Abstract

A microscopic three-dimensional (3-D) shape measurement system based on digital fringe projection has been developed and experimentally investigated. A Digital Micromirror Device along with its illumination optics is integrated into a stereomicroscope, which projects computer-generated fringe patterns with a sinusoidal intensity profile through the microscope objective onto the object surface being measured. The fringe patterns deformed by the object surface are recorded by a CCD camera. The microscopic 3-D shape of the object surface is measured and reconstructed by use of a phase-shifting technique. We discuss design considerations and error analysis of the system. Experimental results successfully demonstrate the capability of this technique for surface profile measurement of rough surfaces at the micrometer level.

© 2002 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  2. K. Leonhardt, U. Droste, H. J. Tiziani, “Microshape and rough-surface analysis by fringe projection,” Appl. Opt. 33, 7477–7488 (1994).
    [CrossRef] [PubMed]
  3. R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
    [CrossRef]
  4. L. J. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in International Electron Devices Technical Digest (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 381–384.
  5. J. M. Younse, “Mirrors on a chip,” IEEE Spectrum 30(11), 27–31 (1993).
    [CrossRef]
  6. P. S. Huang, C. Zhang, F. P. Chiang, “Digital fringe projection technique for high-speed 3D shape measurement,” in Process Control and Inspection for Industry, S. Zhang, W. Gao, eds., Proc. SPIE4222, 54–60 (2000).
    [CrossRef]
  7. C.-M. Chang, H.-P. D. Shieh, “Design of illumination and projection optics for projectors with single digital micromirror devices,” Appl. Opt. 39, 3202–3208 (2000).
    [CrossRef]
  8. K. Kinnstaetter, A. W. Lohmann, J. Schwider, N. Streibl, “Accuracy of phase shifting interferometry,” Appl. Opt. 27, 5082–5089 (1988).
    [CrossRef] [PubMed]
  9. J. V. Wingerden, H. J. Frankena, C. Smorenburg, “Linear approximation for measurement errors in phase shifting interferometry,” Appl. Opt. 30, 2718–2729 (1991).
    [CrossRef] [PubMed]
  10. P. Hariharan, “Phase-shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
    [CrossRef]
  11. Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
    [CrossRef]
  12. V. Srinivasan, H.-C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]
  13. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef] [PubMed]

2000 (3)

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

P. Hariharan, “Phase-shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
[CrossRef]

C.-M. Chang, H.-P. D. Shieh, “Design of illumination and projection optics for projectors with single digital micromirror devices,” Appl. Opt. 39, 3202–3208 (2000).
[CrossRef]

1997 (1)

R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[CrossRef]

1994 (1)

1993 (1)

J. M. Younse, “Mirrors on a chip,” IEEE Spectrum 30(11), 27–31 (1993).
[CrossRef]

1991 (1)

1988 (1)

1984 (1)

1983 (1)

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]

Chang, C.-M.

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]

Chiang, F. P.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
[CrossRef]

P. S. Huang, C. Zhang, F. P. Chiang, “Digital fringe projection technique for high-speed 3D shape measurement,” in Process Control and Inspection for Industry, S. Zhang, W. Gao, eds., Proc. SPIE4222, 54–60 (2000).
[CrossRef]

Droste, U.

Fleischer, M.

R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[CrossRef]

Frankena, H. J.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
[CrossRef]

Halioua, M.

Hariharan, P.

P. Hariharan, “Phase-shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
[CrossRef]

Hornbeck, L. J.

L. J. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in International Electron Devices Technical Digest (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 381–384.

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
[CrossRef]

Huang, P. S.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
[CrossRef]

P. S. Huang, C. Zhang, F. P. Chiang, “Digital fringe projection technique for high-speed 3D shape measurement,” in Process Control and Inspection for Industry, S. Zhang, W. Gao, eds., Proc. SPIE4222, 54–60 (2000).
[CrossRef]

Kinnstaetter, K.

Leonhardt, K.

Liu, H.-C.

Lohmann, A. W.

Mutoh, K.

Schwider, J.

Shieh, H.-P. D.

Smorenburg, C.

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.

Streibl, N.

Takeda, M.

Tiziani, H. J.

R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[CrossRef]

K. Leonhardt, U. Droste, H. J. Tiziani, “Microshape and rough-surface analysis by fringe projection,” Appl. Opt. 33, 7477–7488 (1994).
[CrossRef] [PubMed]

Windecker, R.

R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[CrossRef]

Wingerden, J. V.

Younse, J. M.

J. M. Younse, “Mirrors on a chip,” IEEE Spectrum 30(11), 27–31 (1993).
[CrossRef]

Zhang, C.

P. S. Huang, C. Zhang, F. P. Chiang, “Digital fringe projection technique for high-speed 3D shape measurement,” in Process Control and Inspection for Industry, S. Zhang, W. Gao, eds., Proc. SPIE4222, 54–60 (2000).
[CrossRef]

Appl. Opt. (6)

IEEE Spectrum (1)

J. M. Younse, “Mirrors on a chip,” IEEE Spectrum 30(11), 27–31 (1993).
[CrossRef]

Opt. Eng. (3)

R. Windecker, M. Fleischer, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[CrossRef]

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

P. Hariharan, “Phase-shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
[CrossRef]

Other (3)

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, “Calibration of a 3D surface contouring and ranging system,” in Three-Dimensional Imaging, Optical Metrology, and Inspection V, K. G. Harding, ed., Proc. SPIE3835, 158–166 (1999).
[CrossRef]

L. J. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in International Electron Devices Technical Digest (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 381–384.

P. S. Huang, C. Zhang, F. P. Chiang, “Digital fringe projection technique for high-speed 3D shape measurement,” in Process Control and Inspection for Industry, S. Zhang, W. Gao, eds., Proc. SPIE4222, 54–60 (2000).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Light switching characteristic of a DMD mirror.

Fig. 2
Fig. 2

Optical layout of the fringe projection microscope system.

Fig. 3
Fig. 3

DMD illumination optics.

Fig. 4
Fig. 4

Layout of the optical axes of the illumination optics.

Fig. 5
Fig. 5

Pictures of the microscopic 3-D shape measurement system.

Fig. 6
Fig. 6

(a) Gray-scale curves (a) before and (b) after linearity compensation.

Fig. 7
Fig. 7

Schematic diagram of phase and height conversion.

Fig. 8
Fig. 8

Picture of the step height standard.

Fig. 9
Fig. 9

Cross section of the measured step standard.

Fig. 10
Fig. 10

Measured step height.

Fig. 11
Fig. 11

Phase values at different positions. From top to bottom: phase values at positions from 50 to -50 µm in steps of 10 µm relative to the reference surface.

Fig. 12
Fig. 12

Measurement results of the step standard after error compensation.

Fig. 13
Fig. 13

Measurement results of a paper surface: (a) fringe pattern and (b) 3-D shape.

Fig. 14
Fig. 14

Measurement results of a piece of medium-grade sandpaper: (a) fringe pattern and (b) 3-D shape.

Equations (18)

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

I1i, j=Ii, j+Ii, jcosϕi, j-2π/3,
I2i, j=Ii, j+Ii, jcosϕi, j,
I3i, j=Ii, j+Ii, jcosϕi, j+2π/3,
ϕi, j=arctan3I1-I32I2-I1-I3.
x0.242=y-0.242=z0.940.
fRIin=r0+r1Iin+r2Iin2++riIini,
fGIin=g0+g1Iin+g2Iin2++giIini,
fBIin=b0+b1Iin+b2Iin2++biIini,
upper limit=minfR255, fG255, fB255,
lower limit=maxfR40, fG40, fB40.
Iout=lower limit+upper limit-lower limit255-40Iin-40,
Iin-R=fR-1Iout,
Iin-G=fG-1Iout,
Iin-B=fB-1Iout,
ϕCD=ϕCA=ϕA-ϕC.
h=AC¯d1+AC¯dl.
hAC¯d l=pϕAC2πdl,
hi, j=10 pi, j-ϕn-1i, jϕni, j-ϕn-1i, j+10n-1 if ϕni, jpi, jϕn-1i, j, n=-4 to 510 pi, j-ϕ5i, jϕ5i, j-ϕ4i, j+50 if pi, j>ϕ5i, j10 pi, j-ϕ-5i, jϕ-4i, j-ϕ-5i, j-50 if pi, j<ϕ-5i, j,

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