Abstract

Moiré topography has the advantage of requiring only a single image to obtain a three-dimensional measurement, but it cannot discern the fringe order. Because there is an ambiguity problem when calculating the depth range by use of fringe intensity or phase unwrapping, it is impossible to obtain an absolute phase and an absolute depth range. It is therefore difficult to discern the relation between fringes in the cases in which the fringes are discontinuous or the objects are isolated. An intensity-modulated moiré topography method is presented. By modulation of the transmission factors of the projection and the observation gratings by exponential functions a new moiré pattern whose fringe intensity changes with its order can be produced. The fringe order can be extracted easily from the fringe intensity, and the absolute range of the skeleton line can be obtained solely from its intensity. At the same time, we can segment the moiré pattern by its fringe order. For every segment the absolute phase and the absolute depth range of every point of the moiré pattern can be obtained solely from its intensity with no need for interaction with the user.

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. H. Zhang, X. Wu, “3-D shape measurement with phase-shift and logical moiré method,” Acta Opt. Sinica 14, 408–411 (1994).
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. F. Bremand, “Phase unwrapping technique for object relief determination,” Opt. Lasers Eng. 21, 49–60 (1994).
    [CrossRef]
  13. X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
    [CrossRef]
  14. E. Schubert, “Fast 3-D object recognition using multiple color coded illumination,” in Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 3057–3060.
    [CrossRef]
  15. C. Lu, A. Yamaguchi, S. Inokuchi, “3-D measurement by intensity modulation moiré topography,” in 1996 International Workshop on Interferometry (Optical Society of Japan, Wako, Saitama/Japan, 1996), pp. 127–128.
  16. C. Lu, A. Yamaguchi, S. Inokuchi, “Intensity modulated moiré and its intensity-phase analysis,” in The Fourteenth International Conference on Pattern Recognition ICPR’98 (IEEE Computer Society, Bisbane, Queensland, Australia, 1998), pp. 1791–1793.
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    [CrossRef] [PubMed]

1998 (1)

X. F. Duan, M. Gao, L. M. Peng, “Accurate measurement of phase shift in electron holography,” Appl. Phys. Lett. 72, 771–773 (1998).
[CrossRef]

1996 (2)

1995 (1)

1994 (3)

G. Mauvoision, F. Bremand, A. Lagarde, “Three-dimensional shape reconstruction by phase-shifting shadow moiré,” Appl. Opt. 33, 2163–2169 (1994).
[CrossRef]

H. Zhang, X. Wu, “3-D shape measurement with phase-shift and logical moiré method,” Acta Opt. Sinica 14, 408–411 (1994).

F. Bremand, “Phase unwrapping technique for object relief determination,” Opt. Lasers Eng. 21, 49–60 (1994).
[CrossRef]

1993 (1)

1983 (1)

1970 (2)

Allen, J. B.

Andresn, K.

Arai, Y.

Atkinson, J. T.

X. Xie, J. T. Atkinson, M. J. Lalor, D. R. Burton, “Three-map absolute moiré contouring,” Appl. Opt. 35, 6690–6695 (1996).
[CrossRef]

Bremand, F.

F. Bremand, “Phase unwrapping technique for object relief determination,” Opt. Lasers Eng. 21, 49–60 (1994).
[CrossRef]

G. Mauvoision, F. Bremand, A. Lagarde, “Three-dimensional shape reconstruction by phase-shifting shadow moiré,” Appl. Opt. 33, 2163–2169 (1994).
[CrossRef]

Burton, D. R.

X. Xie, J. T. Atkinson, M. J. Lalor, D. R. Burton, “Three-map absolute moiré contouring,” Appl. Opt. 35, 6690–6695 (1996).
[CrossRef]

Chiang, F. P.

Duan, X. F.

X. F. Duan, M. Gao, L. M. Peng, “Accurate measurement of phase shift in electron holography,” Appl. Phys. Lett. 72, 771–773 (1998).
[CrossRef]

Gao, M.

X. F. Duan, M. Gao, L. M. Peng, “Accurate measurement of phase shift in electron holography,” Appl. Phys. Lett. 72, 771–773 (1998).
[CrossRef]

Halioua, M.

Han, B.

D. Post, B. Han, P. Ifju, High-Sensitivity Moiré (Springer-Verlag, New York, 1994), p. 444.

Huntley, J. M.

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

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffield, ed., Proc. SPIE3100, 185–192 (1997).
[CrossRef]

Ifju, P.

D. Post, B. Han, P. Ifju, High-Sensitivity Moiré (Springer-Verlag, New York, 1994), p. 444.

Inokuchi, S.

C. Lu, A. Yamaguchi, S. Inokuchi, “Intensity modulated moiré and its intensity-phase analysis,” in The Fourteenth International Conference on Pattern Recognition ICPR’98 (IEEE Computer Society, Bisbane, Queensland, Australia, 1998), pp. 1791–1793.

C. Lu, A. Yamaguchi, S. Inokuchi, “3-D measurement by intensity modulation moiré topography,” in 1996 International Workshop on Interferometry (Optical Society of Japan, Wako, Saitama/Japan, 1996), pp. 127–128.

Johnson, W. O.

Junptner, W.

Krishnamurthy, R. S.

Lagarde, A.

Lalor, M. J.

X. Xie, J. T. Atkinson, M. J. Lalor, D. R. Burton, “Three-map absolute moiré contouring,” Appl. Opt. 35, 6690–6695 (1996).
[CrossRef]

Liu, H.

Lu, C.

C. Lu, A. Yamaguchi, S. Inokuchi, “3-D measurement by intensity modulation moiré topography,” in 1996 International Workshop on Interferometry (Optical Society of Japan, Wako, Saitama/Japan, 1996), pp. 127–128.

C. Lu, A. Yamaguchi, S. Inokuchi, “Intensity modulated moiré and its intensity-phase analysis,” in The Fourteenth International Conference on Pattern Recognition ICPR’98 (IEEE Computer Society, Bisbane, Queensland, Australia, 1998), pp. 1791–1793.

Mauvoision, G.

Meadows, D. M.

Osten, W.

Peng, L. M.

X. F. Duan, M. Gao, L. M. Peng, “Accurate measurement of phase shift in electron holography,” Appl. Phys. Lett. 72, 771–773 (1998).
[CrossRef]

Peng, X.

X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
[CrossRef]

Post, D.

D. Post, B. Han, P. Ifju, High-Sensitivity Moiré (Springer-Verlag, New York, 1994), p. 444.

Saldner, H.

Saldner, H. O.

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffield, ed., Proc. SPIE3100, 185–192 (1997).
[CrossRef]

Schubert, E.

E. Schubert, “Fast 3-D object recognition using multiple color coded illumination,” in Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 3057–3060.
[CrossRef]

Takasaki, H.

Tiziani, H. J.

X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
[CrossRef]

Wu, X.

H. Zhang, X. Wu, “3-D shape measurement with phase-shift and logical moiré method,” Acta Opt. Sinica 14, 408–411 (1994).

Xie, X.

X. Xie, J. T. Atkinson, M. J. Lalor, D. R. Burton, “Three-map absolute moiré contouring,” Appl. Opt. 35, 6690–6695 (1996).
[CrossRef]

Yamada, T.

Yamaguchi, A.

C. Lu, A. Yamaguchi, S. Inokuchi, “3-D measurement by intensity modulation moiré topography,” in 1996 International Workshop on Interferometry (Optical Society of Japan, Wako, Saitama/Japan, 1996), pp. 127–128.

C. Lu, A. Yamaguchi, S. Inokuchi, “Intensity modulated moiré and its intensity-phase analysis,” in The Fourteenth International Conference on Pattern Recognition ICPR’98 (IEEE Computer Society, Bisbane, Queensland, Australia, 1998), pp. 1791–1793.

Ye, S. H.

X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
[CrossRef]

Yokozeki, S.

Yu, Q.

Zhang, H.

H. Zhang, X. Wu, “3-D shape measurement with phase-shift and logical moiré method,” Acta Opt. Sinica 14, 408–411 (1994).

Zhu, S. M.

X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
[CrossRef]

Acta Opt. Sinica (1)

H. Zhang, X. Wu, “3-D shape measurement with phase-shift and logical moiré method,” Acta Opt. Sinica 14, 408–411 (1994).

Appl. Opt. (8)

Appl. Phys. Lett. (1)

X. F. Duan, M. Gao, L. M. Peng, “Accurate measurement of phase shift in electron holography,” Appl. Phys. Lett. 72, 771–773 (1998).
[CrossRef]

Opt. Lasers Eng. (1)

F. Bremand, “Phase unwrapping technique for object relief determination,” Opt. Lasers Eng. 21, 49–60 (1994).
[CrossRef]

Other (6)

X. Peng, S. M. Zhu, S. H. Ye, H. J. Tiziani, “Problem of phase unwrapping for fringe pattern overlaid with random noise and segmented discontinuity,” in Automated Optical Inspection for Industry, F. Y. Wu, S. Ye, eds., Proc. SPIE2899, 96–104 (1996).
[CrossRef]

E. Schubert, “Fast 3-D object recognition using multiple color coded illumination,” in Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 3057–3060.
[CrossRef]

C. Lu, A. Yamaguchi, S. Inokuchi, “3-D measurement by intensity modulation moiré topography,” in 1996 International Workshop on Interferometry (Optical Society of Japan, Wako, Saitama/Japan, 1996), pp. 127–128.

C. Lu, A. Yamaguchi, S. Inokuchi, “Intensity modulated moiré and its intensity-phase analysis,” in The Fourteenth International Conference on Pattern Recognition ICPR’98 (IEEE Computer Society, Bisbane, Queensland, Australia, 1998), pp. 1791–1793.

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffield, ed., Proc. SPIE3100, 185–192 (1997).
[CrossRef]

D. Post, B. Han, P. Ifju, High-Sensitivity Moiré (Springer-Verlag, New York, 1994), p. 444.

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Figures (16)

Fig. 1
Fig. 1

Intensity distributions of moiré patterns: (a) classical moiré pattern and (b) intensity-modulated moiré pattern.

Fig. 2
Fig. 2

Relations among coordinates.

Fig. 3
Fig. 3

Principles of the measurement method.

Fig. 4
Fig. 4

Measurement system.

Fig. 5
Fig. 5

Intensity distributions of the projection: (a) exponential type and (b) linear type.

Fig. 6
Fig. 6

Experimental results of moiré topography of a plaster sphere by use of the skeleton method: (a) raw image, (b) deformed grating, (c) intensity-modulated moiré pattern, (d) 3-D representation of the moiré pattern, (e) cross section of the image in (c) along line AA′, (f) classical moiré pattern.

Fig. 7
Fig. 7

Measurement of the nonuniformity of the surface of an object: (a) deformed grating pattern, (b) image used for correction, (c) corrected grating pattern, (d) intensity of a cross section of the image shown in (a), (e) intensity of a cross section of the image shown in (b), (f) intensity of a cross section of the image shown in (c).

Fig. 8
Fig. 8

Results of correction for the image of a volleyball: (a) deformed grating pattern, (b) image used for correction, (c) corrected grating pattern.

Fig. 9
Fig. 9

Results of correction with the deformed grating pattern itself: (a) deformed grating pattern, (b) intensity of a cross section of the image shown in (a), (c) extracted o(x, y) term, (d) intensity of a cross section of the image shown in (c), (e) corrected grating pattern, (f) intensity of a cross section of the image shown in (e).

Fig. 10
Fig. 10

Experimental results of moiré topography by use of the skeleton method for isolated objects: (a) raw image, (b) intensity-modulated moiré pattern, (c) 3-D representation of the modulated moiré pattern.

Fig. 11
Fig. 11

Correlation between the intensity and the phase for a classical moiré pattern.

Fig. 12
Fig. 12

Correlation between the intensity and the phase for an intensity-modulated moiré pattern.

Fig. 13
Fig. 13

Directions of the intensity variation in a moiré pattern.

Fig. 14
Fig. 14

One-dimensional spin filter.

Fig. 15
Fig. 15

Simulation results for intensity–phase analysis: (a) moiré pattern, (b) fringe-orientation map, (c) binary orientation-change map, (d) modulated skeleton, (e) segmented moiré pattern, (f) result of the intensity–phase analysis, (g) 3-D shape of the segmented pattern, (h) cross section of the results shown in (f) when y = 150 (solid curve) and y = 363 (dashed curve).

Fig. 16
Fig. 16

Experimental results of the imaging of a plaster sphere by use of intensity–phase analysis: (a) raw image, (b) intensity-modulated moiré pattern, (c) moiré pattern, (d) fringe-orientation map, (e) binary orientation-change map, (f) modulated skeleton, (g) segmented moiré pattern, (h) results of phase analysis, (i) 3-D plot of the measurement data (points) and the interpolation lines, (j) cross section of the results shown in (h) when y = 200 (solid curve) and y = 250 (dashed curve).

Equations (30)

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

Im=Am cosωh+ω0,
ωhN+ω0=2πN.
hN=2πN-ω0ω.
Δh=hN+1-hN=2πω.
Am=fN.
TS=ak1+x121+sin2πx1S,
TO=ak2-x221+sin2πx2-S,
IS=ak1+x121+sin2πx1SI0,
Im=18 ak1+k2a-dh/h+l cos2πsdh-h+lh+l I0,
Im=ka-sN cos2πN,
Am=ka-sN,
I-inx1, y1=ak1+x121+sin2πx1sox, y,
I-corx1, y1=ox, y.
I-inx1, y1=I-inx1, y1I-corx1, y1=ak1+x121+sin2πx1s,
H256B.
Hm=Hλ  256λB,
es=1HmλB2567.8%,
h=1ω arccosImAm-ω0ω=1ω α-ω0ω,
α=arccosImAm.
Imαi=ImkT-αi=ImkT+αi,
αNα<αN+2π,
hNh<hN+Δh,
αi, j=arccos Imi, jdImdα<02π-arccos Imi, jdImdα0,
hi, j=hN+kαi, j,
I¯i, j, θ=12n+1k=-nn Imi+k cos θ, j+k sin θ,
Di, j, θ=k=-nn |Imi+k cos θ, j+k sin θ-I¯i, j, θ|.
δi, j=θmax,
Di, j, θmax=maxθ=02π Di, j, θ.
Gi, j=sgnk=0k=nImi+k cos δ, j+k sin δ-Imi-k cos δ, j-k sin δ,
Bi, j=255Gi, j>00Gi, j0,

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