 P 0 ,
φ 0 + 2 π n 0 = ( φ 2 + 2 π n 2 ) P 2 P 0 ,
φ 1 + 2 π n 1 = ( φ 2 + 2 π n 2 ) P 2 P 1 ,
n 1 = [ ( φ 0 + 2 π n 0 ) P 0 P 1 φ 1 ] 1 2 π , n 2 = [ ( φ 0 + 2 π n 0 ) P 0 P 2 φ 2 ] 1 2 π ,
[ P 0 P 1 0 P 0 0 P 2 0 P 1 P 2 ] { n 0 n 1 n 2 } = 1 2 π { φ 1 P 1 φ 0 P 0 φ 2 P 2 φ 0 P 0 φ 1 P 1 φ 2 P 2 } .
n 0 = 2 p + h 1 P 1 , n 1 = 1 p + h 1 P 0 .
n 0 = 4 q + h 2 P 2 , n 2 = 1 q + h 2 P 0 .
n 1 = 2 r + h 3 P 2 , n 2 = 1 r + h 3 P 1 .

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