Abstract

Although promised to be a fast and accurate three-dimensional shape measurement technique, grating projection profilometry based on phase measurement has been frequently baffled by the difficulty in phase unwrapping. We introduce the conventional excess fraction method into profilometry and extend it to nonlinear domain. Nonlinear excess fraction method (NLEFM), on the basis of which a multifrequency grating projection profilometry is developed, can work as a robust temporal phase unwrapper, which may extend the reliable measuring range by dozens of times at no cost of accuracy. The principle of NLEFM is detailed, and experimental results are given in which complex profiles are reliably measured with the novel system.

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).
    [CrossRef]
  4. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
    [CrossRef]
  5. H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
    [CrossRef]
  6. J. M. Huntley, H. O. Saldner, “Error reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14, 3188–3196 (1997).
    [CrossRef]
  7. W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
    [CrossRef]
  8. G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
    [CrossRef]
  9. J.-L. Li, H.-J. Su, X.-Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1997 (3)

1996 (1)

K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).
[CrossRef]

1995 (1)

W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
[CrossRef]

1994 (3)

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (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]

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

1987 (1)

1985 (1)

1983 (1)

Andrä, P.

W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
[CrossRef]

Biancardi, L.

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
[CrossRef]

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]

Chen, W.

Creath, K.

K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).
[CrossRef]

Docchio, F.

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
[CrossRef]

Eiju, T.

Halioua, M.

Hariharan, P.

Huntley, J. M.

J. M. Huntley, H. O. Saldner, “Error reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14, 3188–3196 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

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, J.-L.

Liu, H. C.

Minoni, U.

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
[CrossRef]

Mutoh, K.

Nadeborn, W.

W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
[CrossRef]

Oreb, B. F.

Osten, W.

W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
[CrossRef]

Saldner, H. O.

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

J. M. Huntley, H. O. Saldner, “Error reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14, 3188–3196 (1997).
[CrossRef]

Sansoni, G.

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
[CrossRef]

Schmit, J.

K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).
[CrossRef]

Srinivasan, V.

Su, H.-J.

Su, X.-Y.

Takeda, M.

Tan, Y.

Zhao, H.

Appl. Opt. (5)

IEEE Trans. Instrum. Meas. (1)

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–565 (1994).
[CrossRef]

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

Opt. Eng. (1)

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

Opt. Lasers Eng. (3)

W. Nadeborn, P. Andrä, W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24, 245–260 (1995).
[CrossRef]

K. Creath, J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).
[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]

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Figures (7)

Fig. 1
Fig. 1

Typical optical geometry for grating projection profilometry.

Fig. 2
Fig. 2

Experiment and calibration setup.

Fig. 3
Fig. 3

Calibration results at a given pixel.

Fig. 4
Fig. 4

Wrapped phase map (black and white represent 0 and 1, respectively).

Fig. 5
Fig. 5

Coarse and fine measurement results.

Fig. 6
Fig. 6

Reconstructed profile of the object (shadow area removed).

Fig. 7
Fig. 7

Grayscale representation of an upper jaw plaster replica.

Equations (16)

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

k=n+ε.
h=f1-1n1+ε1=f2-1n2+ε2,
f0h=f1h-f2h=n1-n2+ε1-ε2=Δn+Δε.
hmax<f0-11,
hC=f0-1Δεm,
ΔhC=df0-1dk 2e.
df1dh ΔhC<12,
df1dhdf0-1dk<14e
n1=INTf1hC-ε1m+0.5
hF=f1-1n1+ε1m.
ΔhF=df1-1dk e.
kx0, h=fd2+L21/2mLLx0+d-x0hL2+d2-dx0L-L2+2d2-dx0h,
k1h/k2h=f1/f2,
h=f0-1k=λ1λ2λ2-λ1 k=λSk,
λSλ1<14e.
df1dhdf0-1dkmax<14e,

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