Abstract

A new phase-unwrapping algorithm based on fringe frequency analysis is presented that will achieve greater automation and precision in measuring complex objects by phase-measuring profilometry (PMP). The new algorithm, which combines digital weighted filtering in the frequency domain and modulation ordering in the spatial domain, can recognize corrupt pixels automatically and produce a better phase-unwrapping path. By frequency weighted filtering, the analysis of fringe frequency is converted into the analysis of fringe modulation. Then, based on a strong correlation between local spatial frequency and the reliability of phase data, ordering of the filtered modulation produces an optimized unwrapping path. Simulation and experiments verify the new algorithm.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase measuring profilometry of 3-D diffuse object,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef]
  2. X.-Y. Su, W.-S. Zhou, C. von Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
    [CrossRef]
  3. M. Takeda, K. Motoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef] [PubMed]
  4. J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
    [CrossRef]
  5. X.-Y. Su, J. Li, L.-R. Gou, “An improved Fourier transform profilometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 241–244 (1990).
    [CrossRef]
  6. J.-F. Lin, X.-Y. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995).
    [CrossRef]
  7. S. Toyooka, Y. Iwasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 3012–3018 (1986).
  8. S. Tang, Y. Y. Hung, “Fast profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 29, 3012–3018 (1990).
    [CrossRef] [PubMed]
  9. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3260–3270 (1989).
  10. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
    [CrossRef]
  11. H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
    [CrossRef]
  12. A. Asundi, W. S. Zhou, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
    [CrossRef]
  13. H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef] [PubMed]
  14. Y. Hao, Y. Zhao, D. Li, “Multifrequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38, 4106–4110 (1999).
    [CrossRef]
  15. X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
    [CrossRef]
  16. X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
    [CrossRef]
  17. X. Su, W.-S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbielska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
    [CrossRef]
  18. X. Su, “Phase unwrapping techniques for 3-D shape measurement,” in International Conference on Holography and Optical Information Processing (ICHOP ’96), G. Jin, G. Mu, G. C. Sincerbox, eds., Proc. SPIE2866, 460–465 (1996).
    [CrossRef]
  19. J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
    [CrossRef]

1999 (1)

1998 (1)

1997 (3)

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

H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

1995 (1)

J.-F. Lin, X.-Y. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995).
[CrossRef]

1994 (2)

X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
[CrossRef]

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

1993 (1)

X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[CrossRef]

1992 (1)

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

1990 (2)

J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

S. Tang, Y. Y. Hung, “Fast profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 29, 3012–3018 (1990).
[CrossRef] [PubMed]

1989 (1)

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3260–3270 (1989).

1986 (1)

S. Toyooka, Y. Iwasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 3012–3018 (1986).

1984 (1)

1983 (1)

Asundi, A.

Bryanston-Cross, P. J.

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

Gou, L.-R.

J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

X.-Y. Su, J. Li, L.-R. Gou, “An improved Fourier transform profilometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 241–244 (1990).
[CrossRef]

Halioua, M.

Hao, Y.

Hung, Y. Y.

Huntley, J. M.

Iwasa, Y.

S. Toyooka, Y. Iwasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 3012–3018 (1986).

Judge, T. R.

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

Li, D.

Li, J.

H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

X.-Y. Su, J. Li, L.-R. Gou, “An improved Fourier transform profilometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 241–244 (1990).
[CrossRef]

Lin, J.-F.

J.-F. Lin, X.-Y. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995).
[CrossRef]

Liu, H. C.

Motoh, K.

Saldner, H. O.

Srinivasan, V.

Su, H.

H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

Su, X.

H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
[CrossRef]

X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[CrossRef]

X. Su, W.-S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbielska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

X. Su, “Phase unwrapping techniques for 3-D shape measurement,” in International Conference on Holography and Optical Information Processing (ICHOP ’96), G. Jin, G. Mu, G. C. Sincerbox, eds., Proc. SPIE2866, 460–465 (1996).
[CrossRef]

Su, X.-Y.

J.-F. Lin, X.-Y. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995).
[CrossRef]

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

J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

X.-Y. Su, J. Li, L.-R. Gou, “An improved Fourier transform profilometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 241–244 (1990).
[CrossRef]

Takeda, M.

Tang, S.

Toyooka, S.

S. Toyooka, Y. Iwasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 3012–3018 (1986).

von Bally, C.

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

Von Bally, G.

X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
[CrossRef]

X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[CrossRef]

Vukicevic, D.

X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[CrossRef]

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

Zarubin, A. M.

X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
[CrossRef]

Zhao, Y.

Zhou, W. S.

Zhou, W.-S.

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

X. Su, W.-S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbielska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

Appl. Opt. (8)

Opt. Commun. (3)

X. Su, G. Von Bally, D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[CrossRef]

X. Su, A. M. Zarubin, G. Von Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994).
[CrossRef]

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

Opt. Eng. (4)

J. Li, X.-Y. Su, L.-R. Gou, “An improved Fourier transform profilometry for automatic measurement of 3-D object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

J.-F. Lin, X.-Y. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995).
[CrossRef]

H. Su, J. Li, X. Su, “Phase unwrapping without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

Opt. Lasers Eng. (1)

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

Other (3)

X.-Y. Su, J. Li, L.-R. Gou, “An improved Fourier transform profilometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 241–244 (1990).
[CrossRef]

X. Su, W.-S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbielska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

X. Su, “Phase unwrapping techniques for 3-D shape measurement,” in International Conference on Holography and Optical Information Processing (ICHOP ’96), G. Jin, G. Mu, G. C. Sincerbox, eds., Proc. SPIE2866, 460–465 (1996).
[CrossRef]

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 (18)

Fig. 1
Fig. 1

Optical geometry of a PMP system.

Fig. 2
Fig. 2

Flow chart of the new algorithm.

Fig. 3
Fig. 3

Effects of digital weighted filtering: (a) the intensity distribution of a fringe pattern in which the local spatial fringe frequency changes gradually, (b) the filtered modulation function of the fringe in (a) through a rectangular window, and (c) the filtered modulation function of the fringe in (a) through a Hanning window.

Fig. 4
Fig. 4

Simulated object.

Fig. 5
Fig. 5

Simulated object represented in gray scale.

Fig. 6
Fig. 6

Imitated fringe on the simulated surface.

Fig. 7
Fig. 7

Result of unwrapping obtained by a simple flood-fill method.

Fig. 8
Fig. 8

Modulation after digital weighted filtering.

Fig. 9
Fig. 9

Unwrapping result from the new algorithm.

Fig. 10
Fig. 10

Denture measured in the experiment.

Fig. 11
Fig. 11

One fringe pattern captured on the measured surface.

Fig. 12
Fig. 12

Wrapped phase obtained after phase calculation.

Fig. 13
Fig. 13

Modulation after digital weighted filtering.

Fig. 14
Fig. 14

Intermediate step (1) of phase unwrapping.

Fig. 15
Fig. 15

Intermediate step (2) of phase unwrapping.

Fig. 16
Fig. 16

Intermediate step (3) of phase unwrapping.

Fig. 17
Fig. 17

Intermediate step (4) of phase unwrapping.

Fig. 18
Fig. 18

Result of unwrapping with the new algorithm.

Equations (7)

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

Ix, y=I0x, y+ax, ycos ϕx, y.
Ix, y=I0x, yBx, y1+Cx, ycosϕx, y,
ϕx, y=arctann=1N Inx, ysin2πn/N×n=1N Inx, ycos2πn/N-1.
Mx, y=n=1N Inx, ysin2πn/N2+n=1N Inx, ycos2πn/N21/2.
hx, y=AC¯L/d1+AC¯/d.
h=2.4481-x2 exp-x2-y+12-8.16x5-x3-y5exp-x2-y2-0.272×exp-x+12-y2.
h1/4=0.5×h.

Metrics