Abstract

A laser speckle correlator with high optical magnification is presented, and its performance in the measurement of strain is demonstrated experimentally. Two separated areas on a test specimen are illuminated with laser beams, and displacements of each area are measured by performance of laser speckle correlation on successive magnified images. The interplay of magnification, lens aperture, surface roughness, pixel spacing on the CCD array sensor, and the attainable precision of correlation are investigated theoretically and experimentally. Resolutions that are usually considered accessible only to interferometric techniques are achieved: displacement resolutions of less than 50 nm and strain measurements of less than 10 µstrain across distances of the order of 10 mm are demonstrated. At high magnification, speckle decorrelation due to out-of-plane displacement becomes a stringent restriction, and surface height correlation effects may limit speckle contrast and broaden speckle correlation peaks.

© 2000 Optical Society of America

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References

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  1. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
    [CrossRef]
  2. I. Yamaguchi, K. Kobayashi, “Material testing by the laser speckle strain gauge,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. SPIE1554A, 240–249 (1991).
  3. M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.
  4. H. Manser, “Laser-speckle Korrelationsverfahren zur Verschiebungsmessung bei hohen Probentemperaturen,” Ph.D. dissertation (Graz University of Technology, Graz, 1992).
  5. D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
    [CrossRef]
  6. B. Zagar, H. Weiss, B. Weiss, “A high speed laser-optical correlation-based strain sensor,” in Fourteenth International Measurement Confederation (IMEKO) World Congress, Tampere, Vol. 8, Measurement of Geometrical Quantities (Topic 14), J. Halttunen, ed. (Finnish Society of Automation, Helsinki, 1997), pp. 228–233.
  7. M. Sjödahl, L. R. Benckert “Systematic and random errors in electronic speckle photography,” Appl. Opt. 33, 7461–7471 (1994).
    [CrossRef] [PubMed]
  8. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  10. A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 203–253.
  11. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.
  12. M. P. Wernet, A. Pline, “Particle displacement technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery,” Exp. Fluids 15, 295–307 (1993).
  13. M. Matin, “Construction of a small controllable strain,” (Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, 1996).
  14. H. Sakulin, “Measurement of strain with electronic speckle pattern interferometry,” M.S. thesis (Graz University of Technology, Graz, 1998).

1994 (1)

1993 (1)

M. P. Wernet, A. Pline, “Particle displacement technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery,” Exp. Fluids 15, 295–307 (1993).

1992 (1)

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

1981 (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Anwander, M.

M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.

Benckert, L. R.

Chen, D. J.

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

Chiang, F. P.

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 203–253.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Kobayashi, K.

I. Yamaguchi, K. Kobayashi, “Material testing by the laser speckle strain gauge,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. SPIE1554A, 240–249 (1991).

Manser, H.

H. Manser, “Laser-speckle Korrelationsverfahren zur Verschiebungsmessung bei hohen Probentemperaturen,” Ph.D. dissertation (Graz University of Technology, Graz, 1992).

Matin, M.

M. Matin, “Construction of a small controllable strain,” (Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, 1996).

Pline, A.

M. P. Wernet, A. Pline, “Particle displacement technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery,” Exp. Fluids 15, 295–307 (1993).

Sakulin, H.

H. Sakulin, “Measurement of strain with electronic speckle pattern interferometry,” M.S. thesis (Graz University of Technology, Graz, 1998).

Sjödahl, M.

Weiss, B.

B. Zagar, H. Weiss, B. Weiss, “A high speed laser-optical correlation-based strain sensor,” in Fourteenth International Measurement Confederation (IMEKO) World Congress, Tampere, Vol. 8, Measurement of Geometrical Quantities (Topic 14), J. Halttunen, ed. (Finnish Society of Automation, Helsinki, 1997), pp. 228–233.

M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.

Weiss, H.

M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.

B. Zagar, H. Weiss, B. Weiss, “A high speed laser-optical correlation-based strain sensor,” in Fourteenth International Measurement Confederation (IMEKO) World Congress, Tampere, Vol. 8, Measurement of Geometrical Quantities (Topic 14), J. Halttunen, ed. (Finnish Society of Automation, Helsinki, 1997), pp. 228–233.

Wernet, M. P.

M. P. Wernet, A. Pline, “Particle displacement technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery,” Exp. Fluids 15, 295–307 (1993).

Yamaguchi, I.

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

I. Yamaguchi, K. Kobayashi, “Material testing by the laser speckle strain gauge,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. SPIE1554A, 240–249 (1991).

Zagar, B.

M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.

B. Zagar, H. Weiss, B. Weiss, “A high speed laser-optical correlation-based strain sensor,” in Fourteenth International Measurement Confederation (IMEKO) World Congress, Tampere, Vol. 8, Measurement of Geometrical Quantities (Topic 14), J. Halttunen, ed. (Finnish Society of Automation, Helsinki, 1997), pp. 228–233.

Appl. Opt. (1)

Exp. Fluids (1)

M. P. Wernet, A. Pline, “Particle displacement technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery,” Exp. Fluids 15, 295–307 (1993).

Exp. Mech. (1)

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

Opt. Acta (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Other (10)

I. Yamaguchi, K. Kobayashi, “Material testing by the laser speckle strain gauge,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. SPIE1554A, 240–249 (1991).

M. Anwander, B. Weiss, B. Zagar, H. Weiss, “A laser speckle correlation method for strain measurement at elevated temperatures,” in Proceedings of the International Symposium on Local Strain and Temperature Measurements in Nonuniform Fields at Elevated Temperatures, Berlin (Woodhead, Cambridge, UK, 1996), pp. 49–58.

H. Manser, “Laser-speckle Korrelationsverfahren zur Verschiebungsmessung bei hohen Probentemperaturen,” Ph.D. dissertation (Graz University of Technology, Graz, 1992).

B. Zagar, H. Weiss, B. Weiss, “A high speed laser-optical correlation-based strain sensor,” in Fourteenth International Measurement Confederation (IMEKO) World Congress, Tampere, Vol. 8, Measurement of Geometrical Quantities (Topic 14), J. Halttunen, ed. (Finnish Society of Automation, Helsinki, 1997), pp. 228–233.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 203–253.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

M. Matin, “Construction of a small controllable strain,” (Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, 1996).

H. Sakulin, “Measurement of strain with electronic speckle pattern interferometry,” M.S. thesis (Graz University of Technology, Graz, 1998).

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Figures (9)

Fig. 1
Fig. 1

Displacement of two distant regions of a strained specimen.

Fig. 2
Fig. 2

Principal optical setup.

Fig. 3
Fig. 3

Possible in-plane displacement resolution Δξmin versus tolerable out-of-plane movement for λ = 632.8 nm, the smallest speckle diameter, and 10× pixel interpolation.

Fig. 4
Fig. 4

Modified setup of the two-spot geometry with only one lens and one CCD camera.

Fig. 5
Fig. 5

Speckle image with optical magnification, M = 24. Two distant observation regions are directed to the left and right half-plane of one CCD camera. In the middle an overlapping region is visible.

Fig. 6
Fig. 6

Strain in an aluminum plate heated by attached resistors versus time. The two solid curves represent measurements obtained by speckle correlation, the dotted curve shows a speckle pattern interferometer measurement for comparison.

Fig. 7
Fig. 7

Standard deviation of in-plane measurements in the presence of out-of-plane displacements for various aperture values and M = 24.

Fig. 8
Fig. 8

Limit of out-of-plane displacement for speckle correlation with large optical magnification and constant effective F # = 55 for σ u < 0.3 pixel: *, experimental results; theoretical curve, comparison.

Fig. 9
Fig. 9

Normalized autocovariance of speckle images for optical magnification of M = 35 and an effective F # of 55: solid curve, theoretical expected autocovariance for perfectly rough surfaces; dotted curve, speckle pattern generated by an aluminum surface; dash–dotted curve, surface of reflecting paint.

Equations (12)

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

εξ, εη=Δξ1+Δξ2ξ0, Δη1+Δη2η0=Δξξ0, Δηη0.
εξ, εη=Δuu0, Δvv0=MΔξMξ0, MΔηMη0
dP<0.41S,
S=1.221+Mλf#,
f#>2 dP1+Mλ.
Σ=1.22λf#1+MM.
JAu1, v1, u2, v2=hu1, v1h*u2, v2Jαgu1, v1, u2, v2,
Jαgu1, v1, u2, v2=1|M|2 Jαu1M, v1M, u2M, v2M.
Δzmax=2λf#21+M2M2.
Δzmax=1.34 Σ2λ,
Δz<±8 dP2λM2
Δξmin=iP1.16Δzmaxλ1/2,

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