Abstract

We describe a phase-shifting out-of-plane speckle interferometer operating at 1 kHz for studying dynamic events. The system is based on a Pockels cell that is synchronized to a high-speed video camera to ensure that the phase shifting occurs between frames. Phase extraction is performed by use of a standard four-frame algorithm, and temporal phase unwrapping allows sequences of several hundred absolute (rather than relative) displacement maps to be obtained fully automatically. The maximum theoretical surface velocity of 67 µm s-1 is a factor of 40 greater than can be achieved with a speckle interferometer based on a conventional video camera. We test the system using a target that is displaced with constant speed in a direction normal to its surface by means of a piezoelectric transducer. The system’s performance in a practical situation is illustrated with measurements on a thin plate undergoing out-of-plane deformation.

© 1999 Optical Society of America

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References

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  1. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).
  2. R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1995).
  3. A. Fernandez, J. Blanco-Garcia, A. F. Doval, J. Bugarin, B. V. Dorrio, C. Lopez, J. M. Alen, M. Lopez-Amor, J. L. Fernandez, “Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method,” Appl. Opt. 37, 3440–3446 (1998).
    [CrossRef]
  4. D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, D. Kerr, “Measurement of transient deformations with dual-pulse addition electronic speckle pattern interferometry,” Appl. Opt. 37, 7259–7267 (1998).
    [CrossRef]
  5. See, for example, K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.
  6. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]
  7. G. M. Brown, “Dynamic computer aided video holometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed. Proc. SPIE1162, 36–45 (1989).
    [CrossRef]
  8. X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis,” Ph.D. dissertation (Ecole Polytechnique Federal Lausanne, Lausanne, Switzerland, 1997).
  9. C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
    [CrossRef]
  10. C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
    [CrossRef]
  11. A. J. Moore, D. P. Hand, J. S. Barton, J. D. C. Jones, “Transient deformation measurement with electronic speckle pattern interferometry and a high-speed camera,” Appl. Opt. 38, 1159–1162 (1999).
    [CrossRef]
  12. K. A. Stetson, W. R. Brohinsky, “Electrooptic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
    [CrossRef] [PubMed]
  13. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982).
    [CrossRef] [PubMed]
  14. J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” Opt. Lasers Eng. 26, 131–150 (1997).
    [CrossRef]
  15. J. R. Buckland, J. M. Huntley, S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995).
    [CrossRef] [PubMed]

1999

1998

1997

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” Opt. Lasers Eng. 26, 131–150 (1997).
[CrossRef]

1995

1993

1985

1982

Alen, J. M.

Barton, J. S.

Blanco-Garcia, J.

Brohinsky, W. R.

Brown, G. M.

G. M. Brown, “Dynamic computer aided video holometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed. Proc. SPIE1162, 36–45 (1989).
[CrossRef]

Buckland, J. R.

Bugarin, J.

Colonna de Lega, X.

X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis,” Ph.D. dissertation (Ecole Polytechnique Federal Lausanne, Lausanne, Switzerland, 1997).

Creath, K.

See, for example, K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

Dorrio, B. V.

Doval, A. F.

Farrant, D. I.

Fernandez, A.

Fernandez, J. L.

Franze, B.

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[CrossRef]

Haible, P.

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
[CrossRef]

Hand, D. P.

Huntley, J. M.

Itoh, K.

Joenathan, C.

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
[CrossRef]

Jones, J. D. C.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

Kaufmann, G. H.

Kerr, D.

Lopez, C.

Lopez-Amor, M.

Moore, A. J.

Oreb, B. F.

Petzing, J. N.

Saldner, H.

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1995).

Stetson, K. A.

Tiziani, H. J.

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[CrossRef]

Turner, S. R. E.

Tyrer, J. R.

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

Appl. Opt.

A. Fernandez, J. Blanco-Garcia, A. F. Doval, J. Bugarin, B. V. Dorrio, C. Lopez, J. M. Alen, M. Lopez-Amor, J. L. Fernandez, “Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method,” Appl. Opt. 37, 3440–3446 (1998).
[CrossRef]

D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, D. Kerr, “Measurement of transient deformations with dual-pulse addition electronic speckle pattern interferometry,” Appl. Opt. 37, 7259–7267 (1998).
[CrossRef]

J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[CrossRef] [PubMed]

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[CrossRef]

A. J. Moore, D. P. Hand, J. S. Barton, J. D. C. Jones, “Transient deformation measurement with electronic speckle pattern interferometry and a high-speed camera,” Appl. Opt. 38, 1159–1162 (1999).
[CrossRef]

K. A. Stetson, W. R. Brohinsky, “Electrooptic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
[CrossRef] [PubMed]

K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982).
[CrossRef] [PubMed]

J. R. Buckland, J. M. Huntley, S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995).
[CrossRef] [PubMed]

J. Mod. Opt.

C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement,” J. Mod. Opt. 45, 1975–1984 (1998).
[CrossRef]

Opt. Lasers Eng.

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” Opt. Lasers Eng. 26, 131–150 (1997).
[CrossRef]

Other

G. M. Brown, “Dynamic computer aided video holometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed. Proc. SPIE1162, 36–45 (1989).
[CrossRef]

X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis,” Ph.D. dissertation (Ecole Polytechnique Federal Lausanne, Lausanne, Switzerland, 1997).

See, for example, K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1995).

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Figures (9)

Fig. 1
Fig. 1

Dynamic speckle interferometer showing frame store (F), Pockels cell (P), high-voltage driver (D), function generator (G), 90:10 beam splitters (BS), mirrors (M) and lenses (L). PZT, piezoelectric translator.

Fig. 2
Fig. 2

Typical results from the phase calibration stage. Note the four individual steps in each of the four phase cycles. Each step is π/2 rad.

Fig. 3
Fig. 3

Average phase change of target undergoing rigid body motion produced by a triangular wave input to the PZT. Interframe time is 1 ms and oscillation period T = 200 ms.

Fig. 4
Fig. 4

Intensity modulation of a single pixel on the target surface for a triangular wave input to the PZT; oscillation period T = 200 ms.

Fig. 5
Fig. 5

Wrapped phase difference distribution of the target surface between frame 0 and frame 396 of the data capture sequence (black pixels represent -π and white ones represent +π).

Fig. 6
Fig. 6

Cross section through phase map (row 160) shown in Fig. 5 after temporal unwrapping through the intermediate 397 phase maps. Curves A and B were calculated without and with convolution, respectively.

Fig. 7
Fig. 7

Cross section through the phase map shown in Fig. 5 after spatial unwrapping (curves C and D) and by use of modified temporal unwrapping algorithm (curve E).

Fig. 8
Fig. 8

Phase profiles of target displacement along a horizontal line using 100, 200, 300, and 400 frames of the data capture sequence and the modified temporal unwrapping algorithm.

Fig. 9
Fig. 9

Phase distribution showing deformation of plate after temporal unwrapping with the modified algorithm through 400 frames.

Equations (18)

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

It=Ir+Io+2IrIo cosΦt+ϕt,
ϕt=πt/2.
Φwt=tan-1NtDt,
Nt=Imzt, Dt=Rezt,
zt=It-It+2+iIt+3-It+1×exp-iπt/2.
Φt+hΦt+hΦt, h=1, 2,q-1,
ϕt+h=ϕt+hπ/2.
dt=NINTΦwt-Φwt-1/2π, t=1, 2,s,
νt=t=1tdt, t=1, 2,s,
ΔΦut, 0=Φwt-Φw0-2πνt.
ΔΦwt2, t1=tan-1Nt2Dt1-Dt2Nt1Dt2Dt1+Nt2Nt1.
ΔΦut, 0=t=1t ΔΦwt, t-1.
Ax, y=19111111111.
σ=1.2λF1+M
dt=NINTΔΦwt, 0-ΔΦwt-1, 0/2π, t=2, 3,s.
νt=t=2tdt, t=2, 3,s, ν1=0,
ΔΦut, 0=ΔΦwt, 0-2πνt, t=1, 2,s.
ΔΦut, 0=ΔΦut, tκ+k=2κ ΔΦutk, tk-1+ΔΦut1, 0.

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