Abstract

A novel method that uses a two-dimensional (2D) digital image correlation (DIC) based on a single CCD camera to measure three-dimensional (3D) displacement and deformation is proposed. Rigid-body displacement in 3D space consists of both in-plane and out-of-plane components. The presence of an in-plane displacement component results in a shift of the center of the image displacement vector, while the slope of the image displacement vector is related to the out-of-plane displacement component. Global DIC is employed to determine the displaced position of each point on an object based on a linear distribution characteristic of the displacement vector. Speckle images with deformation introduced by 3D displacement are generated to demonstrate the feasibility of the proposed method. In the 3D rigid-body displacement, both in-plane and out-of-plane displacement components are separated by determining the intercept and slope of the image displacement vector. In the 3D deformation, a zero order displacement (pure rigid-body displacement) mode is assumed in a small subset of pixels. Simulated and experimental results demonstrate that both in-plane and out-of-plane displacements can be accurately retrieved using the proposed method.

© 2008 Optical Society of America

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References

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  1. W. H. Peters and W. F. Ranson, "Digital imaging techniques in experimental mechanics," Opt. Eng. 21, 427-431 (1982).
  2. A. Asundi and H. North, "White-light speckle method," Opt. Lasers Eng. 29, 159-169 (1998).
    [CrossRef]
  3. G. Vendroux and W. G. Knauss, "Submicron deformation field measurements: part 2. Improved digital image correlation," Exp. Mech. 38, 86-92 (1998).
    [CrossRef]
  4. H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
    [CrossRef]
  5. P. Cheng, M. A. Sutton, H. W. Schreier, and S. R. McNeill, "Full-field speckle pattern image correlation with B-spline deformation function," Exp. Mech. 42, 344-352 (2002).
    [CrossRef]
  6. J. Abanto-Bueno and J. Lambros, "Investigation of crack growth in functionally graded materials using digital image correlation," Eng. Fract. Mech. 69, 1695-1711 (2002).
    [CrossRef]
  7. P. F. Luo, Y. J. Chao, and M. A. Sutton, "Application of stereo vision to three-dimensional deformations analyses in fracture experiments," Opt. Eng. 33, 981-990 (1994).
    [CrossRef]
  8. J. D. Helm, S. R. McNeill, and M. A. Sutton, "Improved three-dimensional image correlation for surface displacement measurements," Opt. Eng. 35, 1911-1920 (1996).
    [CrossRef]
  9. C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43, 1152-1159 (2004).
    [CrossRef]
  10. C. Quan, C. J. Tay, and Y. H. Huang, "3D deformation measurement using fringe projection and digital image correlation," Optik 115, 164-168 (2004).
    [CrossRef]
  11. K. S. Dharmsaktu, A. Kumar, and K. Singh, "Three-dimensional rigid-body motion measurement using speckle fanning in a photorefractive BaTiO3 crystal," Optik 112, 49-56 (2001).
    [CrossRef]
  12. A. Asundi and F. P. Chiang, "Separation of 3-D displacement components in the white light speckle method," Opt. Laser Technol. 15, 41-45 (1983).
    [CrossRef]
  13. J. Luo, K. Ying, and J. Bai, "Savitzky-Golay smoothing and differentiation filter for even number data," Signal Process. 85, 1429-1434 (2005).
    [CrossRef]
  14. B. Pan, H. M. Xie, Z. Guo, and H. Tao, "Full-field strain measurement using two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601-10 (2007).
    [CrossRef]
  15. A. Savitzky and M. J. E. Golay, "Smoothing and differentiation of data by simplified least squares procedures," Anal. Chem. 36, 1627-1639 (1964).
    [CrossRef]
  16. R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE J. Rob. Auto. 3, 324-344 (1987).
  17. R. S. Sirohi, ed., Speckle Metrology (Dekker, 1993).
  18. H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
    [CrossRef]
  19. T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 9, 232-245 (1985).
    [CrossRef]
  20. P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
    [CrossRef]
  21. W. Sun, C. Quan, C. J. Tay, and X. Y. He, "Global and local coordinates in digital image correlation," Appl. Opt. 46, 1050-1056 (2007).
    [CrossRef] [PubMed]
  22. H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
    [CrossRef]
  23. Y. H. Huang, C. Quan, C. J. Tay, and L. J. Chen, "Shape measurement by the use of digital image correlation," Opt. Eng. 44, 087011-1-7 (2005).
    [CrossRef]
  24. C. J. Tay, C. Quan, Y. H. Huang, and Y. Fu, "Digital image correlation for whole field out-of-plane displacement measurement using a single camera," Opt. Commun. 251, 23-36 (2005).
    [CrossRef]

2007 (2)

B. Pan, H. M. Xie, Z. Guo, and H. Tao, "Full-field strain measurement using two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601-10 (2007).
[CrossRef]

W. Sun, C. Quan, C. J. Tay, and X. Y. He, "Global and local coordinates in digital image correlation," Appl. Opt. 46, 1050-1056 (2007).
[CrossRef] [PubMed]

2005 (3)

Y. H. Huang, C. Quan, C. J. Tay, and L. J. Chen, "Shape measurement by the use of digital image correlation," Opt. Eng. 44, 087011-1-7 (2005).
[CrossRef]

C. J. Tay, C. Quan, Y. H. Huang, and Y. Fu, "Digital image correlation for whole field out-of-plane displacement measurement using a single camera," Opt. Commun. 251, 23-36 (2005).
[CrossRef]

J. Luo, K. Ying, and J. Bai, "Savitzky-Golay smoothing and differentiation filter for even number data," Signal Process. 85, 1429-1434 (2005).
[CrossRef]

2004 (2)

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43, 1152-1159 (2004).
[CrossRef]

C. Quan, C. J. Tay, and Y. H. Huang, "3D deformation measurement using fringe projection and digital image correlation," Optik 115, 164-168 (2004).
[CrossRef]

2002 (3)

P. Cheng, M. A. Sutton, H. W. Schreier, and S. R. McNeill, "Full-field speckle pattern image correlation with B-spline deformation function," Exp. Mech. 42, 344-352 (2002).
[CrossRef]

J. Abanto-Bueno and J. Lambros, "Investigation of crack growth in functionally graded materials using digital image correlation," Eng. Fract. Mech. 69, 1695-1711 (2002).
[CrossRef]

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

2001 (2)

K. S. Dharmsaktu, A. Kumar, and K. Singh, "Three-dimensional rigid-body motion measurement using speckle fanning in a photorefractive BaTiO3 crystal," Optik 112, 49-56 (2001).
[CrossRef]

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

2000 (1)

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

1998 (2)

A. Asundi and H. North, "White-light speckle method," Opt. Lasers Eng. 29, 159-169 (1998).
[CrossRef]

G. Vendroux and W. G. Knauss, "Submicron deformation field measurements: part 2. Improved digital image correlation," Exp. Mech. 38, 86-92 (1998).
[CrossRef]

1996 (1)

J. D. Helm, S. R. McNeill, and M. A. Sutton, "Improved three-dimensional image correlation for surface displacement measurements," Opt. Eng. 35, 1911-1920 (1996).
[CrossRef]

1994 (1)

P. F. Luo, Y. J. Chao, and M. A. Sutton, "Application of stereo vision to three-dimensional deformations analyses in fracture experiments," Opt. Eng. 33, 981-990 (1994).
[CrossRef]

1989 (1)

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

1987 (1)

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE J. Rob. Auto. 3, 324-344 (1987).

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 9, 232-245 (1985).
[CrossRef]

1983 (1)

A. Asundi and F. P. Chiang, "Separation of 3-D displacement components in the white light speckle method," Opt. Laser Technol. 15, 41-45 (1983).
[CrossRef]

1982 (1)

W. H. Peters and W. F. Ranson, "Digital imaging techniques in experimental mechanics," Opt. Eng. 21, 427-431 (1982).

1964 (1)

A. Savitzky and M. J. E. Golay, "Smoothing and differentiation of data by simplified least squares procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Anal. Chem. (1)

A. Savitzky and M. J. E. Golay, "Smoothing and differentiation of data by simplified least squares procedures," Anal. Chem. 36, 1627-1639 (1964).
[CrossRef]

Appl. Opt. (1)

Eng. Fract. Mech. (1)

J. Abanto-Bueno and J. Lambros, "Investigation of crack growth in functionally graded materials using digital image correlation," Eng. Fract. Mech. 69, 1695-1711 (2002).
[CrossRef]

Exp. Mech. (6)

G. Vendroux and W. G. Knauss, "Submicron deformation field measurements: part 2. Improved digital image correlation," Exp. Mech. 38, 86-92 (1998).
[CrossRef]

H. Lu and P. D. Cary, "Deformation measurements by digital image correlation: implementation of a second-order displacement gradient," Exp. Mech. 40, 393-400 (2000).
[CrossRef]

P. Cheng, M. A. Sutton, H. W. Schreier, and S. R. McNeill, "Full-field speckle pattern image correlation with B-spline deformation function," Exp. Mech. 42, 344-352 (2002).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, "Digital-image-correlation using Newton-Raphson method for partial differential correction," Exp. Mech. 29, 261-267 (1989).
[CrossRef]

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, "Applications of digital-image-correlation techniques to experimental mechanics," Exp. Mech. 9, 232-245 (1985).
[CrossRef]

IEEE J. Rob. Auto. (1)

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE J. Rob. Auto. 3, 324-344 (1987).

Opt. Commun. (1)

C. J. Tay, C. Quan, Y. H. Huang, and Y. Fu, "Digital image correlation for whole field out-of-plane displacement measurement using a single camera," Opt. Commun. 251, 23-36 (2005).
[CrossRef]

Opt. Eng. (7)

B. Pan, H. M. Xie, Z. Guo, and H. Tao, "Full-field strain measurement using two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601-10 (2007).
[CrossRef]

P. Zhou and K. E. Goodson, "Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC)," Opt. Eng. 40, 1613-1620 (2001).
[CrossRef]

Y. H. Huang, C. Quan, C. J. Tay, and L. J. Chen, "Shape measurement by the use of digital image correlation," Opt. Eng. 44, 087011-1-7 (2005).
[CrossRef]

W. H. Peters and W. F. Ranson, "Digital imaging techniques in experimental mechanics," Opt. Eng. 21, 427-431 (1982).

P. F. Luo, Y. J. Chao, and M. A. Sutton, "Application of stereo vision to three-dimensional deformations analyses in fracture experiments," Opt. Eng. 33, 981-990 (1994).
[CrossRef]

J. D. Helm, S. R. McNeill, and M. A. Sutton, "Improved three-dimensional image correlation for surface displacement measurements," Opt. Eng. 35, 1911-1920 (1996).
[CrossRef]

C. J. Tay, C. Quan, T. Wu, and Y. H. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43, 1152-1159 (2004).
[CrossRef]

Opt. Laser Technol. (1)

A. Asundi and F. P. Chiang, "Separation of 3-D displacement components in the white light speckle method," Opt. Laser Technol. 15, 41-45 (1983).
[CrossRef]

Opt. Lasers Eng. (1)

A. Asundi and H. North, "White-light speckle method," Opt. Lasers Eng. 29, 159-169 (1998).
[CrossRef]

Optik (2)

C. Quan, C. J. Tay, and Y. H. Huang, "3D deformation measurement using fringe projection and digital image correlation," Optik 115, 164-168 (2004).
[CrossRef]

K. S. Dharmsaktu, A. Kumar, and K. Singh, "Three-dimensional rigid-body motion measurement using speckle fanning in a photorefractive BaTiO3 crystal," Optik 112, 49-56 (2001).
[CrossRef]

Signal Process. (1)

J. Luo, K. Ying, and J. Bai, "Savitzky-Golay smoothing and differentiation filter for even number data," Signal Process. 85, 1429-1434 (2005).
[CrossRef]

Other (1)

R. S. Sirohi, ed., Speckle Metrology (Dekker, 1993).

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Figures (14)

Fig. 1
Fig. 1

Camera geometry with perspective projection.

Fig. 2
Fig. 2

Relation between out-of-plane displacement and apparent in-plane displacement.

Fig. 3
Fig. 3

Reference and deformed images of 3D displacement:(a) reference image and (b) deformed image.

Fig. 4
Fig. 4

Calculated displacement vector:(a) global DIC and (b) Newton–Raphson method.

Fig. 5
Fig. 5

Relation between inclined angle and relative error.

Fig. 6
Fig. 6

Simulated case of 3D deformation:(a) theoretical value, (b) calculated value, and (c) relative error.

Fig. 7
Fig. 7

Flow chart for 3D displacement retrieval.

Fig. 8
Fig. 8

Experimental setup for 3D rigid-body displacement measurement using DIC.

Fig. 9
Fig. 9

Calibration results:(a) slopes in the x direction and (b) slopes in the y direction.

Fig. 10
Fig. 10

Calibration results:(a) intercepts in the x direction and (b) intercepts in the y direction.

Fig. 11
Fig. 11

Calibration results:(a) magnification in the x direction and (b) magnification in the y direction.

Fig. 12
Fig. 12

Image of the wafer:(a) whole wafer and (b) region for calculation.

Fig. 13
Fig. 13

Comparison of prescribed and measured 3D rigid-body displacements.

Fig. 14
Fig. 14

Case of a cantilever beam:(a) calculated value, (b) theoretical value, and (c) relative error.

Tables (3)

Tables Icon

Table 1 Simulation of 3D Displacement in Ideal State

Tables Icon

Table 2 Simulation of 3D Displacement in Actual State

Tables Icon

Table 3 Comparison of Prescribed and Measured 3D Displacements

Equations (18)

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

x o x f / d x = r 11 X + r 12 Y + r 13 Z + t x r 31 X + r 32 Y + r 33 Z + t z ,
y o y f / d y = r 21 X + r 22 Y + r 23 Z + t y r 31 X + r 32 Y + r 33 Z + t z ,
r r = w r p w w r p = M R w p = M r w q ,
u t = u i + u o = u i + M r w q .
v t = v i + M r w q ,
u ( x , y ) = a 0 + a 1 x + a 2 y ,
v ( x , y ) = b 0 + b 1 x + b 2 y ,
X a = u [ 1 M M 1 M + 1 M 1 0 0 1 M 1 M 1 M M ] ( a 0 a 1 a 2 )
= ( u ( M , M ) u ( M + 1 , M ) u ( 0 , 0 ) u ( M 1 , M ) u ( M , M ) ) .
C = { i = 1 m j = 1 n [ f ( x i , y j ) f ¯ ] [ g ( x i * , y j * ) g ¯ ] } 2 i = 1 m j = 1 n [ f ( x i , y j ) f ¯ ] 2 i = 1 m j = 1 n [ g ( x i * , y j * ) g ¯ ] 2 ,
x * = a 1 + a 2 x + a 3 y ,
y * = a 4 + a 5 x + a 6 y ,
ξ = x * x = a 1 + ( a 2 1 ) x + a 3 y ,
η = y * y = a 4 + a 5 x + ( a 6 1 ) y .
ξ = a 1 + ( a 2 1 ) ( x 0 + Δ x ) + a 3 ( y 0 + Δ y ) = ξ 0 + ( a 2 1 ) Δ x + a 3 Δ y ,
η = a 4 + a 5 ( x 0 + Δ x ) + ( a 6 1 ) ( y 0 + Δ y ) = η 0 + a 5 Δ x + ( a 6 1 ) Δ y .
u t = u i + k ( x x 0 ) ,
v t = v i + k ( y y 0 ) ,

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