Abstract

We propose a new method for measuring large-object deformations by using temporal evolution of the speckles in speckle interferometry. The principle of the method is that by deforming the object continuously, one obtains fluctuations in the intensity of the speckle. A large number of frames of the object motion are collected to be analyzed later. The phase data for whole-object deformation are then retrieved by inverse Fourier transformation of a filtered spectrum obtained by Fourier transformation of the signal. With this method one is capable of measuring deformations of more than 100 μm, which is not possible using conventional electronic speckle pattern interferometry. We discuss the underlying principle of the method and the results of the experiments. Some nondestructive testing results are also presented.

© 1998 Optical Society of America

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References

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  1. R. K. Erf, Speckle Metrology (Academic, New York, 1978).
  2. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).
  3. R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993).
  4. C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).
  5. Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), p. 55.
  6. C. Joenathan, B. Franze, H. J. Tiziani, “Oblique incidence and observation electronic speckle pattern interferometry,” Appl. Opt. 33, 7307–7311 (1994).
    [CrossRef] [PubMed]
  7. O. J. Lokberg, O. Kwon, “Electronic speckle pattern interferometry using a CO2 laser,” Opt. Laser Technol. 16, 187–192 (1984).
    [CrossRef]
  8. 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]
  9. H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
    [CrossRef]
  10. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse object with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  11. S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1959), p. 293.
  12. H. J. Tiziani, “Optical metrology of engineering surfaces—scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).

1997 (1)

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

1994 (2)

1984 (1)

O. J. Lokberg, O. Kwon, “Electronic speckle pattern interferometry using a CO2 laser,” Opt. Laser Technol. 16, 187–192 (1984).
[CrossRef]

1982 (1)

Erf, R. K.

R. K. Erf, Speckle Metrology (Academic, New York, 1978).

Franze, B.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

C. Joenathan, B. Franze, H. J. Tiziani, “Oblique incidence and observation electronic speckle pattern interferometry,” Appl. Opt. 33, 7307–7311 (1994).
[CrossRef] [PubMed]

Haible, P.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), p. 55.

Ina, H.

Joenathan, C.

C. Joenathan, B. Franze, H. J. Tiziani, “Oblique incidence and observation electronic speckle pattern interferometry,” Appl. Opt. 33, 7307–7311 (1994).
[CrossRef] [PubMed]

C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).

Jones, R.

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

Kobayashi, S.

Kwon, O.

O. J. Lokberg, O. Kwon, “Electronic speckle pattern interferometry using a CO2 laser,” Opt. Laser Technol. 16, 187–192 (1984).
[CrossRef]

Lokberg, O. J.

O. J. Lokberg, O. Kwon, “Electronic speckle pattern interferometry using a CO2 laser,” Opt. Laser Technol. 16, 187–192 (1984).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993).

Takeda, M.

Timoshenko, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1959), p. 293.

Tiziani, H.

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Tiziani, H. J.

C. Joenathan, B. Franze, H. J. Tiziani, “Oblique incidence and observation electronic speckle pattern interferometry,” Appl. Opt. 33, 7307–7311 (1994).
[CrossRef] [PubMed]

H. J. Tiziani, “Optical metrology of engineering surfaces—scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).

Woinowsky-Krieger, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1959), p. 293.

Wykes, C.

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

Yamamoto, H.

Appl. Opt. (2)

J. Mod. Opt. (1)

H. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Laser Technol. (1)

O. J. Lokberg, O. Kwon, “Electronic speckle pattern interferometry using a CO2 laser,” Opt. Laser Technol. 16, 187–192 (1984).
[CrossRef]

Other (7)

R. K. Erf, Speckle Metrology (Academic, New York, 1978).

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

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993).

C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), p. 55.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, New York, 1959), p. 293.

H. J. Tiziani, “Optical metrology of engineering surfaces—scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, 1997).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the experimental arrangement of the temporal Fourier-transform speckle interferometric method.

Fig. 2
Fig. 2

Experimental results with the aluminum plate tilted: (a) Slice of one horizontal line of pixel from each frame stacked together. Only 600 of the 1024 frames are shown to depict the speckle modulation and the correlation. (b) Intensity fluctuation of one speckle as a function of time. (c) Fourier transformation of the temporal signal shown in (b). (d) Inverse Fourier transform of the filtered spectrum. The phase fluctuates between -π and +π, and only 100 frames are shown for clarity.

Fig. 3
Fig. 3

Data processed by Fourier-transform techniques with no filter for smoothing the random noise: (a) 3-D plot of a small section of the object that was tilted by 0.28 deg. The dotted line shows the region of a slice taken for (b). (b) Slice along the 3-D plot showing the tilt. Displacement of the object at one end is 28 μm, and at the other it is 36 μm.

Fig. 4
Fig. 4

Results with the plate bending ∼80 μm in the direction of observation: (a) 3-D plot of the deformation obtained with FFT procedures with no filter used to smooth the data. The dotted line shows the slice region taken for (b). (b) Arbitrary slice along the 3-D plot showing the plate bending.

Fig. 5
Fig. 5

Results for the circular diaphragm clamped along the edges and loaded at the center. The center of the diaphragm is loaded to 126 μm: (a) 3-D plot of the deformation of the diaphragm; (b) contour plot of the deformation clearly showing a defect at one edge. The defect was later determined to be the airgap between the retroreflective tape and the diaphragm.

Fig. 6
Fig. 6

Different section of the diaphragm with many airgaps. The object was again deformed to 126 μm: (a) 3-D plot of the deformation; (b) contour plots showing the deviation caused by defects.

Fig. 7
Fig. 7

Results with a rubber diaphragm uniformly pressure loaded. The object was loaded to 70 μm at the center. The data were filtered with a spike-removing filter of 5 × 5, which eliminated 0.1% of the pixels. Finally a low-pass filter with a kernel of 5 × 5 was used: (a) 3-D plot; (b) contour plot of the slices showing the deviation of the lines around the defect.

Equations (5)

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I x ,   y ,   t = I 0 x ,   y 1 + V   cos Φ 0 x ,   y + 4 π Z x ,   y ,   t λ ,
f med x ,   y = 2 Δ Z x ,   y ,   t λ t .
Φ x ,   y = Φ 0 x ,   y + 4 π Δ Z x ,   y λ ,
D = 4 λ α 2 ,
I x ,   y ,   t = I 0 x ,   y 1 + V   cos ϕ x ,   y + 4 π Z 0 t λ + 4 π Z x ,   y ,   t λ ,

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