Abstract

Subpixel digital image correlation has been applied to microscope images to analyze surface deformation. Nonintegral pixel shifting and successive approximation are used to calculate the subpixel element of the sample displacement without introducing systematic interpolation errors. Although in-plane displacement precision of better than 2% of a pixel, or < 15 nm at x10 magnification, is shown to be achievable, the use of even moderate numerical aperture microscope objectives render the technique sensitive to errors or variations in sample focusing. The magnitude of this effect is determined experimentally and a focus compensation method is described and demonstrated.

© 2002 Optical Society of America

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References

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  1. H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
    [Crossref]
  2. M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
    [Crossref] [PubMed]
  3. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [Crossref] [PubMed]
  4. Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
    [Crossref]
  5. 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]
  6. D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
    [Crossref]
  7. M. C. Pitter, C. W. See, and M. G. Somekh, “Subpixel microscopic deformation analysis using correlation and artificial neural networks,” Opt. Express 8, 322–327 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-322.
    [Crossref] [PubMed]
  8. B. Han, “Recent advances of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronic devices,” Exp. Mech. 38, 278–288 (1998).
  9. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, Singapore, 1986), Chap. 6.
  10. M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. ICASSP 3 (1998), pp. 1381–1384, http://www.fftw.org/fftw-paper-icassp.pdf.
  11. M. J. Kidger, “Use of the Levenberg-Marquardt (damped least-squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
    [Crossref]

2001 (3)

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]

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

M. C. Pitter, C. W. See, and M. G. Somekh, “Subpixel microscopic deformation analysis using correlation and artificial neural networks,” Opt. Express 8, 322–327 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-322.
[Crossref] [PubMed]

1998 (2)

B. Han, “Recent advances of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronic devices,” Exp. Mech. 38, 278–288 (1998).

M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. ICASSP 3 (1998), pp. 1381–1384, http://www.fftw.org/fftw-paper-icassp.pdf.

1997 (2)

M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
[Crossref] [PubMed]

Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
[Crossref]

1994 (1)

1993 (1)

M. J. Kidger, “Use of the Levenberg-Marquardt (damped least-squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[Crossref]

1989 (1)

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

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, Singapore, 1986), Chap. 6.

Bruck, H. A.

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

Frigo, M.

M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. ICASSP 3 (1998), pp. 1381–1384, http://www.fftw.org/fftw-paper-icassp.pdf.

Goodson, K. E.

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]

Grosser, V.

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

Han, B.

B. Han, “Recent advances of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronic devices,” Exp. Mech. 38, 278–288 (1998).

Johnson, S. G.

M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. ICASSP 3 (1998), pp. 1381–1384, http://www.fftw.org/fftw-paper-icassp.pdf.

Kidger, M. J.

M. J. Kidger, “Use of the Levenberg-Marquardt (damped least-squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[Crossref]

Lyons, J. S.

Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
[Crossref]

McNeill, S. R.

Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
[Crossref]

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

Michel, B.

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

Peters, W. H.

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

Pitter, M. C.

Schubert, A.

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

See, C. W.

Sjödahl, M.

Somekh, M. G.

Sun, Z.

Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
[Crossref]

Sutton, M. A.

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

Vogel, D.

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

Zhou, P.

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]

Appl. Opt. (2)

Exp. Mech. (2)

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

B. Han, “Recent advances of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronic devices,” Exp. Mech. 38, 278–288 (1998).

Opt. Eng. (2)

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]

M. J. Kidger, “Use of the Levenberg-Marquardt (damped least-squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[Crossref]

Opt. Express (1)

Opt. Laser Eng. (2)

D. Vogel, V. Grosser, A. Schubert, and B. Michel, “MicroDAC strain measurements for electronics packaging structure,” Opt. Laser Eng. 36, 195–211 (2001).
[Crossref]

Z. Sun, J. S. Lyons, and S. R. McNeill, “Measuring microscopic deformations with digital image correlation,” Opt. Laser Eng. 27, 409–428 (1997).
[Crossref]

Proc. ICASSP (1)

M. Frigo and S. G. Johnson, “FFTW: an adaptive software architecture for the FFT,” in Proc. ICASSP 3 (1998), pp. 1381–1384, http://www.fftw.org/fftw-paper-icassp.pdf.

Other (1)

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, Singapore, 1986), Chap. 6.

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Figures (6)

Fig. 1.
Fig. 1.

Optical set up used to acquire digital images. Kohler illumination (source S, lenses L2 and L3) is reflected by the sample and imaged by the microscope objective MO and tube lens L1 onto the CCD camera. The sample is mounted on motorized z-stage Z.

Fig. 2.
Fig. 2.

(a) Micrographs of ground glass sample. The upper micrograph was obtained at NA 0.13, the lower at NA 0.25; (b) mean displacement error vs. subimage size m for this sample.

Fig. 3.
Fig. 3.

(a) Micrographs of ground section through a microelectronic device. The upper pair of images are mold compound at NA 0.13 (left) and NA 0.25. The lower pair are the silicon die, also at NA 0.13 (left) and 0.25; (b) mean displacement error vs. m.

Fig. 4.
Fig. 4.

(a) Standard deviation of displacement calculations as a function of sample defocus and (b) unsmoothed in-plane displacement vector plot for a rigid body tilt of 2° with NA = 0.25 and m = 32.

Fig. 5.
Fig. 5.

Flat and tilted sample profiles calculated with adapted auto-focus routine.

Fig. 6.
Fig. 6.

(a) Results using focus compensated MDAC; (b) effect of removing the image compression caused by the tilt. Neither data have been smoothed.

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