Abstract

A whole-field speckle strain sensor is presented. The speckle strain sensor allows the measurement of all three in-plane components of the strain field simultaneously without touching the surface of the sample. The strain fields are extracted from the in-plane motion of defocused laser speckles in a telecentric imaging system. To distinguish the contribution to the speckle motion from surface translation, rotation, and strain, the speckle motion from three lasers with different illumination directions and wavelengths has to be analyzed separately. Simultaneous acquisition of the three individual speckle patterns is achieved by means of splitting the light from the lasers onto separate but synchronized detectors with the aid of dichroic mirrors. The motion of the speckles is calculated with digital speckle photography (speckle correlation), which enables the strain sensor to measure strain fields with noise levels as low as 10 µstrain.

© 2002 Optical Society of America

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References

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  1. D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
    [CrossRef]
  2. M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
    [CrossRef]
  3. Y. Y. Hung, C. Y. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046–1051 (1979).
    [CrossRef] [PubMed]
  4. R. Kästle, E. Hack, U. Sennhauser, “Multiwavelength shearography for quantitative measurements of two-dimensional strain distributions,” Appl. Opt. 38, 96–100 (1999).
    [CrossRef]
  5. P. K. Rastogi, “Direct determination of large in-plane strains using high-resolution moiré,” Opt. Lasers Eng. 29, 97–102 (1998).
    [CrossRef]
  6. P. K. Rastogi, “Determination of surface strains by speckle shear photography,” Opt. Lasers Eng. 29, 103–116 (1998).
    [CrossRef]
  7. I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
    [CrossRef]
  8. M. Sjödahl, “Electronic speckle photography: measurement of in-plane strain fields using defocused laser speckle,” Appl. Opt. 34, 5799–5808 (1995).
    [CrossRef] [PubMed]
  9. P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
    [CrossRef]
  10. M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
    [CrossRef] [PubMed]
  11. M. Sjödahl, “Digital speckle photography,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, UK, 2001), Chap 5, 289–336.

1999 (1)

1998 (3)

P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
[CrossRef]

P. K. Rastogi, “Direct determination of large in-plane strains using high-resolution moiré,” Opt. Lasers Eng. 29, 97–102 (1998).
[CrossRef]

P. K. Rastogi, “Determination of surface strains by speckle shear photography,” Opt. Lasers Eng. 29, 103–116 (1998).
[CrossRef]

1997 (1)

1995 (1)

1991 (1)

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

1981 (1)

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

1979 (2)

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Y. Y. Hung, C. Y. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046–1051 (1979).
[CrossRef] [PubMed]

Bruck, H. A.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Chae, T. A.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Hack, E.

Hung, Y. Y.

Johnson, P.

P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
[CrossRef]

Kästle, R.

Liang, C. Y.

Rastogi, P. K.

P. K. Rastogi, “Direct determination of large in-plane strains using high-resolution moiré,” Opt. Lasers Eng. 29, 97–102 (1998).
[CrossRef]

P. K. Rastogi, “Determination of surface strains by speckle shear photography,” Opt. Lasers Eng. 29, 103–116 (1998).
[CrossRef]

Rowlands, R. E.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Segalman, D. J.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Sennhauser, U.

Sjödahl, M.

Sutton, M. A.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Turner, J. L.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Woyak, D. B.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

Appl. Opt. (4)

Exp. Mech. (2)

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

J. Phys. E (1)

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

Opt. Lasers Eng. (3)

P. Johnson, “Strain field measurements with dual-beam digital speckle photography,” Opt. Lasers Eng. 30, 315–326 (1998).
[CrossRef]

P. K. Rastogi, “Direct determination of large in-plane strains using high-resolution moiré,” Opt. Lasers Eng. 29, 97–102 (1998).
[CrossRef]

P. K. Rastogi, “Determination of surface strains by speckle shear photography,” Opt. Lasers Eng. 29, 103–116 (1998).
[CrossRef]

Other (1)

M. Sjödahl, “Digital speckle photography,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, UK, 2001), Chap 5, 289–336.

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Figures (4)

Fig. 1
Fig. 1

Orientation of illuminating beams in the three-beam configuration. Laser 1 makes an angle of approximately 90° to the x axis, laser 2 makes an angle of approximately -30° to the x-axis, and laser 3 makes an angle of approximately 210° to the x axis. These three beams are orientated so that they make an angle of 45° to the z axis.

Fig. 2
Fig. 2

Drawing of the imaging system.

Fig. 3
Fig. 3

Photograph of the in-plane strain field sensor.

Fig. 4
Fig. 4

In-plane strain field around the hole for a specimen in tension. The arrows show the principal strain field components where arrows pointing toward the positive x and y directions denote tension, and arrows pointing toward the negative x and y directions denote compression.

Tables (2)

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Table 1 Calibration Parameters

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Table 2 Results from the Strain Field Measurements

Equations (12)

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AX=axMd-ΔLMdaxx lx-ayx ly- 1+lzΩy,
AY=ayMd-ΔLMdaxy lx-ayy ly+1+lzΩx,
AZ=azMd+ΔLMd2axx+ayy.
axx =xx, axy=xy-Ωz, ayx=xy+Ωz, ayy=yy,
AX=-ΔLMdaxx lx-ayx ly-Φx,
AY=-ΔLMdaxy lx-ayy ly-Φy,
Ax,foc.=axMd-δLMdΩzly,
Ay,foc.=ayMd+δLMdΩzlx,
Ax,defoc. -Ax,foc.=- ΔLMdΩzly,
Ay,defoc. - Ay,foc. = ΔLMdΩzlx,
lx2+ly2+lz2=1.
ΔΦT=- aTδLΔL2+ΔlzΩT,

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