Abstract

Sinusoidal structured illumination is used widely in three-dimensional (3-D) sensing and machine vision. Phase algorithms, for example, in phase-measuring profilometry, are inherently free of errors only with perfect sinusoidal fringe projection. But it is difficult to produce a perfect sinusoidal grating. We propose a new concept, area modulation, to improve the sinusoidality of structured illumination. A binary-coded picture is made up of many micrometer units. An aperture is open in every micrometer unit, and its area is determined by the value of the sinusoidal function. When such a grating is projected onto an object surface, the image of the grating becomes sinusoidal because of the convolution function of an optical system. We have designed and manufactured an area modulation grating for sinusoidal structure illumination using a large-scale integration technique. The area modulation grating has been used in the high-precision phase-measuring profilometry system, and the phase errors caused by the area modulation grating are reduced to 0.1%. The grating guaranteed the entire measuring accuracy to a 1% equivalent wavelength. The experimental results proved that area modulation grating would be of significant help in improving the phase-measurement accuracy of the 3-D sensing system.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. W. Chen, H. Yang, X. Su, “Error caused by sampling in Fourier transform profilometry,” Opt. Eng. 38, 1029–1034 (1999).
    [CrossRef]
  5. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. Y. D. Hao, Y. Zhao, D. C. Li, “Multifrequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38, 4106–4110 (1999).
    [CrossRef]
  9. 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]
  10. 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]
  11. J. Li, X. Su, J. Li, “Phase unwrapping algorithm based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
    [CrossRef]
  12. A. Asundi, W. Zhou, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
    [CrossRef]
  13. W. Zhou, X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
    [CrossRef]
  14. A. Asundi, W. Zhou, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38, 3556–3561 (1999).
    [CrossRef]
  15. S. Tang, Y. Y. Hung, “Fast profilometer for the automatic measurement of 3-D object shapes,” Appl. Opt. 29, 3012–3018 (1990).
    [CrossRef] [PubMed]
  16. X. Su, L. Su, “New 3D profilometry based on modulation measurement,” in Automated Optical Inspection for Industry: Theory, Technology, and Applications II, S. Ye, ed., Proc. SPIE3558, 1–7 (1998).
  17. L. Su, X. Su, W. Li, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153–1158 (1999).
    [CrossRef]

2000 (1)

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1999 (4)

1998 (1)

1997 (1)

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

1994 (1)

W. Zhou, X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (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 profilometer for the automatic measurement of 3-D object shapes,” Appl. Opt. 29, 3012–3018 (1990).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

1982 (1)

Asundi, A.

Brown, G. M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, W.

W. Chen, H. Yang, X. Su, “Error caused by sampling in Fourier transform profilometry,” Opt. Eng. 38, 1029–1034 (1999).
[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]

Halioua, M.

Hao, Y. D.

Hung, Y. Y.

Ina, H.

Koboyashi, S.

Li, D. C.

Li, J.

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]

Li, W.

Liu, H. C.

Motoh, K.

Song, M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Srinivasan, V.

Su, L.

L. Su, X. Su, W. Li, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153–1158 (1999).
[CrossRef]

X. Su, L. Su, “New 3D profilometry based on modulation measurement,” in Automated Optical Inspection for Industry: Theory, Technology, and Applications II, S. Ye, ed., Proc. SPIE3558, 1–7 (1998).

Su, X.

L. Su, X. Su, W. Li, “Application of modulation measurement profilometry to objects with surface holes,” Appl. Opt. 38, 1153–1158 (1999).
[CrossRef]

W. Chen, H. Yang, X. Su, “Error caused by sampling in Fourier transform profilometry,” Opt. Eng. 38, 1029–1034 (1999).
[CrossRef]

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

W. Zhou, X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (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, L. Su, “New 3D profilometry based on modulation measurement,” in Automated Optical Inspection for Industry: Theory, Technology, and Applications II, S. Ye, ed., Proc. SPIE3558, 1–7 (1998).

Su, X.-Y.

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]

Takeda, M.

Tang, S.

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, 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]

Yang, H.

W. Chen, H. Yang, X. Su, “Error caused by sampling in Fourier transform profilometry,” Opt. Eng. 38, 1029–1034 (1999).
[CrossRef]

Zhao, Y.

Zhou, W.

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. (7)

J. Mod. Opt. (1)

W. Zhou, X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (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]

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]

Opt. Eng. (4)

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

W. Chen, H. Yang, X. Su, “Error caused by sampling in Fourier transform profilometry,” Opt. Eng. 38, 1029–1034 (1999).
[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]

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

Other (2)

X. Su, L. Su, “New 3D profilometry based on modulation measurement,” in Automated Optical Inspection for Industry: Theory, Technology, and Applications II, S. Ye, ed., Proc. SPIE3558, 1–7 (1998).

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]

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Figures (8)

Fig. 1
Fig. 1

Optical geometry of PMP.

Fig. 2
Fig. 2

Area modulation grating (magnified).

Fig. 3
Fig. 3

Spatial-frequency spectrum of the area modulation grating.

Fig. 4
Fig. 4

Sinusoidal illumination structure obtained when the filter ξ = 10f x 0 .

Fig. 5
Fig. 5

Residual error between the image field of the area modulation and the standard sinusoidal grating.

Fig. 6
Fig. 6

Image of the area modulation grating captured by the CCD.

Fig. 7
Fig. 7

Spatial-frequency spectrum of the practical area modulation gratings.

Fig. 8
Fig. 8

Comprehensive residual error of the PMP calibration measurement: (a) errors of the centerline in the vertical direction; (b) errors of the centerline in the horizontal direction.

Tables (2)

Tables Icon

Table 1 Phase Errors Caused by the Area Modulation Grating (in radians) with Sampling Point Ma

Tables Icon

Table 2 Phase Errors Caused by the Area Modulation Grating (in radians) with Phase-Shifting Steps Sa

Equations (12)

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

Ix, y=Ax, y+Bx, ycos2πp x+ϕx, y,
ϕx, y=arctann=1S Inx, ysin2πn/Nn=1S Inx, ycos2πn/N.
hx, y=ACL/d1+AC/d.
hx, y=AC Ld=p0tgθδϕ2π=λeδϕ2π,
fx=0.5+0.5 cos2πp0 x+ϕ,  fx0, 1,
tunitx, y=rectxδx, yqx  combxΔx,
qx=mod2fxpy, ΔyΔy.
tx, y=tunitx, y  combxpx, ypy=rectxΔx, yqx  combxΔx combxpx, ypy.
Tfx, fy=FTtx, y=FTrectxΔx, yqx×FTcombxΔxFTcombxpx, ypy=T1fx, fyl=-+ δfx-lΔx×m=-+n=-+ δfx-mPxδfy-nPy.
l=-+ δfx-lΔxm=-+ δfx-mPx=l=-+m=-+ δfx-lMPxδfx-mPx=m=-+ δfx-mPx.
Tfx, fy=m=-+n=-+ T1fx, fyδfx-mPxδfy-nPy=m=-+n=-+ T1mPx, nPyδfx-mPxδfy-nPy,
T1fx, fy=FTrectxΔx, yqx=FTrectxΔx,×ymod1+cos2πp xPy, ΔyΔy.

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