Abstract

We present a method that uses two groups of fringe patterns on one grating for phase-measuring profilometry. A two-frequency grating is projected onto the object. The high frequency is N(N = 3, 4, 5, …) times greater than the low frequency. Using a proper phase shift, we calculated the wrapped phases of the two frequencies. When the linearity of the two phases are considered, an accurate phase of the high frequency can be unwrapped. Because the low frequency is N times more insensitive to height discontinuity, the system is more tolerable to height discontinuity.

© 1997 Optical Society of America

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References

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  1. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]
  2. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985).
    [CrossRef] [PubMed]
  3. M. Takeda, K. Mutoh, “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. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
    [CrossRef]
  5. X.-Y. 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]
  6. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [CrossRef] [PubMed]
  7. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
    [CrossRef]
  8. D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
    [CrossRef]
  9. M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.
  10. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]
  11. M. Takeda, M. Kitoh, “Spatiotemporal frequency multiplex heterodyne interferometry,” J. Opt. Soc. Am. A 9, 1607–1614 (1992).
    [CrossRef]
  12. D. R. Burton, M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33, 2939–2948 (1994).
    [CrossRef] [PubMed]
  13. 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]
  14. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
    [CrossRef]

1994 (3)

1993 (2)

X.-Y. 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]

J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[CrossRef] [PubMed]

1992 (1)

1991 (2)

D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
[CrossRef] [PubMed]

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

1990 (1)

J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

1987 (1)

1985 (1)

1984 (1)

1983 (1)

Bone, D. J.

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]

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Burton, D. R.

Chen, W.

Ghiglia, D. C.

Guo, L.-R.

J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Halioua, M.

Huntley, J. M.

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]

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Kitoh, M.

Lalor, M. J.

Li, J.

J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Liu, H. C.

Mastin, G. A.

Mutoh, K.

Natome, K.

M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.

Romero, L. A.

Saldner, H.

Srinivasan, V.

Su, X.-Y.

X.-Y. 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]

J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Takeda, M.

M. Takeda, M. Kitoh, “Spatiotemporal frequency multiplex heterodyne interferometry,” J. Opt. Soc. Am. A 9, 1607–1614 (1992).
[CrossRef]

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

M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.

Tan, Y.

Towers, D. P.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

von Bally, G.

X.-Y. 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.-Y. 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]

Watanabe, Y.

M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.

Zhao, H.

Appl. Opt. (7)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

X.-Y. 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]

Opt. Eng. (1)

J. Li, X.-Y. Su, L.-R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Opt. Lasers Eng. (2)

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[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]

Other (1)

M. Takeda, K. Natome, Y. Watanabe, “Phase unwrapping by neural network,” in Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns. W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 136–141.

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Figures (4)

Fig. 1
Fig. 1

Optical geometry of the PMP system: P1, P2, entrance and exit pupils of projector; I1, I2, entrance and exit pupils of imaging optics; Dc, CCD detector; D, point tested; A. C, D, reference points on reference plane; d, distance between P and I2;L, distance between I2 and O.

Fig. 2
Fig. 2

Simulation of the phase distribution on a plane.

Fig. 3
Fig. 3

(a) Tested platform. A1 to A3 are isolated. (b) Image modulated by a two-frequency grating. (The equivalent wavelengths are 7.2 and36 mm separately.)

Fig. 4
Fig. 4

Three-dimensional profile of the platform.

Equations (17)

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I x ,   y = A x ,   y + B x ,   y cos   ϕ x ,   y ,
ϕ x ,   y = arctan N 2 B x ,   y sin ϕ x ,   y N 2 B x ,   y cos ϕ x ,   y = arctan n = 1 N   I n x ,   y sin 2 π n / N n = 1 N   I n x ,   y cos 2 π n / N .
ϕ h x ,   y = ϕ x ,   y - ϕ r x ,   y .
h x ,   y = AC ¯ L / d 1 + AC ¯ / d .
λ e = p 0 / tan   θ ,
p 0 = p 1 / N N = 3 ,   4 ,   5 ,   .
I x ,   y = A x ,   y + B 0 x ,   y cos   ϕ 0 x ,   y + B 1 x ,   y cos   ϕ 1 x ,   y ,
I 1 n x ,   y = A x ,   y + B 0 x ,   y cos ϕ 0 x ,   y + 2 n π + B 1 x ,   y cos ϕ 1 x ,   y + 2 π n / N .
BS = B 1   sin   ϕ 1 x ,   y = 2 N n = 1 N   I 1 n   sin 2 π n / N ,
BC = B 1   cos   ϕ 1 x ,   y = 2 N n = 1 N   I 1 n   cos 2 π n / N ,
ϕ 1 x ,   y = arctan BS BC .
I 0 n x ,   y = A x ,   y + B 0 x ,   y cos ϕ 0 x ,   y + 2 n π / N + B 1 x ,   y cos ϕ 1 x ,   y + 2 π n / N 2 .
I 0 n x ,   y = A x ,   y + B 0 x ,   y cos ϕ 0 x ,   y + 2 n π / N + BC   cos 2 n π / N 2 - BS   sin 2 n π / N 2 = I 0 n x ,   y + BC   cos 2 n π / N 2 - BS   sin 2 n π / N 2 ,
ϕ 0 x ,   y = arctan n = 1 N   I 0 n x ,   y sin 2 π n / N n = 1 N   I 0 n x ,   y cos 2 π n / N .
ϕ 1 h x ,   y = U ϕ 1 x ,   y - ϕ 1 r x ,   y ,
ϕ 0 h x ,   y = U ϕ 0 x ,   y - ϕ 0 r x ,   y .
ϕ 0 h x ,   y = N ϕ 1 h x ,   y .

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