Abstract

A simple, cost-effective but practical microscopic 3D-DIC method using a single camera and a transmission diffraction grating is proposed for surface profile and deformation measurement of small-scale objects. By illuminating a test sample with quasi-monochromatic source, the transmission diffraction grating placed in front of the camera can produce two laterally spaced first-order diffraction views of the sample surface into the two halves of the camera target. The single image comprising negative and positive first-order diffraction views can be used to reconstruct the profile of the test sample, while the two single images acquired before and after deformation can be employed to determine the 3D displacements and strains of the sample surface. The basic principles and implementation procedures of the proposed technique for microscopic 3D profile and deformation measurement are described in detail. The effectiveness and accuracy of the presented microscopic 3D-DIC method is verified by measuring the profile and 3D displacements of a regular cylinder surface.

© 2013 Optical Society of America

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References

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  1. M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image correlation for shape, motion and deformation measurements (Springer, 2009).
  2. B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
    [CrossRef]
  3. J. J. Orteu, “3-D computer vision in experimental mechanics,” Opt. Lasers Eng.47(3-4), 282–291 (2009).
    [CrossRef]
  4. M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
    [CrossRef]
  5. B. Pan, L. P. Yu, and D. F. Wu, “High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification,” Exp. Mech., doi:.
    [CrossRef]
  6. P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
    [CrossRef]
  7. B. Pan, D. F. Wu, and L. P. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt.51(19), 4409–4419 (2012).
    [CrossRef] [PubMed]
  8. H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
    [CrossRef]
  9. M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
    [CrossRef]
  10. Z. X. Hu, H. Y. Luo, Y. J. Du, and H. B. Lu, “Fluorescent stereo microscopy for 3D surface profilometry and deformation mapping,” Opt. Express21(10), 11808–11818 (2013).
    [CrossRef] [PubMed]
  11. http://www.correlatedsolutions.com
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    [CrossRef]
  13. M. Trivi and H. J. Rabal, “Stereoscopic uses of diffraction gratings,” Appl. Opt.27(6), 1007–1009 (1988).
    [CrossRef] [PubMed]
  14. B. Pan and K. Li, “A fast digital image correlation method for deformation measurement,” Opt. Lasers Eng.49(7), 841–847 (2011).
    [CrossRef]
  15. B. Pan, H. M. Xie, and Z. Y. Wang, “Equivalence of digital image correlation criteria for pattern matching,” Appl. Opt.49(28), 5501–5509 (2010).
    [CrossRef] [PubMed]
  16. H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech.40(4), 393–400 (2000).
    [CrossRef]
  17. P. F. Luo and J. N. Chen, “Measurement of curved-surface Deformation in cylindrical coordinates,” Exp. Mech.40(4), 345–350 (2000).
    [CrossRef]

2013 (2)

S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction assisted image correlation: a novel method for measuring three-dimensional deformation using two-dimension digital image correlation,” Exp. Mech.53(5), 755–765 (2013).
[CrossRef]

Z. X. Hu, H. Y. Luo, Y. J. Du, and H. B. Lu, “Fluorescent stereo microscopy for 3D surface profilometry and deformation mapping,” Opt. Express21(10), 11808–11818 (2013).
[CrossRef] [PubMed]

2012 (1)

2011 (1)

B. Pan and K. Li, “A fast digital image correlation method for deformation measurement,” Opt. Lasers Eng.49(7), 841–847 (2011).
[CrossRef]

2010 (1)

2009 (2)

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

J. J. Orteu, “3-D computer vision in experimental mechanics,” Opt. Lasers Eng.47(3-4), 282–291 (2009).
[CrossRef]

2008 (2)

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

2004 (1)

H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
[CrossRef]

2000 (2)

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech.40(4), 393–400 (2000).
[CrossRef]

P. F. Luo and J. N. Chen, “Measurement of curved-surface Deformation in cylindrical coordinates,” Exp. Mech.40(4), 345–350 (2000).
[CrossRef]

1993 (1)

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

1988 (1)

Asundi, A.

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

Cary, P. D.

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech.40(4), 393–400 (2000).
[CrossRef]

Chao, Y. J.

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

Chen, J. N.

P. F. Luo and J. N. Chen, “Measurement of curved-surface Deformation in cylindrical coordinates,” Exp. Mech.40(4), 345–350 (2000).
[CrossRef]

Du, Y. J.

Garcia, D.

H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
[CrossRef]

Gdoutou, A.

S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction assisted image correlation: a novel method for measuring three-dimensional deformation using two-dimension digital image correlation,” Exp. Mech.53(5), 755–765 (2013).
[CrossRef]

Goldbach, M.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Hu, Z. X.

Ke, X.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Lessner, S. M.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Li, K.

B. Pan and K. Li, “A fast digital image correlation method for deformation measurement,” Opt. Lasers Eng.49(7), 841–847 (2011).
[CrossRef]

Lu, H.

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech.40(4), 393–400 (2000).
[CrossRef]

Lu, H. B.

Luo, H. Y.

Luo, P. F.

P. F. Luo and J. N. Chen, “Measurement of curved-surface Deformation in cylindrical coordinates,” Exp. Mech.40(4), 345–350 (2000).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

Orteu, J. J.

J. J. Orteu, “3-D computer vision in experimental mechanics,” Opt. Lasers Eng.47(3-4), 282–291 (2009).
[CrossRef]

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

Pan, B.

B. Pan, D. F. Wu, and L. P. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt.51(19), 4409–4419 (2012).
[CrossRef] [PubMed]

B. Pan and K. Li, “A fast digital image correlation method for deformation measurement,” Opt. Lasers Eng.49(7), 841–847 (2011).
[CrossRef]

B. Pan, H. M. Xie, and Z. Y. Wang, “Equivalence of digital image correlation criteria for pattern matching,” Appl. Opt.49(28), 5501–5509 (2010).
[CrossRef] [PubMed]

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

B. Pan, L. P. Yu, and D. F. Wu, “High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification,” Exp. Mech., doi:.
[CrossRef]

Peters, W. H.

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

Qian, K. M.

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

Rabal, H. J.

Ravichandran, G.

S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction assisted image correlation: a novel method for measuring three-dimensional deformation using two-dimension digital image correlation,” Exp. Mech.53(5), 755–765 (2013).
[CrossRef]

Schreier, H. W.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
[CrossRef]

Schreier, W. H.

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

Sutton, M. A.

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

Tiwari, V.

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

Trivi, M.

Wang, Z. Y.

Wu, D. F.

B. Pan, D. F. Wu, and L. P. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt.51(19), 4409–4419 (2012).
[CrossRef] [PubMed]

B. Pan, L. P. Yu, and D. F. Wu, “High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification,” Exp. Mech., doi:.
[CrossRef]

Xia, S.

S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction assisted image correlation: a novel method for measuring three-dimensional deformation using two-dimension digital image correlation,” Exp. Mech.53(5), 755–765 (2013).
[CrossRef]

Xie, H. M.

B. Pan, H. M. Xie, and Z. Y. Wang, “Equivalence of digital image correlation criteria for pattern matching,” Appl. Opt.49(28), 5501–5509 (2010).
[CrossRef] [PubMed]

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

Yan, J. H.

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

Yost, M.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Yu, L. P.

B. Pan, D. F. Wu, and L. P. Yu, “Optimization of a three-dimensional digital image correlation system for deformation measurements in extreme environments,” Appl. Opt.51(19), 4409–4419 (2012).
[CrossRef] [PubMed]

B. Pan, L. P. Yu, and D. F. Wu, “High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification,” Exp. Mech., doi:.
[CrossRef]

Zhao, F.

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Appl. Opt. (3)

Exp. Mech. (6)

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech.40(4), 393–400 (2000).
[CrossRef]

P. F. Luo and J. N. Chen, “Measurement of curved-surface Deformation in cylindrical coordinates,” Exp. Mech.40(4), 345–350 (2000).
[CrossRef]

S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction assisted image correlation: a novel method for measuring three-dimensional deformation using two-dimension digital image correlation,” Exp. Mech.53(5), 755–765 (2013).
[CrossRef]

H. W. Schreier, D. Garcia, and M. A. Sutton, “Advances in light microscope stereo vision,” Exp. Mech.44(3), 278–288 (2004).
[CrossRef]

B. Pan, L. P. Yu, and D. F. Wu, “High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification,” Exp. Mech., doi:.
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech.33(2), 123–132 (1993).
[CrossRef]

J. Biomed. Mater. Res. (1)

M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurement on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res.84A(1), 178–190 (2008).
[CrossRef]

Meas. Sci. Technol. (1)

B. Pan, K. M. Qian, H. M. Xie, and A. Asundi, “Two-dimensional Digital Image Correlation for In-plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol.20(6), 062001 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (3)

J. J. Orteu, “3-D computer vision in experimental mechanics,” Opt. Lasers Eng.47(3-4), 282–291 (2009).
[CrossRef]

M. A. Sutton, J. H. Yan, V. Tiwari, W. H. Schreier, and J. J. Orteu, “The effect of out-of-plane motion on 2D and 3D digital image correlation measurements,” Opt. Lasers Eng.46(10), 746–757 (2008).
[CrossRef]

B. Pan and K. Li, “A fast digital image correlation method for deformation measurement,” Opt. Lasers Eng.49(7), 841–847 (2011).
[CrossRef]

Other (2)

M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image correlation for shape, motion and deformation measurements (Springer, 2009).

http://www.correlatedsolutions.com

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of optical arrangement of the single-camera microscopic 3D-DIC method

Fig. 2
Fig. 2

The imaging model of the single-camera microscopic 3D-DIC method

Fig. 3
Fig. 3

Calculation of image displacements for profile and 3D displacement measurement using subset-based 2D-DIC.

Fig. 4
Fig. 4

Experimental setup for the proposed single-camera microscopic 3D-DIC method

Fig. 5
Fig. 5

(a) Diffraction images of a cylinder rod; (b) computed x-directional image displacements of the ROI; (c) computed y-directional image displacements of the ROI; (d) computed ZNCC coefficients of the ROI

Fig. 6
Fig. 6

(a) Reconstructed surface topography of the cylinder rod using Eqs. (7)-(9); (b) Inversed surface topography after applying coordinate transformation based on best plane fitting.

Fig. 7
Fig. 7

(a) Comparison of Z-displacements calculated by Eq. (18) of this work and Eq. (8) of Ref [12] respectively; (b) Measured displacement vector field at a Z-displacement of 0.5mm

Tables (1)

Tables Icon

Table 1 Comparison of measured Z displacements by the original and proposed methods for out-of-plane translations

Equations (20)

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

Z ±1 = Z cos 3 θ
X ±1 =XZtanθ
Y ±1 =Y
x 0 = ( x 0 c x , y 0 c y ) = ( L i m g X Z o b j P s z , L i m g Y Z o b j P s z ) = ( M X , M Y )
x 1 = ( x 1 c x , y 1 c y ) = ( L i m g ( X + Z tan θ ) Z o b j P s z , L i m g Y Z o b j P s z ) = ( M ( X + Z tan θ ) , M Y )
x + 1 = ( x + 1 c x , y + 1 c y ) = ( L i m g ( X Z tan θ ) Z o b j P s z , L i m g Y Z o b j P s z ) = ( M ( X Z tan θ ) , M Y )
X= ( x +1 + x 1 2 c x ) 2M
Y= ( y +1 + y 1 2 c y ) 2M
Z= ( x +1 x 1 ) 2Mtanθ
x 0 =( x 0 c x , y 0 c y )=( L img ( X+U ) ( Z obj +W ) P sz , L img ( Y+V ) ( Z obj +W ) P sz )
x 1 =( x 1 c x , y 1 c y )=( L img ( X+U+( Z+W )tanθ ) ( Z obj + W cos 3 θ ) P sz , L img ( Y+V ) ( Z obj + W cos 3 θ ) P sz )
x +1 =( x +1 c x , y +1 c y )=( L img ( X+U( Z+W )tanθ ) ( Z obj + W cos 3 θ ) P sz , L img ( Y+V ) ( Z obj + W cos 3 θ ) P sz )
( x 1 c x , y 1 c y )( L img ( X+U+( Z+W )tanθ ) Z obj P sz ( 1 W Z obj ), L img ( Y+V ) Z obj P sz ( 1 W Z obj ) ) =( M( X+U+( Z+W )tanθ )( 1 W Z obj ),M( Y+V )( 1 W Z obj ) )
( x +1 c x , y +1 c y )( L img ( X+U( Z+W )tanθ ) Z obj P sz ( 1 W Z obj ), L img ( Y+V ) Z obj P sz ( 1 W Z obj ) ) =( M( X+U( Z+W )tanθ )( 1 W Z obj ),M( Y+V )( 1 W Z obj ) )
u +1 u 1 =( x +1 x +1 )( x 1 x 1 )=2Mtanθ( Z+W )( 1 W Z obj )2MtanθZ =2Mtanθ[ ( Z+W )( 1 W Z obj )Z ]=2Mtanθ( 1 Z+W Z obj )W2Mtanθ( 1 Z Z obj )W
u +1 + u 1 =( x +1 x +1 )+( x 1 x 1 )=2MX2M( X+U )( 1 W Z obj ) 2M XW Z obj 2MU2MU
v +1 + v 1 =( y +1 y +1 )+( y 1 y 1 )=2M( Y+V )( 1 W Z obj )2MY 2MV2M YW Z obj 2MV
W u +1 u 1 2Mtanθ ( Z obj Z obj Z )
U u +1 + u 1 2M
V v +1 + v 1 2M

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