Abstract

We report a novel optical microscope for full-field, noncontact measurements of three-dimensional (3D) surface deformation and topography at the microscale. The microscope system is based on a seamless integration of the diffraction-assisted image correlation (DAIC) method with fluorescent microscopy. We experimentally demonstrate the microscope’s capability for 3D measurements with submicrometer spatial resolution and subpixel measurement accuracy.

© 2014 Optical Society of America

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  1. S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.
  2. B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
    [CrossRef]
  3. H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
    [CrossRef]
  4. N. Balasubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (July20, 1982).
  5. W. Welford, Opt. Acta 16, 371 (1969).
    [CrossRef]
  6. T. Darrell and K. Wohn, Proceedings CVPR ’88: The Computer Society Conference on Computer Vision and Pattern Recognition (1988), pp. 504–509.
  7. A. P. Pentland, Proc. IEEE Trans. Pattern Anal. Machine Intell. 9, 523 (1987).
  8. P. Grossmann, Pattern Recogn. Lett. 5, 63 (1987).
    [CrossRef]
  9. P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
    [CrossRef]
  10. J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
    [CrossRef]
  11. R. Jones, Holographic and Speckle Interferometry (Cambridge University, 1989).
  12. M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
    [CrossRef]
  13. Z. Hu, H. Luo, Y. Du, and H. Lu, Opt. Express 21, 11808 (2013).
    [CrossRef]
  14. L. Li and A. Y. Yi, J. Opt. Soc. Am. A 27, 2613 (2010).
    [CrossRef]
  15. S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
    [CrossRef]
  16. Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).
  17. W. Peters and W. Ranson, Opt. Eng. 21, 427 (1982).
  18. M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
    [CrossRef]

2013 (2)

Z. Hu, H. Luo, Y. Du, and H. Lu, Opt. Express 21, 11808 (2013).
[CrossRef]

S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
[CrossRef]

2010 (1)

2008 (2)

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

2003 (1)

H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
[CrossRef]

1996 (1)

J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
[CrossRef]

1993 (1)

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

1987 (2)

A. P. Pentland, Proc. IEEE Trans. Pattern Anal. Machine Intell. 9, 523 (1987).

P. Grossmann, Pattern Recogn. Lett. 5, 63 (1987).
[CrossRef]

1983 (1)

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

1982 (1)

W. Peters and W. Ranson, Opt. Eng. 21, 427 (1982).

1969 (1)

W. Welford, Opt. Acta 16, 371 (1969).
[CrossRef]

Balasubramanian, N.

N. Balasubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (July20, 1982).

Boyce, B. L.

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

Chao, Y.

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

Darrell, T.

T. Darrell and K. Wohn, Proceedings CVPR ’88: The Computer Society Conference on Computer Vision and Pattern Recognition (1988), pp. 504–509.

Du, Y.

Espinosa, H.

H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
[CrossRef]

Fischer, M.

H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
[CrossRef]

Gdoutou, A.

S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
[CrossRef]

Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).

Goldbach, M.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Grazier, J. M.

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

Grossmann, P.

P. Grossmann, Pattern Recogn. Lett. 5, 63 (1987).
[CrossRef]

Helm, J. D.

J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
[CrossRef]

Hezeltine, W.

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

Hu, Z.

Jones, R.

R. Jones, Holographic and Speckle Interferometry (Cambridge University, 1989).

Jones, R. E.

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

Ke, X.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Kovalchick, C.

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

Lessner, S.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Li, L.

Liang, F.

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

Lu, H.

Luo, H.

Luo, P.

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

McAllister, A.

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

McNeill, S.

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

McNeill, S. R.

J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
[CrossRef]

Nguyen, T. D.

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

Pan, Z.

Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).

Pentland, A. P.

A. P. Pentland, Proc. IEEE Trans. Pattern Anal. Machine Intell. 9, 523 (1987).

Peters, W.

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

W. Peters and W. Ranson, Opt. Eng. 21, 427 (1982).

Peters, W. H.

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

Prorok, B.

H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
[CrossRef]

Ranson, W.

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

W. Peters and W. Ranson, Opt. Eng. 21, 427 (1982).

Ravichandran, G.

S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
[CrossRef]

Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).

Schreier, H.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Sutton, M.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

Sutton, M. A.

J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
[CrossRef]

Walwadkar, S.

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

Welford, W.

W. Welford, Opt. Acta 16, 371 (1969).
[CrossRef]

Wohn, K.

T. Darrell and K. Wohn, Proceedings CVPR ’88: The Computer Society Conference on Computer Vision and Pattern Recognition (1988), pp. 504–509.

Wolters, W.

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

Xia, S.

S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
[CrossRef]

Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).

Yi, A. Y.

Yost, M.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Zhao, F.

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

Biomaterials (1)

B. L. Boyce, J. M. Grazier, R. E. Jones, and T. D. Nguyen, Biomaterials 29, 3896 (2008).
[CrossRef]

Exp. Mech. (2)

P. Luo, Y. Chao, M. Sutton, and W. H. Peters, Exp. Mech. 33, 123 (1993).
[CrossRef]

S. Xia, A. Gdoutou, and G. Ravichandran, Exp. Mech. 53, 755 (2013).
[CrossRef]

Image Vision Comput. (1)

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. McNeill, Image Vision Comput. 1, 133 (1983).
[CrossRef]

J. Biomed. Mater. Res. A (1)

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, J. Biomed. Mater. Res. A 84, 178 (2008).
[CrossRef]

J. Mech. Phys. Solids (1)

H. Espinosa, B. Prorok, and M. Fischer, J. Mech. Phys. Solids 51, 47 (2003).
[CrossRef]

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

Opt. Acta (1)

W. Welford, Opt. Acta 16, 371 (1969).
[CrossRef]

Opt. Eng. (2)

J. D. Helm, S. R. McNeill, and M. A. Sutton, Opt. Eng. 35, 1911 (1996).
[CrossRef]

W. Peters and W. Ranson, Opt. Eng. 21, 427 (1982).

Opt. Express (1)

Pattern Recogn. Lett. (1)

P. Grossmann, Pattern Recogn. Lett. 5, 63 (1987).
[CrossRef]

Proc. IEEE Trans. Pattern Anal. Machine Intell. (1)

A. P. Pentland, Proc. IEEE Trans. Pattern Anal. Machine Intell. 9, 523 (1987).

Other (5)

S. Walwadkar, C. Kovalchick, W. Hezeltine, F. Liang, and A. McAllister, Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, MEMS and Nanotechnology (Springer, 2013), Vol. 5, pp. 23–31.

R. Jones, Holographic and Speckle Interferometry (Cambridge University, 1989).

T. Darrell and K. Wohn, Proceedings CVPR ’88: The Computer Society Conference on Computer Vision and Pattern Recognition (1988), pp. 504–509.

N. Balasubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (July20, 1982).

Z. Pan, S. Xia, A. Gdoutou, and G. Ravichandran, “Diffraction-assisted image correlation for three-dimensional surface profiling,” Exp. Mech. (to be published).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Photograph of the newly developed optical microscope for three-dimensional (3D) surface displacement and profile measurements and (b) schematic layout of the microscope.

Fig. 2.
Fig. 2.

Negative and positive first-order views of a speckle-patterned region on a flat-glass slide.

Fig. 3.
Fig. 3.

In-plane displacement maps of the two first-order diffracted views due to an out-of-plane rigid-body translation of 10.0 μm: (a) negative first-order (up), (b) positive first-order (up+), (c) negative first-order (vp), and (d) positive first-order (vp+).

Fig. 4.
Fig. 4.

Measured 3D displacement fields due to an out-of-plane translation of 10.0 μm: (a) up, (b) vp, (c) wp, and (d) displacement profiles along the dashed section line shown in (c).

Fig. 5.
Fig. 5.

(a) Measured z-displacement field due to an out-of-plane tilt of 6 deg and (b) displacement profiles along the dashed section line shown in (a).

Fig. 6.
Fig. 6.

(a) Negative and positive first-order views of a speckle-patterned spherical surface, (b) measured topography of the test surface, and (c) height profiles along the two dashed section lines shown in (b).

Equations (11)

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

up=Mxyup+αx(xxc)wp,
vp=Mxyvp+αy(yyc)wp,
wp=Mzwp,
up=Nxy(up+wptanθ),
up+=Nxy(upwptanθ),
vp=vp+=Nxyvp,
wp=(upup+)2NxyMztanθ=β1(upup+)2,
up=(up+up+)2NxyMzαx(xxc)Mxywp=β2(up+up+)2β3(xxc)wp,
vp=(vp+vp+)2NxyMzαy(yyc)Mxywp=β2(vp+vp+)2β4(yyc)wp.
w(xp,yp)=β12[(xpXp)(xp+Xp+)]=β12up+C,
h(xp,yp)=w(xpβ2,ypβ2)=β1up.

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