Abstract

A method for recording and evaluating digital image-plane holograms is presented. Hundreds of holograms of an object that has been subjected to dynamic deformation (e.g., vibrations) are recorded. The phase of the wave front is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. By temporal phase unwrapping it is possible to determine the absolute deformation (included the direction of motion) of the object. Experimental results are presented, and the advantages of temporal phase unwrapping compared with spatial phase unwrapping are discussed.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), Chap. 9.
  2. R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 5.
  3. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  4. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989), Chap. 3.
  5. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  6. G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse-holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
    [CrossRef]
  7. H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
    [CrossRef] [PubMed]
  8. G. Pedrini, H. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
    [CrossRef]
  9. G. Pedrini, H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, N.Y., 2001), Chap. 6, pp. 337–362.
  10. G. Pedrini, Ph. Froening, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
    [CrossRef]
  11. S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100–103 (2001).
    [CrossRef]
  12. C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106–5110 (2001).
    [CrossRef]
  13. S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
    [CrossRef]
  14. E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.
  15. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef] [PubMed]
  19. J. M. Huntley, G. H. Kaufmann, D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556–6563 (1999).
    [CrossRef]
  20. 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]
  21. T. E. Carlsson, A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39, 2628–2637 (2000).
    [CrossRef]
  22. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  23. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
    [CrossRef]
  24. G. Pedrini, H. J. Tiziani, I. Alexeenko, “Digital-holographic interferometry with an image-intensifier system,” Appl. Opt. 41, 648–653 (2002).
    [CrossRef] [PubMed]

2002

2001

2000

1999

1998

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]

1997

1996

1995

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse-holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

1994

1993

1986

1982

Aggarwal, A. K.

Alexeenko, I.

Barton, J. S.

Baumbach, T.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
[CrossRef]

Burckhard, C. B.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 5.

Carlsson, T. E.

Cathey, W. T.

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), Chap. 9.

Collier, R. J.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 5.

Franze, B.

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]

Froening, Ph.

Gusev, M. E.

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.

Ina, H.

Joenathan, C.

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]

Jones, J. D. C.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989), Chap. 3.

Jüptner, W.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
[CrossRef]

E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.

Kaufmann, G. H.

Kerr, D.

Kobayashi, S.

Kolenovic, E.

E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.

Kreis, T.

Lai, S.

E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.

Lin, L. H.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 5.

Mendoza Santoyo, F.

Molin, N.-E.

Moore, A. J.

Osten, W.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
[CrossRef]

E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.

Pedrini, G.

Perez-Lopez, C.

Saldner, H.

Saldner, H. O.

Schedin, S.

Schnars, U.

Seebacher, S.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
[CrossRef]

Stetson, K. A.

Takeda, M.

Tiziani, H.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Tiziani, H. J.

G. Pedrini, H. J. Tiziani, I. Alexeenko, “Digital-holographic interferometry with an image-intensifier system,” Appl. Opt. 41, 648–653 (2002).
[CrossRef] [PubMed]

S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100–103 (2001).
[CrossRef]

C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106–5110 (2001).
[CrossRef]

G. Pedrini, Ph. Froening, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[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]

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]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse-holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, N.Y., 2001), Chap. 6, pp. 337–362.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Wei, A.

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989), Chap. 3.

Zou, Y.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse-holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Appl. Opt.

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

H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[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]

G. Pedrini, Ph. Froening, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

J. M. Huntley, G. H. Kaufmann, D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556–6563 (1999).
[CrossRef]

T. E. Carlsson, A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39, 2628–2637 (2000).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100–103 (2001).
[CrossRef]

C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106–5110 (2001).
[CrossRef]

G. Pedrini, H. J. Tiziani, I. Alexeenko, “Digital-holographic interferometry with an image-intensifier system,” Appl. Opt. 41, 648–653 (2002).
[CrossRef] [PubMed]

J. Mod. Opt.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse-holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[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]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Laser Eng.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Laser Eng. 36, 103–126 (2001).
[CrossRef]

Other

E. Kolenovic, S. Lai, W. Osten, W. Jüptner, “A miniaturized digital holographic endoscopic system for shape and deformation measurement,” in International Symposium on Photonics and Measurement, VDI report 1694 (VDI Verlag GmbH, Düsseldorf, Germany, 2002), pp. 79–84.

G. Pedrini, H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, N.Y., 2001), Chap. 6, pp. 337–362.

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), Chap. 9.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 5.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989), Chap. 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Optical arrangement for temporal digital holography: L, positive lens; AP, aperture; OF, optical fiber; M, mirror; NL, negative lens; BS, beam splitter.

Fig. 2
Fig. 2

Procedure for calculating the phase from a digital hologram: FFT, fast Fourier transformation; IFFT, inverse fast Fourier transformation.

Fig. 3
Fig. 3

Investigation of an object rotating at a frequency of 1000 rpm by use of the double-pulse technique and spatial phase unwrapping12: (a) wrapped phase, (b) pseudo-three-dimensional representation of the deformation.

Fig. 4
Fig. 4

Procedure for temporal phase unwrapping of a sequence of digital holograms: (a) reconstruction of the wrapped phase for each hologram, (b) temporal phase unwrapping of each point: FFT, fast Fourier transformation; IFFT, inverse fast Fourier transformation.

Fig. 5
Fig. 5

Simulations of the phase-sampling problem: (a) linear phase variation as a function of time, (b) wrapped phase sampling of 10 points/period, (c) phase unwrapping of (b), (d) wrapped phase sampling of 2 points/period, (e) phase unwrapping of (d). τ is the frame integration time.

Fig. 6
Fig. 6

Investigation of a metallic plate vibrating at a frequency of 5 Hz: (a) wrapped phase change as a function of time for a single point; (b) unwrapped phase; (c), (d), (e), displacement of the plate (compared with the initial position) at three times (0, 120, and 210 ms, respectively).

Fig. 7
Fig. 7

Investigation of an object with a defect: (a), (b) displacement of the object (compared with the initial position) at two times (105 and 163 ms, respectively).

Equations (6)

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

IHx, y=|RHx, y|2+|UHx, y|2+RHx, yUH*x, y+RH*x, yUHx, y,
fmax=2λsinθmax2,
ϕHwmΔx, nΔy=arctanImUHmΔx, nΔyReUHmΔx, nΔy,
Δϕ=2πλds,
UHx, y, t=|UHx, y, t|expiϕHx, y, t,
IHmΔx, nΔy, kΔτ=k-1ΔτkΔτ IHmΔx, nΔy, tdt,

Metrics