Abstract

We investigate experimentally the optimal rate at which the reference speckle pattern should be updated when dynamic speckle interferometry is used to measure transient in-plane displacement fields. Images are captured with a high-speed camera and phase shifting and phase unwrapping are done temporally. For a wide range of in-plane velocities, up to a maximum of 40% of the Nyquist limit, the random errors in the calculated displacement field are minimized by updating the reference speckle pattern after a speckle displacement of 1/10 of the pixel spacing. The technique is applied to measurements of microscale deformation fields within an adhesive joint in a carbon-fiber epoxy composite.

© 2003 Optical Society of America

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References

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  1. J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
    [CrossRef]
  2. P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements, and three-dimensional surface shapes,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed., (Wiley, Chichester, UK, 2001), pp. 141–224.
  3. P. Gren, S. Schedin, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
    [CrossRef] [PubMed]
  4. P. Gren, “Four-pulse interferometric recordings of transient events by pulsed TV holography,” personal communication.
  5. J. M. Huntley, G. H. Kaufmann, D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556–6563 (1999).
    [CrossRef]
  6. P. Haible, M. P. Kothiyal, H. J. Tiziani, “Heterodyne temporal speckle-pattern interferometry,” Appl. Opt. 39, 114–117 (2000).
    [CrossRef]
  7. J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, C. Buckberry, “Measurement of complex surface deformation at audio acoustic frequencies by high-speed dynamic phase-stepped ESPI,” Opt. Lett. 25, 1068–1070 (2000).
    [CrossRef]
  8. X. C. de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Ph.D. dissertation, (Ecole Polytechnique Federale de Lausanne, Lausanne1997).
  9. P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
    [CrossRef]
  10. A. Andersson, A. Runnemalm, M. Sjödahl, “Digital speckle-pattern interferometry: fringe retrieval for large in-plane deformations with digital speckle photography,” Appl. Opt. 38, 5408–5412 (1999).
    [CrossRef]

2000

1999

1997

1971

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[CrossRef]

1966

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Andersson, A.

Barton, J. S.

Buckberry, C.

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[CrossRef]

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

de Lega, X. C.

X. C. de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Ph.D. dissertation, (Ecole Polytechnique Federale de Lausanne, Lausanne1997).

Gren, P.

P. Gren, S. Schedin, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
[CrossRef] [PubMed]

P. Gren, “Four-pulse interferometric recordings of transient events by pulsed TV holography,” personal communication.

Haible, P.

Huntley, J. M.

Jones, J. D. C.

Kaufmann, G. H.

Kerr, D.

Kilpatrick, J. M.

Kothiyal, M. P.

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[CrossRef]

Moore, A. J.

Rastogi, P. K.

P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements, and three-dimensional surface shapes,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed., (Wiley, Chichester, UK, 2001), pp. 141–224.

Reeves, M.

Runnemalm, A.

Schedin, S.

Sjödahl, M.

Tiziani, H. J.

Appl. Opt.

Metrologia

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Laser Technol.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26–30 (1971).
[CrossRef]

Opt. Lett.

Other

P. K. Rastogi, “Measurement of static surface displacements, derivatives of displacements, and three-dimensional surface shapes,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed., (Wiley, Chichester, UK, 2001), pp. 141–224.

P. Gren, “Four-pulse interferometric recordings of transient events by pulsed TV holography,” personal communication.

X. C. de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Ph.D. dissertation, (Ecole Polytechnique Federale de Lausanne, Lausanne1997).

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Figures (7)

Fig. 1
Fig. 1

Schematic sketch of the optical in-plane setup. HWP—half wave plate, PBS—polarizing beam splitter, P—Pockels cell, OF—optical fiber, BC—beam collimator, D—high voltage driver, G—function generator, F—frame store, and M—mirror.

Fig. 2
Fig. 2

Photograph of the high-speed camera on the left-hand side, beam collimators and the object on the right-hand side.

Fig. 3
Fig. 3

Master curves showing the effect of the re-referencing rate (five different α values) on the calculated mean phase change for four different speeds: (a) 1 μm s-1, (b) 2 μm s-1, (c) 4 μm s-1, (d) 8 μm s-1.

Fig. 4
Fig. 4

Master curves showing the effect of the re-referencing rate (five different α values) on the standard deviation in unwrapped phase values for four different speeds: (a) 1 μm s-1, (b) 2 μm s-1, (c) 4 μm s-1, (d) 8 μm s-1.

Fig. 5
Fig. 5

Schematic picture of the adhesive composite where the studied area is marked.

Fig. 6
Fig. 6

Unwrapped phase map of the deformation obtained from the composite. The grayscale gives the deformation (u) in μm. The sensitivity direction is along the x axis.

Fig. 7
Fig. 7

Deformation along the line x = 0.6 mm for three different values of the re-referencing parameter: α = 0.0, 0.1, and 0.4.

Equations (11)

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

It=Ir+Io+2IrIo1/2 cosϕt+φt,
φt=tπ2.
Δϕ=4πλ u sin θ,
umax=λ8 sin θ.
ϕwt=tan-1signIt+1-It+2It-It+3+It+1-It+23It+1-3It+2-It+It+3It+1+It+2-It-It+31/2 =tan-1NtDt,
Δϕwt2, t1=tan-1Nt2Dt1-Dt2Nt1Dt2Dt1+Nt2Nt1.
dt=NINTΔϕwt, 0-Δϕwt-1, 0/2π,t=2, 3,, s,
vt=k=2t dk, t=2, 3,, s v1=0
Δϕut, 0=Δϕwt, 0-2πvt, t=1, 2,, s.
Δϕut, 0=Δϕut, tκ+k=2κ Δϕutk, tk-1+Δϕut1, 0.
σ=1.2λF#1+m,

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