Abstract

A projection moiré profilometer is presented in which both projection and optical demodulation are realized with liquid crystal light modulators. The computer generated grids, realized on thin film transistor matrices, allow phase-stepping and discrete grid averaging without the need for any mechanically moving component. Spatial line pitch and phase steps can thus be readily adjusted to suit the measurement precision and object geometry. The device is able to perform topographic measurements with a height resolution of 15µm on every pixel of the recording device.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. F. Chen, G.-M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
    [CrossRef]
  2. R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, "Modified temporal-phaseunwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil," Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).
  3. J. Dirckx and W. Decraemer, "Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane," J. Biomed. Opt. 2, 176-185 (1997).
    [CrossRef]
  4. M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, "Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion," Hearing Res. 82, 184-196 (1995).
    [CrossRef]
  5. M. Takeda, H. Ina, and S. Koboyashi, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22, 3977-3982 (1982).
    [CrossRef]
  6. W.-H. Su and H. Liu, "Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities," Opt. Express 14, 9178-9187 (2006).
    [CrossRef] [PubMed]
  7. D. Meadows, W. Johnson, and J. Allen, "Generation of surface contours by moiré patterns," Appl. Opt. 9, 942-947 (1970).
    [CrossRef] [PubMed]
  8. H. Takasaki, "Moiré topography," Appl. Opt. 9, 1467-1472 (1970).
    [CrossRef] [PubMed]
  9. M. Halioua, R. Krishnamurthy, H. Liu, and F.-P. Chiang, "Projection moiré with moving gratings for automated 3-D topography," Appl. Opt. 22, 850-855 (1983).
    [CrossRef] [PubMed]
  10. J. Dirckx and W. Decraemer, "Interferometer for eardrum shape measurement, based on projection of straight line rulings," Lasers Med. Sci. 15, 131-139 (2000).
    [CrossRef]
  11. J. Buytaert and J. Dirckx, "Design considerations in projection phase shift moiré topography, based on theoretical analysis of fringe formation," J. Opt. Soc. Am. A 24, 2003-2013 (2007).
    [CrossRef]
  12. K. Creath, "Phase-shifting interferometry techniques," in Progress in Optics, Vol. 26, pg. 357-373 (1988).
  13. J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, "An optical profilometer for surface characterization of magnetic media," ASLE Trans. 27, 101-113 (1982).
    [CrossRef]
  14. J. Wyant, "Interferometric optical metrology: basic principles and new systems," Laser Focus (includes Electro-Optics) 18, 65-71 (1982).
  15. J. Dirckx and W. Decraemer, "Grating noise removal in moiré topography," Optik  86, 107-110 (1990).
  16. A. Asundi, Second intl. conf. on photomechanics and speckle metrology: moire techniques, holographic interferometry, optical NDT, and applications to fluid mechanics, chapter. Novel grating methods for optical inspection, Proc. SPIE 1554B, 708-715 (1991).
  17. A. Asundi and C. Chan, "Phase shifted projection grid - effect of pitch and profile," Opt. Lasers Eng. 21, 31-47 (1994).
    [CrossRef]
  18. C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42, 2326-2335 (2003).
    [CrossRef]
  19. Y. Fujin, H. Xiaoyuan, and S. Wei, "Digital shadow moir’e method with phase-shifting based on liquid crystal display projector," Acta Opt. Sin. 25, 1057-1061 (2005).
  20. W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection moiré method," Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).
  21. J. Dirckx and W. Decraemer, "Coating techniques in optical interferometric metrology," Appl. Opt. 36, 2776-2782 (1997).
    [CrossRef] [PubMed]
  22. J. Dirckx and W. Decraemer, "Automatic calibration method for phase shift shadow moire interferometry," Appl. Opt. 29, 1474-1476 (1990).
    [CrossRef] [PubMed]
  23. T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, "Interactive fringe analysis system: applications to moir’e contourogram and interferogram," Opt. Eng. 21, 901-906 (1982).
  24. S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, "Hybrid holographic interferometer for measuring threedimensional deformations," Opt. Eng. 20, 246-252 (1981).
  25. W. Osten, Optical methods in experimental solid mechanics, chap. Digital processing and evaluation of fringe patterns in optical metrology and non-destructive testing, pp. 308-363 (Springer-Verlag, 2000). Section: Techniques for digital phase reconstruction.
  26. B. Drerup, "Some problems in analytical reconstruction of biological shapes from moiré topograms," in Optics in Biomedical Sciences (Springer-Verlag, 1982) pp. 258-261.
  27. U. Mieth and W. Osten, Proc. SPIE Vol. 1163: Interferometry ’89, chap. Three methods for the interpolation of phase values between fringe pattern skeleton, pp. 151-154 (SPIE, 1989).
  28. J. Dirckx and W. Decraemer, "Effect of middle ear components on eardrum quasi-static deformation," Hearing Res. 157, 124-137 (2001).
    [CrossRef]
  29. X. Xie, J. Atkinson,M. Lalor, and D. Burton, "Three-map absolute moiré contouring," Appl. Opt. 35, 6990-6995 (1996).
    [CrossRef] [PubMed]
  30. M.-S. Jeong and S.-W. Kim, "Color grating projection moir’e with time-integral fringe capturing for high-speed 3-D imaging," Opt. Eng. 41, 1912-1917 (2002).
    [CrossRef]

2007 (1)

2006 (1)

2005 (1)

Y. Fujin, H. Xiaoyuan, and S. Wei, "Digital shadow moir’e method with phase-shifting based on liquid crystal display projector," Acta Opt. Sin. 25, 1057-1061 (2005).

2003 (1)

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42, 2326-2335 (2003).
[CrossRef]

2002 (1)

M.-S. Jeong and S.-W. Kim, "Color grating projection moir’e with time-integral fringe capturing for high-speed 3-D imaging," Opt. Eng. 41, 1912-1917 (2002).
[CrossRef]

2001 (1)

J. Dirckx and W. Decraemer, "Effect of middle ear components on eardrum quasi-static deformation," Hearing Res. 157, 124-137 (2001).
[CrossRef]

2000 (2)

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

J. Dirckx and W. Decraemer, "Interferometer for eardrum shape measurement, based on projection of straight line rulings," Lasers Med. Sci. 15, 131-139 (2000).
[CrossRef]

1997 (2)

J. Dirckx and W. Decraemer, "Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane," J. Biomed. Opt. 2, 176-185 (1997).
[CrossRef]

J. Dirckx and W. Decraemer, "Coating techniques in optical interferometric metrology," Appl. Opt. 36, 2776-2782 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, "Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion," Hearing Res. 82, 184-196 (1995).
[CrossRef]

1994 (1)

A. Asundi and C. Chan, "Phase shifted projection grid - effect of pitch and profile," Opt. Lasers Eng. 21, 31-47 (1994).
[CrossRef]

1991 (1)

A. Asundi, Second intl. conf. on photomechanics and speckle metrology: moire techniques, holographic interferometry, optical NDT, and applications to fluid mechanics, chapter. Novel grating methods for optical inspection, Proc. SPIE 1554B, 708-715 (1991).

1990 (2)

1983 (1)

1982 (3)

M. Takeda, H. Ina, and S. Koboyashi, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22, 3977-3982 (1982).
[CrossRef]

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, "Interactive fringe analysis system: applications to moir’e contourogram and interferogram," Opt. Eng. 21, 901-906 (1982).

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, "An optical profilometer for surface characterization of magnetic media," ASLE Trans. 27, 101-113 (1982).
[CrossRef]

1981 (1)

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, "Hybrid holographic interferometer for measuring threedimensional deformations," Opt. Eng. 20, 246-252 (1981).

1970 (2)

Acta Opt. Sin. (1)

Y. Fujin, H. Xiaoyuan, and S. Wei, "Digital shadow moir’e method with phase-shifting based on liquid crystal display projector," Acta Opt. Sin. 25, 1057-1061 (2005).

Appl. Opt. (8)

ASLE Trans. (1)

J. Wyant, C. Koliopoulos, B. Bhushan, and O. George, "An optical profilometer for surface characterization of magnetic media," ASLE Trans. 27, 101-113 (1982).
[CrossRef]

Hearing Res. (2)

M. von Unge, W. Decraemer, J. Dirckx, and D. Bagger-Sjöbäck, "Shape and displacement patterns of the gerbil tympanic membrane in experimental otitis media with effusion," Hearing Res. 82, 184-196 (1995).
[CrossRef]

J. Dirckx and W. Decraemer, "Effect of middle ear components on eardrum quasi-static deformation," Hearing Res. 157, 124-137 (2001).
[CrossRef]

J. Biomed. Opt. (1)

J. Dirckx and W. Decraemer, "Optoelectronic moiré projector for real-time shape and deformation studies of the tympanic membrane," J. Biomed. Opt. 2, 176-185 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Lasers Med. Sci. (1)

J. Dirckx and W. Decraemer, "Interferometer for eardrum shape measurement, based on projection of straight line rulings," Lasers Med. Sci. 15, 131-139 (2000).
[CrossRef]

Opt. Eng. (4)

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

T. Yatagai, M. Idesawa, Y. Yamaashi, and M. Suzuki, "Interactive fringe analysis system: applications to moir’e contourogram and interferogram," Opt. Eng. 21, 901-906 (1982).

S. Nakadate, N. Magome, T. Honda, and J. Tsujiuchi, "Hybrid holographic interferometer for measuring threedimensional deformations," Opt. Eng. 20, 246-252 (1981).

M.-S. Jeong and S.-W. Kim, "Color grating projection moir’e with time-integral fringe capturing for high-speed 3-D imaging," Opt. Eng. 41, 1912-1917 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

A. Asundi and C. Chan, "Phase shifted projection grid - effect of pitch and profile," Opt. Lasers Eng. 21, 31-47 (1994).
[CrossRef]

Optik (1)

J. Dirckx and W. Decraemer, "Grating noise removal in moiré topography," Optik  86, 107-110 (1990).

Proc. SPIE (1)

A. Asundi, Second intl. conf. on photomechanics and speckle metrology: moire techniques, holographic interferometry, optical NDT, and applications to fluid mechanics, chapter. Novel grating methods for optical inspection, Proc. SPIE 1554B, 708-715 (1991).

Other (7)

J. Wyant, "Interferometric optical metrology: basic principles and new systems," Laser Focus (includes Electro-Optics) 18, 65-71 (1982).

R. Martínez-Celorio, J. Dirckx, J. Buytaert, L. M. López, and W. Decraemer, "Modified temporal-phaseunwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil," Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2007.05.005) (2007).

K. Creath, "Phase-shifting interferometry techniques," in Progress in Optics, Vol. 26, pg. 357-373 (1988).

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection moiré method," Opt. Int. J. Light Electron. Opt. (in Press doi:10.1016/j.ijleo.2006.12.016) (2007).

W. Osten, Optical methods in experimental solid mechanics, chap. Digital processing and evaluation of fringe patterns in optical metrology and non-destructive testing, pp. 308-363 (Springer-Verlag, 2000). Section: Techniques for digital phase reconstruction.

B. Drerup, "Some problems in analytical reconstruction of biological shapes from moiré topograms," in Optics in Biomedical Sciences (Springer-Verlag, 1982) pp. 258-261.

U. Mieth and W. Osten, Proc. SPIE Vol. 1163: Interferometry ’89, chap. Three methods for the interpolation of phase values between fringe pattern skeleton, pp. 151-154 (SPIE, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

A: moiré interferogram of a sphere with fringes and grid noise after optical demodulation. B: moiré topogram of the sphere with altitude contour fringes using grid averaging: grid noise is no longer present. E: the 4-bucket phase-stepped algorithm delivers a wrapped phasemap with 2π jumps. F: after unwrapping and calibration a continuous height map is obtained.

Fig. 2.
Fig. 2.

Schematic layout of the liquid crystal grids setup for projection moiré. Lens L 1 projects the light going through liquid crystal grid unit LCG1 onto the surface, creating a shadow of grid G 1 on it. The projected line pattern is modulated by the object’s geometry, and projected onto grid G 2 of LCG2 by lens L 2. The created interferogram is recorded by a CCD imaging device with lens L 3. A light path from point (x 1, y 1, z 1) on G 1 to surface point S(x, y, z), and from S to (x 2, y 2, z 2) on G 2 is drawn.

Fig. 3.
Fig. 3.

Standard deviation on height measurements when using the discrete grid averaging theory with N images.

Fig. 4.
Fig. 4.

TOP: difference between themeasured profile and an ideal straight plane along a horizontal cross section for three representative measurements. A (systematic) error with amplitude of about 15µm is present. BOTTOM: difference between two subsequent recorded shape profiles, showing a noise floor of about 5µm.

Fig. 5.
Fig. 5.

Ratio of the measured height over the actual mechanical height displacement at Z-steps of 350µm for pixel coordinates (100,100), (100,550), (240,320), (350,100) and (350,550). Deviation of unity is less than 5% over a 5mm range.

Fig. 6.
Fig. 6.

The 3-D representation of the sphere in Fig. 1 obtained with digital LCD moiré.

Fig. 7.
Fig. 7.

A: moiré topogramof a diagonally white-gray painted sphere. B: cross sections along the lines in A show ×10 intensity difference between the two regions. C: the differences in reflectivity have no influence on the calibrated height map. D: cross sections along the lines in C, with arrows indicating the bright-dark boundary. E: the 3-D representation of C with one of its topograms mapped on the surface, shows again no problems.

Fig. 8.
Fig. 8.

Triangular Fresnel prism with depth β=0.49mm and width γ=1.00mm. A: cross section through the calibrated height profile shows right-angled isosceles triangles. B and C: 3-D representations of the shape with a topogram mapped on the surface.

Equations (30)

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

T 1 ( x 1 ) = 1 2 + 1 2 sin ( 2 π x 1 p + ϕ 1 )
T ( x ) = 1 2 + 2 π n = 1 , odd 1 n sin ( 2 π nx p + ϕ 1 )
I ( x , y , z ) = T 2 ( x 2 ) ρ 2 R ( x , y ) ρ 1 T 1 ( x 1 ) I 0 r 2 ( x , y , z )
= A ( x , y , z ) [ 1 2 + 1 2 sin ( 2 π ( 2 D x + d x 1 ) P + ϕ 1 ) ]
× [ 1 2 + 1 2 sin ( 2 π ( 2 D x d x 2 ) p + ϕ 2 ) ]
x 1 = 2 D x + d x 1 y 1 = y 2 = y d y
x 2 = 2 D x d x 2 z 1 = z 2 = 2 L = 4 f
I ( x , y , z ) = A 4 { 1 + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 ) + sin ( 2 π ( 2 D x z D + x L z ) p + ϕ 2 ) . . .
+ 1 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 ) + cos ( 2 π ( 4 D z 2 D L z ) p + ϕ 1 ϕ 2 ) ] }
sin ( 2 π ( 2 D + z D x L z ) p + ϕ 1 ) cos ( 2 π x p ) cos ( 2 π ( 2 D + z D x L z ) p + ϕ 1 ) sin ( 2 π x p )
ϕ i ϕ i + 2 π v p t
A 4 0 T [ sin ( 2 π ( 2 D x + D x L z + v t ) p + ϕ 1 ) ] d t
= pA 8 π v [ cos ( 2 π ( 2 D x + D x L z ) p + ϕ 1 ) cos ( 2 π ( 2 D x + D x L z + v T ) p + ϕ 1 ) ]
I T ( x , y , z ) = TA ( x , y , z ) 4 { 1 + cos ( 2 π ( 4 D z 2 D L z ) p ) }
T i ( x i ) = 1 2 + 1 2 sin ( 2 π x i p + ϕ i + k Φ )
ϕ i ϕ i + k Φ
I N ( x , y , z ) = TA ( x , y , z ) 4 N k = 1 N { 1 + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) . . .
+ sin ( 2 π ( 2 D x + z D + x L z ) p + ϕ 2 + k Φ ) . . .
+ 1 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 2 k Φ ) + cos ( 2 π ( z 2 D L z ) p ) ] }
= TA ( x , y , z ) 4 { 1 + 1 2 cos ( 2 π ( 2 zD L z ) p ) . . .
+ 1 N k = 1 N [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) + sin ( 2 π ( 2 D x z D + x L z ) p + ϕ 2 + k Φ ) ] . . .
1 2 N k = 1 N cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 2 k Φ ) }
TA 4 N k = 1 N [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) ]
= TA 4 N k = 1 N 2 [ sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + k Φ ) + sin ( 2 π ( 2 D x + z D x L z ) p + ϕ 1 + ( N 2 + k ) Φ ) ]
= TA 2 N k = 1 N 2 [ sin ( 2 π ( 2 D x + z D x L z ) p + 2 ϕ 1 + ( N 2 + 2 k ) Φ ) cos N Φ 4 ]
TA 4 N k = 1 N 2 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + ( N 2 + 2 k ) Φ ) cos N Φ 2 ]
= TA 2 N k = 1 N 4 [ cos ( 2 π ( 2 x z 2 x L z ) p + ϕ 1 + ϕ 2 + 3 π 2 + 2 k Φ ) cos π 2 ]
Φ = 2 π N ( 2 l + 1 ) Δ = p 2 π Φ = p N ( 2 l + 1 ) Δ pix = p pix N ( 2 l + 1 )
I ( x , y , z ) = TA ( x , y ) 4 [ 1 + 1 2 cos ( 2 π ( 2 zD L z ) p ) ] + B ( x , y )
arctan ( I 4 I 2 I 3 I 1 ) = 4 π D p z L z 4 π D p z L

Metrics