Abstract

A one-shot technique for surfaces with depth, color, and reflectivity discontinuities is presented. It uses windowed Fourier transform to extract the fringe phases and a binary-encoded scheme to unwrap the phases. Experiments show that absolute phases could be obtained with high reliability.

© 2017 Optical Society of America

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References

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  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
    [Crossref] [PubMed]
  2. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
    [Crossref]
  3. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
    [Crossref] [PubMed]
  4. Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47(29), 5408–5419 (2008).
    [Crossref] [PubMed]
  5. S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
    [Crossref]
  6. Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
    [Crossref]
  7. F. Da and F. Dong, “Windowed Fourier transform profilometry based on improved S-transform,” Opt. Lett. 37(17), 3561–3563 (2012).
    [Crossref] [PubMed]
  8. W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
    [Crossref]
  9. M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).
  10. G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,” Appl. Opt. 36(19), 4463–4472 (1997).
    [Crossref] [PubMed]
  11. 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(31), 6565–6573 (1999).
    [Crossref] [PubMed]
  12. J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
    [Crossref]
  13. H. J. Chen, J. Zhang, D. J. Lv, and J. Fang, “3-D shape measurement by composite pattern projection and hybrid processing,” Opt. Express 15(19), 12318–12330 (2007).
    [Crossref] [PubMed]
  14. W. H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15(20), 13167–13181 (2007).
    [Crossref] [PubMed]
  15. W. H. Su, “Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects,” Opt. Express 16(4), 2590–2596 (2008).
    [Crossref] [PubMed]
  16. S. Fernandez and J. Salvi, “One-shot absolute pattern for dense reconstruction using DeBruijn coding and Windowed Fourier Transform,” Opt. Commun. 291(15), 70–78 (2013).
    [Crossref]
  17. W. H. Su, C. Y. Kuo, and F. J. Kao, “Three-dimensional trace measurements for fast-moving objects using binary-encoded fringe projection techniques,” Appl. Opt. 53(24), 5283–5289 (2014).
    [Crossref] [PubMed]
  18. D. R. Burton and M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33(14), 2939–2948 (1994).
    [Crossref] [PubMed]
  19. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36(22), 5347–5354 (1997).
    [Crossref] [PubMed]
  20. 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(20), 9178–9187 (2006).
    [Crossref] [PubMed]
  21. C. A. García-Isáis and N. Alcalá Ochoa, “One shot profilometry using a composite fringe pattern,” Opt. Lasers Eng. 53, 25–30 (2014).
    [Crossref]
  22. H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
    [Crossref]
  23. W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
    [Crossref]
  24. P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in SIGGRAPH ’93 Proceedings, J. T. Kajiya, ed. 27, (1993), pp. 165–174.
  25. E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
    [Crossref]
  26. F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
    [Crossref]

2014 (2)

2013 (2)

S. Fernandez and J. Salvi, “One-shot absolute pattern for dense reconstruction using DeBruijn coding and Windowed Fourier Transform,” Opt. Commun. 291(15), 70–78 (2013).
[Crossref]

W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
[Crossref]

2012 (2)

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

F. Da and F. Dong, “Windowed Fourier transform profilometry based on improved S-transform,” Opt. Lett. 37(17), 3561–3563 (2012).
[Crossref] [PubMed]

2011 (2)

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

2008 (3)

2007 (2)

2006 (1)

2004 (1)

2003 (3)

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
[Crossref]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

2001 (1)

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

1999 (1)

1997 (2)

1994 (1)

1983 (1)

1981 (1)

M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).

Alcalá Ochoa, N.

C. A. García-Isáis and N. Alcalá Ochoa, “One shot profilometry using a composite fringe pattern,” Opt. Lasers Eng. 53, 25–30 (2014).
[Crossref]

Berryman, F.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
[Crossref]

Burton, D.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

Burton, D. R.

Busca, G.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[Crossref]

Carocci, M.

Chen, H. J.

Chen, W.

W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
[Crossref]

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

Corini, S.

Cubillo, J.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
[Crossref]

Da, F.

Docchio, F.

Dong, F.

Fang, J.

Fernandez, S.

S. Fernandez and J. Salvi, “One-shot absolute pattern for dense reconstruction using DeBruijn coding and Windowed Fourier Transform,” Opt. Commun. 291(15), 70–78 (2013).
[Crossref]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

Gao, W.

García-Isáis, C. A.

C. A. García-Isáis and N. Alcalá Ochoa, “One shot profilometry using a composite fringe pattern,” Opt. Lasers Eng. 53, 25–30 (2014).
[Crossref]

Gdeisat, M. A.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

Geng, J.

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Gu, Q.

Jing, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Kanade, T.

M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).

Kao, F. J.

Kemao, Q.

Kinoshita, M.

Kuang, D.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Kuo, C. Y.

Lalor, M. J.

Lazzari, S.

Liu, H.

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(20), 9178–9187 (2006).
[Crossref] [PubMed]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

Lv, D. J.

Minou, M.

M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).

Mutoh, K.

Pynsent, P.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
[Crossref]

Reichard, K.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Rodella, R.

Sakai, T.

M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).

Salvi, J.

S. Fernandez and J. Salvi, “One-shot absolute pattern for dense reconstruction using DeBruijn coding and Windowed Fourier Transform,” Opt. Commun. 291(15), 70–78 (2013).
[Crossref]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

Sansoni, G.

Shen, Q.

W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
[Crossref]

Su, W. H.

Su, X.

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

Takahashi, Y.

Takai, H.

Takeda, M.

Wang, H.

Wang, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Yin, S.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

Yu, F. T. S.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

Zappa, E.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[Crossref]

Zhang, J.

Zhang, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Zhong, M.

W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
[Crossref]

Adv. Opt. Photonics (1)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Appl. Opt. (8)

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[Crossref] [PubMed]

D. R. Burton and M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33(14), 2939–2948 (1994).
[Crossref] [PubMed]

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,” Appl. Opt. 36(19), 4463–4472 (1997).
[Crossref] [PubMed]

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(31), 6565–6573 (1999).
[Crossref] [PubMed]

M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36(22), 5347–5354 (1997).
[Crossref] [PubMed]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[Crossref] [PubMed]

Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47(29), 5408–5419 (2008).
[Crossref] [PubMed]

W. H. Su, C. Y. Kuo, and F. J. Kao, “Three-dimensional trace measurements for fast-moving objects using binary-encoded fringe projection techniques,” Appl. Opt. 53(24), 5283–5289 (2014).
[Crossref] [PubMed]

Opt. Commun. (3)

S. Fernandez and J. Salvi, “One-shot absolute pattern for dense reconstruction using DeBruijn coding and Windowed Fourier Transform,” Opt. Commun. 291(15), 70–78 (2013).
[Crossref]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).
[Crossref]

Opt. Eng. (1)

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42(6), 1730–1740 (2003).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (5)

C. A. García-Isáis and N. Alcalá Ochoa, “One shot profilometry using a composite fringe pattern,” Opt. Lasers Eng. 53, 25–30 (2014).
[Crossref]

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

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

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[Crossref]

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39(1), 35–50 (2003).
[Crossref]

Opt. Lett. (1)

Optik (Stuttg.) (1)

W. Chen, Q. Shen, and M. Zhong, “Comparison of 2D S-Transform Profilometry and 2D Windowed Fourier Transform Profilometry,” Optik (Stuttg.) 124(24), 6732–6736 (2013).
[Crossref]

Trans. IECE Japan (1)

M. Minou, T. Kanade, and T. Sakai, “A method of time-coded parallel planes of light for depth measurement,” Trans. IECE Japan 64(8), 521–528 (1981).

Other (1)

P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in SIGGRAPH ’93 Proceedings, J. T. Kajiya, ed. 27, (1993), pp. 165–174.

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Figures (22)

Fig. 1
Fig. 1 Optical configuration of Fourier transform profilometry.
Fig. 2
Fig. 2 Flow chart of the band-pass selection scheme.
Fig. 3
Fig. 3 (a) Appearance of the encoded pattern. (b) Transmittance distribution of the encoded pattern. (c) Fringes denoted with the binary digits and the fringe orders. (d) Fringe orders represented by the binary digits.
Fig. 4
Fig. 4 (a) A stream of 69 binary digits formed by partially overlapping 64 codewords. (b) Correspondence between the fringe orders and the 69 binary digits. (c) Appearance of the encoded pattern generated with reference to the 69 binary digits.
Fig. 5
Fig. 5 (a) Appearance of the fringe pattern using 5 binary digits to form a codeword. (b) Correspondence of the fringe orders and the binary digits.
Fig. 6
Fig. 6 Flow chart of the decoding procedure.
Fig. 7
Fig. 7 (a) Appearance of the colorful objects. (b) Binary-encoded fringes projected on the inspected objects.
Fig. 8
Fig. 8 (a) Appearance of an image row marked with a red frame across a windowed area. (b) Gray-level distribution with an unexpected fluctuation along the marked image row. (c) Gray-level distribution addressed with a corrected period set.
Fig. 9
Fig. 9 (a) Appearance of an image row marked with a red frame in a windowed area. (b) Gray-level distribution along the marked image row.
Fig. 10
Fig. 10 Phase distribution extracted from (a) Fig. 8(b), and (b) Fig. 9(b).
Fig. 11
Fig. 11 Phase extracted based on (a) the proposed scheme, and (b) conventional Fourier transform method.
Fig. 12
Fig. 12 (a) An image row marked with a red frame for the task of phase unwrapping. (b) Gray-level distribution along the marked image row. (c) Phase distribution along the marked image row. (d) Local minimum gray-levels marked in blue and green circles. (e) A close-up view of the marked image labeled with the corresponding binary digits and codewords. (f) Fringe orders produced with reference to the look-up table.
Fig. 13
Fig. 13 (a) Unwrapped phase recovered for Fig. 11(a). (b) Phase distribution along one image row.
Fig. 14
Fig. 14 Retrieved profile.
Fig. 15
Fig. 15 (a) Appearance of the standard gauge block projected with the encoded fringes. (b) Appearance of the standard gauge block projected with the sinusoidal fringes. (c) Profile retrieved by the proposed method. (d) Profile retrieved with the five-step phase-shifting technique. (e) One-dimensional surface profile retrieved by the proposed method. (f) One-dimensional surface profile retrieved the five-step phase-shifting technique.
Fig. 16
Fig. 16 (a) Appearance of the flat surface painted with a colorful piano keyboard. (b) Appearance of the flat surface projected with the encoded fringes.
Fig. 17
Fig. 17 (a) Gray-level distribution along the image row marked with a red frame. (b) Gray-level distribution along the image row marked with a green frame. (c) Binary digits decoded from the image row marked with a red frame. (d) Binary digits decoded from the image row marked with a green frame.
Fig. 18
Fig. 18 (a) Appearance of area-encoded fringes [17]. (b) Appearance of the flat surface projected with the area-encoded fringes.
Fig. 19
Fig. 19 (a) Appearance of the flat surface with sinusoidal reflectance. (b) Appearance of the flat surface illuminated by an encoded fringe pattern. (c) One-dimensional distribution along the marked image row.
Fig. 20
Fig. 20 (a) Appearance of the flat surface with discontinuous reflectance. (b) Appearance of the flat surface illuminated by an encoded fringe pattern. (c) One-dimensional distribution along the image row marked with a red frame. (d) One-dimensional distribution along the image row marked with a green frame.
Fig. 21
Fig. 21 Appearance of the pattern in which the codeword is formed by 4 binary digits.
Fig. 22
Fig. 22 (a) Optical configuration of an encoded fringe projection system. (b) Encoded fringes on the surface with a large depth discontinuity. (c) Encoded fringes projected onto objects A and B.

Tables (1)

Tables Icon

Table 1 Codewords formed by 6 binary numbers and their serial numbers.

Equations (14)

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

I( x d , y d )=A( x d , y d )+B( x d , y d )cos[ϕ( x d , y d )] =A( x d , y d )+B( x d , y d )cos[ 2π x d T d +Δϕ( x d , y d )],
{ z= n=0 N c n ϕ unwrapped n x= n=0 1 a n z n y= n=0 1 b n z n ,
s {I( x d , y d )}= F s ( f x , x o , y d )= I( x d , y d )w( x d x o ) e j2π f x x d d x d ,
1 { F s ( f x , x o , y d )}=I( x d , y d )w( x d x o )= F s ( f x , x o , y d ) e j2π f x x d d f x .
I( x d , y d )=A( x d , y d )+ 1 2 B ˜ ( x d , y d ) e j 2π x d T d + 1 2 B ˜ * ( x d , y d ) e j 2π x d T d ,
s {I( x d , y d )}= A s ( f x , x o , y d )+ 1 2 ˜ s ( f x 1 T d , x o , y d )+ 1 2 ˜ s * ( f x + 1 T d , x o , y d ),
1 { ˜ s ( f x 1 T d , x o , y d )}= B ˜ ( x d , y d ) e j 2π T d x w( x d x o )=B( x d , y d ) e jϕ( x d , y d ) w( x d x o ).
ϕ wrapped ( x d , y d )rect( x d x o W )= tan 1 { Im{ s 1 { ˜ s ( f x 1/ T d , x o , y d )}} Re{ s 1 { ˜ s ( f x 1/ T d , x o , y d )}} },
rect(t)={ 0, if | t |>1/2 1/2, if | t |=1/2 . 1, if | t |<1/2
ϕ wrapped ( x d , y d )= [ ϕ wrapped ( x d , y d )rect( x d x o W ) ]δ( x d x o ) d x o ,
δ(t)={ 0, if | t |0 , if | t |=0.
N MAX = 2 n +n1,
ϕ unwrapped = ϕ wrapped +2nπ,
z a = 2 n T x tanθ,

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