Abstract

A projection moiré profilometer is presented in which both projection and optical demodulation are realized with liquid crystal light modulators. The computer generated grids, realized on thin film transistor matrices, allow phase-stepping and discrete grid averaging without the need for any mechanically moving component. Spatial line pitch and phase steps can thus be readily adjusted to suit the measurement precision and object geometry. The device is able to perform topographic measurements with a height resolution of 15µm on every pixel of the recording device.

© 2008 Optical Society of America

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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]
  2. R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).
  3. J. Dirckx and W. Decraemer, “Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2, 176–185 (1997).
    [CrossRef]
  4. M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
    [CrossRef]
  5. M. Takeda, H. Ina, and S. Koboyashi, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1982).
    [CrossRef]
  6. W.-H. Su and H. Liu, “Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities,” Opt. Express 14, 9178–9187 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. M. Halioua, R. Krishnamurthy, H. Liu, and F.-P. Chiang, “Projection moiré with moving gratings for automated 3-D topography,” Appl. Opt. 22, 850–855 (1983).
    [CrossRef] [PubMed]
  10. J. Dirckx and W. Decraemer, “Interferometer for eardrum shape measurement, based on projection of straight line rulings,” Lasers Med. Sci. 15, 131–139 (2000).
    [CrossRef]
  11. J. Buytaert and J. Dirckx, “Design considerations in projection phase shift moiré topography, based on theoretical analysis of fringe formation,” J. Opt. Soc. Am. A 24, 2003–2013 (2007).
    [CrossRef]
  12. K. Creath, Progress in optics XXVI, chap. Phase-shifting interferometry techniques, pp. 357–373 (1988).
  13. J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
    [CrossRef]
  14. J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus (includes Electro-Optics) 18, 65–71 (1982).
  15. J. Dirckx and W. Decraemer, “Grating noise removal in moiré topography,” Opt. Int. J. Light Electron. Opt. 86, 107–110 (1990).
  16. A. Asundi, Proc. SPIE vol. 1554B: Second intl conf on photomechanics and speckle metrology: moire techniques, holographic interferometry, optical NDT, and applications to fluid mechanics, chap. Novel grating methods for optical inspection, pp. 708–715 (SPIE, 1991).
  17. A. Asundi and C. Chan, “Phase shifted projection grid - effect of pitch and profile,” Opt. Lasers Eng. 21, 31–47 (1994).
    [CrossRef]
  18. C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
    [CrossRef]
  19. Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).
  20. W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).
  21. J. Dirckx and W. Decraemer, “Coating techniques in optical interferometric metrology,” Appl. Opt. 36, 2776–2782 (1997).
    [CrossRef] [PubMed]
  22. J. Dirckx and W. Decraemer, “Automatic calibration method for phase shift shadow moire interferometry,” Appl. Opt. 29, 1474–1476 (1990).
    [CrossRef] [PubMed]
  23. T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).
  24. S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).
  25. W. Osten, Optical methods in experimental solid mechanics, chap. Digital processing and evaluation of fringe patterns in optical metrology and non-destructive testing, pp. 308–363 (Springer-Verlag, 2000). Section: Techniques for digital phase reconstruction.
  26. B. Drerup, Optics in biomedical sciences, chap. Some problems in analytical reconstruction of biological shapes from moiré topograms, pp. 258–261 (Springer-Verlag, 1982).
  27. U. Mieth and W. Osten, Proc. SPIE vol. 1163: Interferometry ’89, chap. Three methods for the interpolation of phase values between fringe pattern skeleton, pp. 151–154 (SPIE, 1989).
  28. J. Dirckx and W. Decraemer, “Effect of middle ear components on eardrum quasi-static deformation,” Hearing Res. 157, 124–137 (2001).
    [CrossRef]
  29. X. Xie, J. Atkinson, M. Lalor, and D. Burton, “Three-map absolute moiré contouring,” Appl. Opt. 35, 6990–6995 (1996).
    [CrossRef] [PubMed]
  30. M.-S. Jeong and S.-W. Kim, “Color grating projection moiré with time-integral fringe capturing for high-speed 3-D imaging,” Opt. Eng. 41, 1912–1917 (2002).
    [CrossRef]

2007 (1)

2006 (1)

2005 (1)

Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).

2003 (1)

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[CrossRef]

2002 (1)

M.-S. Jeong and S.-W. Kim, “Color grating projection moiré with time-integral fringe capturing for high-speed 3-D imaging,” Opt. Eng. 41, 1912–1917 (2002).
[CrossRef]

2001 (1)

J. Dirckx and W. Decraemer, “Effect of middle ear components on eardrum quasi-static deformation,” Hearing Res. 157, 124–137 (2001).
[CrossRef]

2000 (2)

J. Dirckx and W. Decraemer, “Interferometer for eardrum shape measurement, based on projection of straight line rulings,” Lasers Med. Sci. 15, 131–139 (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]

1997 (2)

J. Dirckx and W. Decraemer, “Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2, 176–185 (1997).
[CrossRef]

J. Dirckx and W. Decraemer, “Coating techniques in optical interferometric metrology,” Appl. Opt. 36, 2776–2782 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

1994 (1)

A. Asundi and C. Chan, “Phase shifted projection grid - effect of pitch and profile,” Opt. Lasers Eng. 21, 31–47 (1994).
[CrossRef]

1990 (2)

J. Dirckx and W. Decraemer, “Grating noise removal in moiré topography,” Opt. Int. J. Light Electron. Opt. 86, 107–110 (1990).

J. Dirckx and W. Decraemer, “Automatic calibration method for phase shift shadow moire interferometry,” Appl. Opt. 29, 1474–1476 (1990).
[CrossRef] [PubMed]

1983 (1)

1982 (4)

M. Takeda, H. Ina, and S. Koboyashi, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1982).
[CrossRef]

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[CrossRef]

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus (includes Electro-Optics) 18, 65–71 (1982).

1981 (1)

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

1970 (2)

Allen, J.

Asundi, A.

A. Asundi and C. Chan, “Phase shifted projection grid - effect of pitch and profile,” Opt. Lasers Eng. 21, 31–47 (1994).
[CrossRef]

A. Asundi, Proc. SPIE vol. 1554B: Second intl conf on photomechanics and speckle metrology: moire techniques, holographic interferometry, optical NDT, and applications to fluid mechanics, chap. Novel grating methods for optical inspection, pp. 708–715 (SPIE, 1991).

Atkinson, J.

Bagger-Sjöbäck, D.

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

Baik, S.-H.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

Bhushan, B.

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[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]

Burton, D.

Buytaert, J.

J. Buytaert and J. Dirckx, “Design considerations in projection phase shift moiré topography, based on theoretical analysis of fringe formation,” J. Opt. Soc. Am. A 24, 2003–2013 (2007).
[CrossRef]

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

Chan, C.

A. Asundi and C. Chan, “Phase shifted projection grid - effect of pitch and profile,” Opt. Lasers Eng. 21, 31–47 (1994).
[CrossRef]

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]

Chiang, F.-P.

Creath, K.

K. Creath, Progress in optics XXVI, chap. Phase-shifting interferometry techniques, pp. 357–373 (1988).

Decraemer, W.

J. Dirckx and W. Decraemer, “Effect of middle ear components on eardrum quasi-static deformation,” Hearing Res. 157, 124–137 (2001).
[CrossRef]

J. Dirckx and W. Decraemer, “Interferometer for eardrum shape measurement, based on projection of straight line rulings,” Lasers Med. Sci. 15, 131–139 (2000).
[CrossRef]

J. Dirckx and W. Decraemer, “Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2, 176–185 (1997).
[CrossRef]

J. Dirckx and W. Decraemer, “Coating techniques in optical interferometric metrology,” Appl. Opt. 36, 2776–2782 (1997).
[CrossRef] [PubMed]

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

J. Dirckx and W. Decraemer, “Automatic calibration method for phase shift shadow moire interferometry,” Appl. Opt. 29, 1474–1476 (1990).
[CrossRef] [PubMed]

J. Dirckx and W. Decraemer, “Grating noise removal in moiré topography,” Opt. Int. J. Light Electron. Opt. 86, 107–110 (1990).

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

Dirckx, J.

J. Buytaert and J. Dirckx, “Design considerations in projection phase shift moiré topography, based on theoretical analysis of fringe formation,” J. Opt. Soc. Am. A 24, 2003–2013 (2007).
[CrossRef]

J. Dirckx and W. Decraemer, “Effect of middle ear components on eardrum quasi-static deformation,” Hearing Res. 157, 124–137 (2001).
[CrossRef]

J. Dirckx and W. Decraemer, “Interferometer for eardrum shape measurement, based on projection of straight line rulings,” Lasers Med. Sci. 15, 131–139 (2000).
[CrossRef]

J. Dirckx and W. Decraemer, “Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2, 176–185 (1997).
[CrossRef]

J. Dirckx and W. Decraemer, “Coating techniques in optical interferometric metrology,” Appl. Opt. 36, 2776–2782 (1997).
[CrossRef] [PubMed]

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

J. Dirckx and W. Decraemer, “Automatic calibration method for phase shift shadow moire interferometry,” Appl. Opt. 29, 1474–1476 (1990).
[CrossRef] [PubMed]

J. Dirckx and W. Decraemer, “Grating noise removal in moiré topography,” Opt. Int. J. Light Electron. Opt. 86, 107–110 (1990).

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

Drerup, B.

B. Drerup, Optics in biomedical sciences, chap. Some problems in analytical reconstruction of biological shapes from moiré topograms, pp. 258–261 (Springer-Verlag, 1982).

Fujin, Y.

Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).

George, O.

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[CrossRef]

Halioua, M.

He, X.

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[CrossRef]

Honda, T.

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

Idesawa, M.

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

Ina, H.

Jeong, M.-S.

M.-S. Jeong and S.-W. Kim, “Color grating projection moiré with time-integral fringe capturing for high-speed 3-D imaging,” Opt. Eng. 41, 1912–1917 (2002).
[CrossRef]

Johnson, W.

Kang, S.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

Kang, X.

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[CrossRef]

Kang, Y.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

Kim, S.-W.

M.-S. Jeong and S.-W. Kim, “Color grating projection moiré with time-integral fringe capturing for high-speed 3-D imaging,” Opt. Eng. 41, 1912–1917 (2002).
[CrossRef]

Koboyashi, S.

Koliopoulos, C.

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[CrossRef]

Krishnamurthy, R.

Lalor, M.

Liu, H.

López, L. M.

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

Magome, N.

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

Martínez-Celorio, R.

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, “Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

Meadows, D.

Mieth, U.

U. Mieth and W. Osten, Proc. SPIE vol. 1163: Interferometry ’89, chap. Three methods for the interpolation of phase values between fringe pattern skeleton, pp. 151–154 (SPIE, 1989).

Nakadate, S.

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

Osten, W.

W. Osten, Optical methods in experimental solid mechanics, chap. Digital processing and evaluation of fringe patterns in optical metrology and non-destructive testing, pp. 308–363 (Springer-Verlag, 2000). Section: Techniques for digital phase reconstruction.

U. Mieth and W. Osten, Proc. SPIE vol. 1163: Interferometry ’89, chap. Three methods for the interpolation of phase values between fringe pattern skeleton, pp. 151–154 (SPIE, 1989).

Quan, C.

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[CrossRef]

Ryu, W.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

Shang, H.

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[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, W.-H.

Suzuki, M.

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

Takasaki, H.

Takeda, M.

Tay, C.

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2326–2335 (2003).
[CrossRef]

Tsujiuchi, J.

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

von Unge, M.

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

Wei, S.

Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).

Wyant, J.

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus (includes Electro-Optics) 18, 65–71 (1982).

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[CrossRef]

Xiaoyuan, H.

Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).

Xie, X.

Yamaashi, Y.

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

Yatagai, T.

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

Acta Optica Sinica (1)

Y. Fujin, H. Xiaoyuan, and S. Wei, “Digital shadow moiré method with phase-shifting based on liquid crystal display projector,” Acta Optica Sinica 25, 1057–1061 (2005).

Appl. Opt. (8)

ASLE trans. (1)

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, “An optical profilometer for surface characterization of magnetic media,” ASLE trans. 27, 101–113 (1982).
[CrossRef]

Hearing Res. (2)

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, “Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion,” Hearing Res. 82, 184–196 (1995).
[CrossRef]

J. Dirckx and W. Decraemer, “Effect of middle ear components on eardrum quasi-static deformation,” Hearing Res. 157, 124–137 (2001).
[CrossRef]

J. Biomed. Opt. (1)

J. Dirckx and W. Decraemer, “Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane,” J. Biomed. Opt. 2, 176–185 (1997).
[CrossRef]

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

Laser Focus (includes Electro-Optics) (1)

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus (includes Electro-Optics) 18, 65–71 (1982).

Lasers Med. Sci. (1)

J. Dirckx and W. Decraemer, “Interferometer for eardrum shape measurement, based on projection of straight line rulings,” Lasers Med. Sci. 15, 131–139 (2000).
[CrossRef]

Opt. Eng. (4)

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

M.-S. Jeong and S.-W. Kim, “Color grating projection moiré with time-integral fringe capturing for high-speed 3-D imaging,” Opt. Eng. 41, 1912–1917 (2002).
[CrossRef]

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, “Interactive fringe analysis system: applications to moiré contourogram and interferogram,” Opt. Eng. 21, 901–906 (1982).

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, “Hybrid holographic interferometer for measuring threedimensional deformations,” Opt. Eng. 20, 246–252 (1981).

Opt. Express (1)

Opt. Int. J. Light Electron. Opt. (1)

J. Dirckx and W. Decraemer, “Grating noise removal in moiré topography,” Opt. Int. J. Light Electron. Opt. 86, 107–110 (1990).

Opt. Lasers Eng. (1)

A. Asundi and C. Chan, “Phase shifted projection grid - effect of pitch and profile,” Opt. Lasers Eng. 21, 31–47 (1994).
[CrossRef]

Other (7)

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, “A study on the 3-D measurement by using digital projection moiré method,” Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

W. Osten, Optical methods in experimental solid mechanics, chap. Digital processing and evaluation of fringe patterns in optical metrology and non-destructive testing, pp. 308–363 (Springer-Verlag, 2000). Section: Techniques for digital phase reconstruction.

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Figures (8)

Fig. 1.
Fig. 1.

A: moiré interferogram of a sphere with fringes and grid noise after optical demodulation. B: moiré topogram of the sphere with altitude contour fringes using grid averaging: grid noise is no longer present. E: the 4-bucket phase-stepped algorithm delivers a wrapped phasemap with 2π jumps. F: after unwrapping and calibration a continuous height map is obtained.

Fig. 2.
Fig. 2.

Schematic layout of the liquid crystal grids setup for projection moiré. Lens L 1 projects the light going through liquid crystal grid unit LCG1 onto the surface, creating a shadow of grid G 1 on it. The projected line pattern is modulated by the object’s geometry, and projected onto grid G 2 of LCG2 by lens L 2. The created interferogram is recorded by a CCD imaging device with lens L 3. A light path from point (x 1, y 1, z 1) on G 1 to surface point S(x, y, z), and from S to (x 2, y 2, z 2) on G 2 is drawn.

Fig. 3.
Fig. 3.

Standard deviation on height measurements when using the discrete grid averaging theory with N images.

Fig. 4.
Fig. 4.

TOP: difference between themeasured profile and an ideal straight plane along a horizontal cross section for three representative measurements. A (systematic) error with amplitude of about 15µm is present. BOTTOM: difference between two subsequent recorded shape profiles, showing a noise floor of about 5µm.

Fig. 5.
Fig. 5.

Ratio of the measured height over the actual mechanical height displacement at Z-steps of 350µm for pixel coordinates (100,100), (100,550), (240,320), (350,100) and (350,550). Deviation of unity is less than 5% over a 5mm range.

Fig. 6.
Fig. 6.

The 3-D representation of the sphere in Fig. 1 obtained with digital LCD moiré.

Fig. 7.
Fig. 7.

A: moiré topogramof a diagonally white-gray painted sphere. B: cross sections along the lines in A show ×10 intensity difference between the two regions. C: the differences in reflectivity have no influence on the calibrated height map. D: cross sections along the lines in C, with arrows indicating the bright-dark boundary. E: the 3-D representation of C with one of its topograms mapped on the surface, shows again no problems.

Fig. 8.
Fig. 8.

Triangular Fresnel prism with depth β=0.49mm and width γ=1.00mm. A: cross section through the calibrated height profile shows right-angled isosceles triangles. B and C: 3-D representations of the shape with a topogram mapped on the surface.

Equations (30)

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T 1 ( x 1 ) = 1 2 + 1 2 sin ( 2 π x 1 p + ϕ 1 )
T ( x ) = 1 2 + 2 π n = 1 , odd 1 n sin ( 2 π nx p + ϕ 1 )
I ( x , y , z ) = T 2 ( x 2 ) ρ 2 R ( x , y ) ρ 1 T 1 ( x 1 ) I 0 r 2 ( x , y , z )
= A ( x , y , z ) [ 1 2 + 1 2 sin ( 2 π ( 2 D x + d x 1 ) P + ϕ 1 ) ]
× [ 1 2 + 1 2 sin ( 2 π ( 2 D x d x 2 ) p + ϕ 2 ) ]
x 1 = 2 D x + d x 1 y 1 = y 2 = y d y
x 2 = 2 D x d x 2 z 1 = z 2 = 2 L = 4 f
I ( x , y , z ) = A 4 { 1 + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 ) + sin ( 2 π ( 2 D x z D + x L z ) p + ϕ 2 ) . . .
+ 1 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 ) + cos ( 2 π ( 4 D z 2 D L z ) p + ϕ 1 ϕ 2 ) ] }
sin ( 2 π ( 2 D + z D x L z ) p + ϕ 1 ) cos ( 2 π x p ) cos ( 2 π ( 2 D + z D x L z ) p + ϕ 1 ) sin ( 2 π x p )
ϕ i ϕ i + 2 π v p t
A 4 0 T [ sin ( 2 π ( 2 D x + D x L z + v t ) p + ϕ 1 ) ] d t
= pA 8 π v [ cos ( 2 π ( 2 D x + D x L z ) p + ϕ 1 ) cos ( 2 π ( 2 D x + D x L z + v T ) p + ϕ 1 ) ]
I T ( x , y , z ) = TA ( x , y , z ) 4 { 1 + cos ( 2 π ( 4 D z 2 D L z ) p ) }
T i ( x i ) = 1 2 + 1 2 sin ( 2 π x i p + ϕ i + k Φ )
ϕ i ϕ i + k Φ
I N ( x , y , z ) = TA ( x , y , z ) 4 N k = 1 N { 1 + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) . . .
+ sin ( 2 π ( 2 D x + z D + x L z ) p + ϕ 2 + k Φ ) . . .
+ 1 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 2 k Φ ) + cos ( 2 π ( z 2 D L z ) p ) ] }
= TA ( x , y , z ) 4 { 1 + 1 2 cos ( 2 π ( 2 zD L z ) p ) . . .
+ 1 N k = 1 N [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) + sin ( 2 π ( 2 D x z D + x L z ) p + ϕ 2 + k Φ ) ] . . .
1 2 N k = 1 N cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 2 k Φ ) }
TA 4 N k = 1 N [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) ]
= TA 4 N k = 1 N 2 [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + ( N 2 + k ) Φ ) ]
= TA 2 N k = 1 N 2 [ sin ( 2 π ( 2 D x + z D x L z ) p + 2 ϕ 1 + ( N 2 + 2 k ) Φ ) cos N Φ 4 ]
TA 4 N k = 1 N 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + ( N 2 + 2 k ) Φ ) cos N Φ 2 ]
= TA 2 N k = 1 N 4 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 3 π 2 + 2 k Φ ) cos π 2 ]
Φ = 2 π N ( 2 l + 1 ) Δ = p 2 π Φ = p N ( 2 l + 1 ) Δ pix = p pix N ( 2 l + 1 )
I ( x , y , z ) = TA ( x , y ) 4 [ 1 + 1 2 cos ( 2 π ( 2 zD L z ) p ) ] + B ( x , y )
arctan ( I 4 I 2 I 3 I 1 ) = 4 π D p z L z 4 π D p z L

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