Abstract

Phase-shifting profilometry combined with Gray-code patterns projection has been widely used for 3D measurement. In this technique, a phase-shifting algorithm is used to calculate the wrapped phase, and a set of Gray-code binary patterns is used to determine the unwrapped phase. In the real measurement, the captured Gray-code patterns are no longer binary, resulting in phase unwrapping errors at a large number of erroneous pixels. Although this problem has been attended and well resolved by a few methods, it remains challenging when a measured object has step-heights and the captured patterns contain invalid pixels. To effectively remove unwrapping errors and simultaneously preserve step-heights, in this paper, an effective method using an adaptive median filter is proposed. Both simulations and experiments can demonstrate its effectiveness.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Ternary Gray code-based phase unwrapping for 3D measurement using binary patterns with projector defocusing

Dongliang Zheng, Qian Kemao, Feipeng Da, and Hock Soon Seah
Appl. Opt. 56(13) 3660-3665 (2017)

High-speed three-dimensional shape measurement based on shifting Gray-code light

Zhoujie Wu, Wenbo Guo, and Qican Zhang
Opt. Express 27(16) 22631-22644 (2019)

References

  • View by:
  • |
  • |
  • |

  1. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [Crossref]
  2. B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
    [Crossref] [PubMed]
  3. S. Zhang, “Flexible 3D shape measurement using projector defocusing: extended measurement range,” Opt. Lett. 35(7), 934–936 (2010).
    [Crossref] [PubMed]
  4. D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase error analysis and compensation for phase shifting profilometry with projector defocusing,” Appl. Opt. 55(21), 5721–5728 (2016).
    [Crossref] [PubMed]
  5. H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
    [Crossref] [PubMed]
  6. M. Servin, J. A. Quiroga, and J. M. Padilla, Fringe Pattern Analysis for Optical Metrology (Wiley-Vch, 2014).
  7. Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed Fourier transform: A note on the threshold selection,” Opt. Laser Technol. 39(7), 1364–1369 (2007).
    [Crossref]
  8. Y. Xu, D. Darga, J. Smid, A. M. Zysk, D. Teh, S. A. Boppart, and P. S. Carney, “Filtering and Unwrapping Doppler Optical Coherence Tomography Velocity Maps,” in Imaging and Applied Optics 2016, OSA Technical Digest (online) (Optical Society of America, 2016), paper CW1C.4.
  9. D. C. Ghiglia, and M. D. Pritt, eds., Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  10. J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55(16), 4395–4401 (2016).
    [Crossref] [PubMed]
  11. J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
    [Crossref]
  12. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry,” Opt. Lett. 28(11), 887–889 (2003).
    [Crossref] [PubMed]
  13. L. Song, Y. Chang, Z. Li, P. Wang, G. Xing, and J. Xi, “Application of global phase filtering method in multi frequency measurement,” Opt. Express 22(11), 13641–13647 (2014).
    [Crossref] [PubMed]
  14. M. Servin, J. M. Padilla, A. Gonzalez, and G. Garnica, “Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns,” Opt. Express 23(12), 15806–15815 (2015).
    [Crossref] [PubMed]
  15. M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
    [Crossref]
  16. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12(9), 2071–2074 (1973).
    [Crossref] [PubMed]
  17. Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984).
    [Crossref] [PubMed]
  18. Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. 36(13), 2518–2520 (2011).
    [Crossref] [PubMed]
  19. 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]
  20. D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. 50(8), 1130–1139 (2012).
    [Crossref]
  21. Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
    [Crossref]
  22. S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
    [Crossref]
  23. L. Q. Bui and S. Lee, “Boundary Inheritance Codec for high-accuracy structured light three-dimensional reconstruction with comparative performance evaluation,” Appl. Opt. 52(22), 5355–5370 (2013).
    [Crossref] [PubMed]
  24. J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
    [Crossref]
  25. J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
    [Crossref]
  26. N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
    [Crossref]
  27. Y. An, J. S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24(16), 18445–18459 (2016).
    [Crossref] [PubMed]
  28. H. Wang, Q. Kemao, and S. H. Soon, “Valid point detection in fringe projection profilometry,” Opt. Express 23(6), 7535–7549 (2015).
    [Crossref] [PubMed]
  29. J. Lu, R. Mo, H. Sun, Z. Chang, and X. Zhao, “Invalid phase values removal method for absolute phase recovery,” Appl. Opt. 55(2), 387–394 (2016).
    [Crossref] [PubMed]
  30. T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
    [Crossref]
  31. E. Arias-Castro and D. L. Donoho, “Does median filtering truly preserve edges better than linear filtering?” Ann. Stat. 37(3), 1172–1206 (2009).
    [Crossref]
  32. Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).
  33. L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. 49(9), 1539–1548 (2010).
    [Crossref] [PubMed]
  34. S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48(10), 105601 (2009).
    [Crossref]
  35. B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53(16), 3415–3426 (2014).
    [Crossref] [PubMed]

2016 (6)

2015 (2)

2014 (3)

2013 (1)

2012 (2)

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. 50(8), 1130–1139 (2012).
[Crossref]

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

2011 (2)

Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. 36(13), 2518–2520 (2011).
[Crossref] [PubMed]

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

2010 (3)

2009 (3)

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref] [PubMed]

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48(10), 105601 (2009).
[Crossref]

E. Arias-Castro and D. L. Donoho, “Does median filtering truly preserve edges better than linear filtering?” Ann. Stat. 37(3), 1172–1206 (2009).
[Crossref]

2008 (1)

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

2007 (1)

Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed Fourier transform: A note on the threshold selection,” Opt. Laser Technol. 39(7), 1364–1369 (2007).
[Crossref]

2006 (1)

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

2003 (1)

1999 (1)

1997 (1)

1984 (1)

1979 (1)

T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
[Crossref]

1973 (1)

An, Y.

Arias-Castro, E.

E. Arias-Castro and D. L. Donoho, “Does median filtering truly preserve edges better than linear filtering?” Ann. Stat. 37(3), 1172–1206 (2009).
[Crossref]

Asundi, A.

Belenguer, T.

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

Bui, L. Q.

Carocci, M.

Chang, Y.

Chang, Z.

Chen, V.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

Cheng, Y.-Y.

Chicharo, J.

Chua, P. S. K.

Crespo, D.

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

Da, F.

Ding, Y.

Donoho, D. L.

E. Arias-Castro and D. L. Donoho, “Does median filtering truly preserve edges better than linear filtering?” Ann. Stat. 37(3), 1172–1206 (2009).
[Crossref]

Garnica, G.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
[Crossref]

M. Servin, J. M. Padilla, A. Gonzalez, and G. Garnica, “Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns,” Opt. Express 23(12), 15806–15815 (2015).
[Crossref] [PubMed]

Gomez-Pedrero, J. A.

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

Gonzalez, A.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
[Crossref]

M. Servin, J. M. Padilla, A. Gonzalez, and G. Garnica, “Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns,” Opt. Express 23(12), 15806–15815 (2015).
[Crossref] [PubMed]

Gool, L. V.

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

Gorthi, S.

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

Hoke, M.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

Huang, L.

Huang, T.

T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
[Crossref]

Huntley, J. M.

Hyun, J. S.

Hyun, J.-S.

Jones, J. D. C.

Karpinsky, N.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53(16), 3415–3426 (2014).
[Crossref] [PubMed]

Kemao, Q.

Koninckx, T.

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

Lee, S.

Li, B.

Li, Z.

Lu, J.

Mo, R.

Padilla, J. M.

Padilla, M.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
[Crossref]

Pan, B.

Polhemus, C.

Quiroga, J. A.

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

Rastogi, P.

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

Restrepo, R.

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

Rodella, R.

Saldner, H. O.

Sansoni, G.

Seah, H. S.

Servin, M.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
[Crossref]

M. Servin, J. M. Padilla, A. Gonzalez, and G. Garnica, “Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns,” Opt. Express 23(12), 15806–15815 (2015).
[Crossref] [PubMed]

Song, L.

Soon, S. H.

Su, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Sun, H.

Sun, X.

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Tang, G.

T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
[Crossref]

Towers, C. E.

Towers, D. P.

Vargas, J.

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

Wang, H.

Wang, P.

Wu, H.

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Wyant, J. C.

Xi, J.

Xiang, L.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Xing, G.

Yang, G.

T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
[Crossref]

Yu, S.

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Yu, X.

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Yu, Y.

Zhang, J.

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Zhang, Q.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Zhang, S.

Zhao, X.

Zheng, D.

Ann. Stat. (1)

E. Arias-Castro and D. L. Donoho, “Does median filtering truly preserve edges better than linear filtering?” Ann. Stat. 37(3), 1172–1206 (2009).
[Crossref]

Appl. Opt. (10)

J. Lu, R. Mo, H. Sun, Z. Chang, and X. Zhao, “Invalid phase values removal method for absolute phase recovery,” Appl. Opt. 55(2), 387–394 (2016).
[Crossref] [PubMed]

L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. 49(9), 1539–1548 (2010).
[Crossref] [PubMed]

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53(16), 3415–3426 (2014).
[Crossref] [PubMed]

D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase error analysis and compensation for phase shifting profilometry with projector defocusing,” Appl. Opt. 55(21), 5721–5728 (2016).
[Crossref] [PubMed]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[Crossref] [PubMed]

J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55(16), 4395–4401 (2016).
[Crossref] [PubMed]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12(9), 2071–2074 (1973).
[Crossref] [PubMed]

Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984).
[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]

L. Q. Bui and S. Lee, “Boundary Inheritance Codec for high-accuracy structured light three-dimensional reconstruction with comparative performance evaluation,” Appl. Opt. 52(22), 5355–5370 (2013).
[Crossref] [PubMed]

IEEE Trans. Acoust. Speech Signal Process. (1)

T. Huang, G. Yang, and G. Tang, “A fast two-dimensional median filtering algorithm,” IEEE Trans. Acoust. Speech Signal Process. 27(1), 13–18 (1979).
[Crossref]

Opt. Commun. (2)

J. Vargas, R. Restrepo, J. A. Quiroga, and T. Belenguer, “High dynamic range imaging method for interferometry,” Opt. Commun. 284(18), 4141–4145 (2011).
[Crossref]

S. Yu, J. Zhang, X. Yu, X. Sun, and H. Wu, “Unequal-period combination approach of gray code and phase-shifting for 3-D visual measurement,” Opt. Commun. 374(1), 97–106 (2016).
[Crossref]

Opt. Eng. (4)

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48(10), 105601 (2009).
[Crossref]

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

J. Vargas, T. Koninckx, J. A. Quiroga, and L. V. Gool, “Three-dimensional measurement of microchips using structured light techniques,” Opt. Eng. 47(5), 053602 (2008).
[Crossref]

J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, “Adaptive spatiotemporal structured light method for fast three-dimensional measurement,” Opt. Eng. 47(10), 107203 (2006).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

Q. Kemao, “A simple phase unwrapping approach based on filtering by windowed Fourier transform: A note on the threshold selection,” Opt. Laser Technol. 39(7), 1364–1369 (2007).
[Crossref]

Opt. Lasers Eng. (4)

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

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Peofilometry of three-dimensional discontinuous solids by combiing two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Lasers Eng. 87(76), 75–82 (2016).
[Crossref]

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng. 50(8), 1130–1139 (2012).
[Crossref]

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng. 50(4), 574–579 (2012).
[Crossref]

Opt. Lett. (4)

Other (4)

Y. Xu, D. Darga, J. Smid, A. M. Zysk, D. Teh, S. A. Boppart, and P. S. Carney, “Filtering and Unwrapping Doppler Optical Coherence Tomography Velocity Maps,” in Imaging and Applied Optics 2016, OSA Technical Digest (online) (Optical Society of America, 2016), paper CW1C.4.

D. C. Ghiglia, and M. D. Pritt, eds., Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

M. Servin, J. A. Quiroga, and J. M. Padilla, Fringe Pattern Analysis for Optical Metrology (Wiley-Vch, 2014).

Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1 Schematic diagram of phase unwrapping process.
Fig. 2
Fig. 2 (a) One sinusoidal pattern; (b) one Gray-code pattern; (c) unwrapped phase; (d) the congruent phase.
Fig. 3
Fig. 3 (a) One isolated erroneous pixel; (b) two adjacent erroneous pixels.
Fig. 4
Fig. 4 (a) The continuous phase; (b) the ideal phase; (c) the EPs; (d) the simulated phase.
Fig. 5
Fig. 5 The congruent phase obtained by: (a) the 1×3 median filter; (b) the 1×5 median filter; (c) the 13×13 median filter; (d) the 21×21 median filter, and EPs of: (e) the 1×3 median filter; (f) the 1×5 median filter; (g) the 13×13 median filter; (h) the 21×21 median filter.
Fig. 6
Fig. 6 The flowchart of the adaptive median filter.
Fig. 7
Fig. 7 (a) The congruent phase obtained by the 1×5 median filter; (b) the EPs of the 1×5 median filter; (c) the final phase obtained by the adaptive median filter; (d) the remaining EPs of the adaptive median filter.
Fig. 8
Fig. 8 (a) The simulated phase with a high noise level; (b) the EPs; (c) the EPs of the 1×5 median filter; (d) the remaining EPs of the adaptive median filter.
Fig. 9
Fig. 9 (a) The David plaster; (b) one sinusoidal pattern; (c) one Gray-code pattern.
Fig. 10
Fig. 10 The phase obtained by: (a) the traditional Gray-code method; (b) the adaptive median filter; (c) the 1×3 median filter;(d) the 1×5 median filter; (e) the 13×13 median filter; (f) the 21×21 median filter.
Fig. 11
Fig. 11 Performance of removing unwrapping errors: (a) the traditional Gray-code method; (b) the adaptive median filter; (c) the 1×3 median filter; (d) the 1×5 median filter; (e) the 13×13 median filter; (f) the 21×21 median filter.
Fig. 12
Fig. 12 Performance of preserving step-heights: (a) the traditional Gray-code method; (b) the adaptive median filter; (c) the 1×3 median filter; (d) the median filter; (e) the median filter; (f) the 21×21 median filter.
Fig. 13
Fig. 13 The 3D profile of the David plaster constructed from: (a) the traditional Gray-code method; (b) the adaptive median filter; (c) the 1×3 median filter; (d) the median filter; (e) the median filter; (f) the 21×21 median filter.
Fig. 14
Fig. 14 (a) Two isolated objects including one step-ladder and one blade; (b) one sinusoidal pattern; (c) one Gray-code pattern.
Fig. 15
Fig. 15 The 3D profile of two isolated objects from: (a) the traditional Gray-code method; (b) the adaptive median filter; (c) the median filter; (d) the median filter; (e) the median filter; (f) the 21×21 median filter.

Tables (4)

Tables Icon

Table 1 The numbers of erroneous pixels at different distances.

Tables Icon

Table 2 The number of EPs for the median filter in the simulation

Tables Icon

Table 3 The number of EPs for the adaptive median filter in the simulation.

Tables Icon

Table 4 The number of the detected EPs for the adaptive median filter in the experiment.

Equations (8)

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

I n ( x,y )=a( x,y )+b( x,y )cos[ φ( x,y )+ δ n ],
δ n = 2π( n1 ) /N ,n=1,2,,N.
φ( x,y )=arctan{ n=1 N I n ( x,y )sin δ n n=1 N I n ( x,y )cos δ n }.
s n = δ n T / 2π = ( n1 )T /N ,n=1,2,,N.
C( x,y )= i=1 m [ G i ( x,y )× 2 mi ] ,
Φ( x,y )=φ( x,y )+K( x,y )×2π.
Φ M ( x,y )=medfilt2[ Φ( x,y ); s x × s y ],
Φ C ( x,y )=φ( x,y )+2π×Round[ Φ M ( x,y )φ( x,y ) 2π ],

Metrics