Abstract

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.

© 1997 Optical Society of America

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References

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  1. A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
    [CrossRef]
  2. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  3. 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]
  4. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  5. J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
    [CrossRef]
  6. T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
    [CrossRef]
  7. P. Hariharan, B. F. Oreb, N. Brown, “Real-time holographic interferometry: a microcomputer system for the measurement of vector displacement,” Appl. Opt. 22, 876–880 (1983).
    [CrossRef]
  8. A. A. M. Maas, H. A. Vrooman, “In-plane strain measurement by digital shifting speckle interferometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. SPIE1162, 248–256 (1989).
    [CrossRef]
  9. A. J. Moore, J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane displacement measurement,” Meas. Sci. Technol. 1, 1024–1030 (1990).
    [CrossRef]
  10. G. Pedrini, H. J. Tiziani, “Double-pulse electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
    [CrossRef] [PubMed]
  11. R. Arizaga, H. Rabal, M. Trivi, “Simultaneous multiple-viewpoint processing in digital speckle pattern interferometry,” Appl. Opt. 33, 4369–4372 (1994).
    [CrossRef] [PubMed]
  12. See, for example, T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
    [CrossRef]
  13. J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 246–257 (1995).
    [CrossRef]
  14. T. Yoshimura, M. Zhou, K. Yamahai, Z. Liyan, “Optimum determination of speckle size to be used in electronic speckle pattern interferometry,” Appl. Opt. 34, 87–91 (1995).
    [CrossRef] [PubMed]

1995 (1)

1994 (3)

1990 (1)

A. J. Moore, J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane displacement measurement,” Meas. Sci. Technol. 1, 1024–1030 (1990).
[CrossRef]

1989 (1)

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

1985 (1)

1983 (1)

1982 (1)

Arizaga, R.

Brown, N.

Bryanston-Cross, P. J.

See, for example, T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Creath, K.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
[CrossRef]

Fairman, P. S.

T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
[CrossRef]

Farrant, D. I.

T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
[CrossRef]

Field, J. E.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

Hariharan, P.

Huntley, J. M.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 246–257 (1995).
[CrossRef]

Ina, H.

Judge, T. R.

See, for example, T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Kobayashi, S.

Liyan, Z.

Maas, A. A. M.

A. A. M. Maas, H. A. Vrooman, “In-plane strain measurement by digital shifting speckle interferometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. SPIE1162, 248–256 (1989).
[CrossRef]

Moore, A. J.

A. J. Moore, J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane displacement measurement,” Meas. Sci. Technol. 1, 1024–1030 (1990).
[CrossRef]

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, “Real-time holographic interferometry: a microcomputer system for the measurement of vector displacement,” Appl. Opt. 22, 876–880 (1983).
[CrossRef]

T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
[CrossRef]

Pedrini, G.

Rabal, H.

Takatsuji, T.

T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
[CrossRef]

Takeda, M.

Tiziani, H. J.

Trivi, M.

Tyrer, J. R.

A. J. Moore, J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane displacement measurement,” Meas. Sci. Technol. 1, 1024–1030 (1990).
[CrossRef]

Vest, C. M.

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

Vrooman, H. A.

A. A. M. Maas, H. A. Vrooman, “In-plane strain measurement by digital shifting speckle interferometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. SPIE1162, 248–256 (1989).
[CrossRef]

Yamahai, K.

Yoshimura, T.

Zhou, M.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

A. J. Moore, J. R. Tyrer, “An electronic speckle pattern interferometer for complete in-plane displacement measurement,” Meas. Sci. Technol. 1, 1024–1030 (1990).
[CrossRef]

Opt. Eng. (1)

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

Opt. Lasers Eng. (1)

See, for example, T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Other (5)

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 246–257 (1995).
[CrossRef]

T. Takatsuji, B. F. Oreb, D. I. Farrant, P. S. Fairman, “Simultaneous measurement of vector components of displacement by ESPI and FFT techniques,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 309–316 (1995).
[CrossRef]

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

A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
[CrossRef]

A. A. M. Maas, H. A. Vrooman, “In-plane strain measurement by digital shifting speckle interferometry,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputniewicz, ed., Proc. SPIE1162, 248–256 (1989).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Optical configuration of the experiment. Object beams HP, HN, and V illuminate the object at angles θHP, θHN, and θV, respectively, with respect to the Z axis. The scattered light is combined with the reference beam (R) through the beam splitter (BS) and captured with the CCD TV camera (TVC). s HP, s HN, and s V are the sensitivity vectors of the interferometer composed of HP and R beams, HN and R beams, and HN and R beams, respectively; t HP, t HN, and t V are the directions of tilt of the object beams to generate carrier fringes.

Fig. 2
Fig. 2

Schematic diagram of the measured metallic object; three-dimensional deformation is created by hanging a weight and inserting a wedge.

Fig. 3
Fig. 3

(a) Difference of the speckle image between the tilted and untilted beams for the undeformed object. Straight carrier fringes are created. (b) Schematic drawing of (a); the bottom legend indicates the directions of the interference fringes, and the asterisk denotes the undesirable interference fringes that were created by the interference of HP and HN object beams. (c) Modulated carrier fringes.

Fig. 4
Fig. 4

(a) Fourier transformed image of the interferogram shown in Fig. 3(a). The central 128 × 128 pixels are shown. (b) Schematic drawing of 4(a), showing the correspondence of each interferometer to the peak in the Fourier plane. Each gray box shows the mask used to extract the peak inside the box. Signs correspond to those used in Fig. 3(b). (c) Fourier transformed image of the interferogram shown in Fig. 3(c). The central 128 × 128 pixels are shown.

Fig. 5
Fig. 5

Displacement maps in the (a) X, (b) Y, (c) Z directions are rewrapped in the range 0–0.129 µm to facilitate observation. The central 384 × 384 pixels corresponding to 13.5 (X) mm × 14.3 (Y) mm are shown.

Fig. 6
Fig. 6

Three-dimensional perspective displacement map, composed of the three phase maps shown in Fig. 5. The unit of the length of the displacement vectors is arbitrary and an offset was added to each component of the displacement vector.

Fig. 7
Fig. 7

Displacement measurement error in each direction is plotted against the ratio of the speckle size to the pixel size. Bars and symbols represent the range and the mean of the measured values; RMS, root-mean-square.

Equations (6)

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

s=s1-s2.
ϕ=2πs·D/λ,
ϕVϕHPϕHN=2πSλ · dXdYdZ,
S=rXrY-sin θVrZ+cos θVrX+sin θHPrYrZ+cos θHPrX-sin θHNrYrZ+cos θHN,
S=0-1/21+1/21/201+1/2-1/201+1/2.
σs=1.21+MλF,

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