Abstract

A grating projection system is a low-cost surface contour measurement technique that can be applied to a wide range of applications. There has been a resurgence of interest in the technique in recent years because of developments in computer hardware and image processing algorithms. We describe a method that projects a phase-shifted grating through a lens on an object surface. The deformed grating image on the object surface is captured by a CCD camera for subsequent analysis. Phase variation is achieved by a linear translation stage on which the grating is mounted. We compare the experimental results with the test results using a mechanical stylus method.

© 2005 Optical Society of America

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  1. T. Yatagai, M. Idesawa, “Automatic fringe analysis for moiré topography,” Opt. Laser Eng. 3, 73–83 (1982).
    [CrossRef]
  2. Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
    [CrossRef]
  3. J. D. Hovanesian, Y. Y. Hung, “Moire contour-sum contour difference and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).
    [CrossRef] [PubMed]
  4. R. Thalmann, R. Dandliker, “Holographic contouring using electronic phase measurement,” Opt. Eng. 24, 930–935 (1985).
    [CrossRef]
  5. C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
    [CrossRef]
  6. P. K. Rastogi, “Visualisation of the contours of equal slope of an arbitrarily-shaped object using holographic moiré,” Opt. Eng. 33, 2373–2377 (1994).
    [CrossRef]
  7. M. Takeda, K. Mutoh, “Fourier transform profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25, 1630–1633 (1986).
    [CrossRef]
  8. M. Suganuma, T. Yoshizawa, “Three-dimensional shape analysis by use of a projected grating image,” Opt. Eng. 30, 1529–1533 (1991).
    [CrossRef]
  9. M. K. Kalm, W. Juptner, W. Osten, “Automatic adaption of projected fringe pattern using a programmable LCD-projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed., Proc. SPIE3100, 156–165 (1997).
    [CrossRef]
  10. M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
    [CrossRef]
  11. X. Y. Su, W. S. Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
    [CrossRef]
  12. G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
    [CrossRef]
  13. F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  14. S. H. Rowe, W. T. Welford, “Surface topography of non-optical surface by projected interference fringes,” Nature (London) 216, 786–787 (1967).
    [CrossRef]
  15. R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
    [CrossRef] [PubMed]
  16. R. Windecker, S. Franz, H. J. Tiziani, “Optical roughness measurement with fringe projection,” Appl. Opt. 38, 2837–2842 (1999).
    [CrossRef]
  17. H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
    [CrossRef]
  18. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
  19. M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
    [CrossRef]
  20. K. Creath, Temporal Phase Measurement Methods, 2nd ed. (Institute of Physics, Bristol, UK, 1993).
  21. C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
    [CrossRef]
  22. F. P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, J. F. Doyel, J. W. Phillips, eds. (Society for Experimental Mechanics, Bethel, Conn., 1989), Chap. 7, pp. 107–135.

2002

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
[CrossRef]

2000

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

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
[CrossRef]

1999

1998

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

1995

R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
[CrossRef] [PubMed]

1994

P. K. Rastogi, “Visualisation of the contours of equal slope of an arbitrarily-shaped object using holographic moiré,” Opt. Eng. 33, 2373–2377 (1994).
[CrossRef]

1992

X. Y. Su, W. S. Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

1991

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

M. Suganuma, T. Yoshizawa, “Three-dimensional shape analysis by use of a projected grating image,” Opt. Eng. 30, 1529–1533 (1991).
[CrossRef]

1989

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

1986

1985

R. Thalmann, R. Dandliker, “Holographic contouring using electronic phase measurement,” Opt. Eng. 24, 930–935 (1985).
[CrossRef]

1982

T. Yatagai, M. Idesawa, “Automatic fringe analysis for moiré topography,” Opt. Laser Eng. 3, 73–83 (1982).
[CrossRef]

1971

1967

S. H. Rowe, W. T. Welford, “Surface topography of non-optical surface by projected interference fringes,” Nature (London) 216, 786–787 (1967).
[CrossRef]

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]

Bryanston-Cross, P. J.

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

Burton, D. R.

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (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]

Chiang, F. P.

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

F. P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, J. F. Doyel, J. W. Phillips, eds. (Society for Experimental Mechanics, Bethel, Conn., 1989), Chap. 7, pp. 107–135.

Creath, K.

K. Creath, Temporal Phase Measurement Methods, 2nd ed. (Institute of Physics, Bristol, UK, 1993).

Dai, Y. Z.

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Dandliker, R.

R. Thalmann, R. Dandliker, “Holographic contouring using electronic phase measurement,” Opt. Eng. 24, 930–935 (1985).
[CrossRef]

Franz, S.

Halioua, M.

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

He, X. Y.

C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
[CrossRef]

Hovanesian, J. D.

Hung, Y. Y.

Idesawa, M.

T. Yatagai, M. Idesawa, “Automatic fringe analysis for moiré topography,” Opt. Laser Eng. 3, 73–83 (1982).
[CrossRef]

Juptner, W.

M. K. Kalm, W. Juptner, W. Osten, “Automatic adaption of projected fringe pattern using a programmable LCD-projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed., Proc. SPIE3100, 156–165 (1997).
[CrossRef]

Kalm, M. K.

M. K. Kalm, W. Juptner, W. Osten, “Automatic adaption of projected fringe pattern using a programmable LCD-projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed., Proc. SPIE3100, 156–165 (1997).
[CrossRef]

Lalor, M. J.

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
[CrossRef]

Liu, H. C.

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

Mutoh, K.

Osten, W.

M. K. Kalm, W. Juptner, W. Osten, “Automatic adaption of projected fringe pattern using a programmable LCD-projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed., Proc. SPIE3100, 156–165 (1997).
[CrossRef]

Pedrini, G.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
[CrossRef]

Quan, C.

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, “Visualisation of the contours of equal slope of an arbitrarily-shaped object using holographic moiré,” Opt. Eng. 33, 2373–2377 (1994).
[CrossRef]

Rowe, S. H.

S. H. Rowe, W. T. Welford, “Surface topography of non-optical surface by projected interference fringes,” Nature (London) 216, 786–787 (1967).
[CrossRef]

Schedin, S.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
[CrossRef]

Shang, H. M.

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
[CrossRef]

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]

Su, X. Y.

X. Y. Su, W. S. Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Suganuma, M.

M. Suganuma, T. Yoshizawa, “Three-dimensional shape analysis by use of a projected grating image,” Opt. Eng. 30, 1529–1533 (1991).
[CrossRef]

Takeda, M.

Tay, C. J.

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
[CrossRef]

Thalmann, R.

R. Thalmann, R. Dandliker, “Holographic contouring using electronic phase measurement,” Opt. Eng. 24, 930–935 (1985).
[CrossRef]

Tiziani, H. J.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
[CrossRef]

R. Windecker, S. Franz, H. J. Tiziani, “Optical roughness measurement with fringe projection,” Appl. Opt. 38, 2837–2842 (1999).
[CrossRef]

R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
[CrossRef] [PubMed]

Welford, W. T.

S. H. Rowe, W. T. Welford, “Surface topography of non-optical surface by projected interference fringes,” Nature (London) 216, 786–787 (1967).
[CrossRef]

Windecker, R.

R. Windecker, S. Franz, H. J. Tiziani, “Optical roughness measurement with fringe projection,” Appl. Opt. 38, 2837–2842 (1999).
[CrossRef]

R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
[CrossRef] [PubMed]

Wu, F.

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
[CrossRef]

Yatagai, T.

T. Yatagai, M. Idesawa, “Automatic fringe analysis for moiré topography,” Opt. Laser Eng. 3, 73–83 (1982).
[CrossRef]

Yoshizawa, T.

M. Suganuma, T. Yoshizawa, “Three-dimensional shape analysis by use of a projected grating image,” Opt. Eng. 30, 1529–1533 (1991).
[CrossRef]

Zhang, H.

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
[CrossRef]

Zhou, W. S.

X. Y. Su, W. S. Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Appl. Opt.

R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
[CrossRef] [PubMed]

Appl. Opt.

Exp. Mech.

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Nature (London)

S. H. Rowe, W. T. Welford, “Surface topography of non-optical surface by projected interference fringes,” Nature (London) 216, 786–787 (1967).
[CrossRef]

Opt. Eng.

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

M. Suganuma, T. Yoshizawa, “Three-dimensional shape analysis by use of a projected grating image,” Opt. Eng. 30, 1529–1533 (1991).
[CrossRef]

Opt. Commun.

X. Y. Su, W. S. Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Opt. Eng.

R. Thalmann, R. Dandliker, “Holographic contouring using electronic phase measurement,” Opt. Eng. 24, 930–935 (1985).
[CrossRef]

P. K. Rastogi, “Visualisation of the contours of equal slope of an arbitrarily-shaped object using holographic moiré,” Opt. Eng. 33, 2373–2377 (1994).
[CrossRef]

H. Zhang, F. Wu, M. J. Lalor, D. R. Burton, “Spatiotemporal phase unwrapping and its application in fringe projection fiber optics phase-shifting profilometry,” Opt. Eng. 39, 1958–1964 (2000).
[CrossRef]

Opt. Laser Eng.

T. Yatagai, M. Idesawa, “Automatic fringe analysis for moiré topography,” Opt. Laser Eng. 3, 73–83 (1982).
[CrossRef]

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

M. Halioua, H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Laser Eng. 11, 185–215 (1989).
[CrossRef]

Opt. Laser Eng.

C. Quan, H. M. Shang, C. J. Tay, P. J. Bryanston-Cross, “Holographic contouring using double-source technique and Fourier transform analysis,” Opt. Laser Eng. 30, 351–362 (1998).
[CrossRef]

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Laser Eng. 38, 117–129 (2002).
[CrossRef]

Other

M. K. Kalm, W. Juptner, W. Osten, “Automatic adaption of projected fringe pattern using a programmable LCD-projector,” in Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed., Proc. SPIE3100, 156–165 (1997).
[CrossRef]

K. Creath, Temporal Phase Measurement Methods, 2nd ed. (Institute of Physics, Bristol, UK, 1993).

C. Quan, X. Y. He, C. J. Tay, H. M. Shang, “3D surface profile measurement using LCD fringe projection,” in Second International Conference on Experimental Mechanics, F. S. Chan, C. Quan, eds., Proc. SPIE4317, 511–516 (2001).
[CrossRef]

F. P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, J. F. Doyel, J. W. Phillips, eds. (Society for Experimental Mechanics, Bethel, Conn., 1989), Chap. 7, pp. 107–135.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

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Figures (8)

Fig. 1
Fig. 1

Optical geometry of fringe projection.

Fig. 2
Fig. 2

Experimental arrangement.

Fig. 3
Fig. 3

Specimen 1 and area of interest.

Fig. 4
Fig. 4

(a) Projected fringe pattern on specimen 1, (b) wrapped phase map, (c) unwrapped phase map, (d) contour map of specimen 1, (e) 3-D plot of specimen 1.

Fig. 5
Fig. 5

Comparison of the surface profile of specimen 1 on the cross-sectional D–D between the present and the mechanical stylus method.

Fig. 6
Fig. 6

Specimen 2 and area of interest.

Fig. 7
Fig. 7

(a) Projected fringe pattern on specimen 2, (b) wrapped phase map, (c) unwrapped phase map, (d) 3-D plot of specimen 2.

Fig. 8
Fig. 8

Comparison of the surface profile of specimen 2 at the cross-sectional C–C between the present and the mechanical stylus method.

Equations (11)

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

T ( x ) = A m ( 1 + cos 2 π x p ) ,
I p = A + B cos ( 2 π O C / p ) ,
I D = R [ A + B cos ( 2 π O A / p ) ] .
A C = ( p / 2 π ) ϕ ,
h = A C / ( tan θ 1 + tan θ 2 ) ,
h = A C / ( tan θ 1 ) = ( p / 2 π ) ϕ / tan θ 1 = k ϕ ,
I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + Δ ] ,
I 1 ( x , y ) = a ( x , y ) + b ( x , y ) cos ϕ ( x , y ) ,
I 2 ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + π / 2 ] ,
I 3 ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + π ] .
ϕ ( x , y ) = arctan [ I 1 ( x , y ) - 2 I 2 ( x , y ) + I 3 ( x , y ) I 1 ( x , y ) - I 3 ( x , y ) ] .

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