Abstract

We outline a novel method for determining the shape of an object by use of temporal Fourier-transform analysis in dual-beam illumination speckle interferometry. The object whose shape is to be determined is rotated about an axis, and a number of frames of the image of the object motion are acquired. Temporal in-plane displacement that is due to the object rotation is related to the shape of the object and is retrieved from this large set of data by Fourier transformation. With this method one can determine the absolute height of the object with variable resolution, thereby allowing shapes of objects with large and small slopes to be determined. The theory of the method along with experimental results is 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 (Dekker, New York, 1993).
  4. C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Methods for Testing, P. Rastogi, ed. (Artech House, London, 1997).
  5. 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]
  6. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of a diffuse object with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  7. S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
    [CrossRef] [PubMed]
  8. A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 327–332 (1988).
    [CrossRef]
  9. C. Joenathan, B. Pfister, H. J. Tiziani, “Contouring by electronic speckle pattern interferometry using dual beam illumination,” Appl. Opt. 29, 1905–1911 (1990).
    [CrossRef] [PubMed]
  10. 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]

1998 (1)

1997 (2)

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]

S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
[CrossRef] [PubMed]

1994 (1)

1990 (1)

Erf, R. K.

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

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]

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]

Ganesan, A. R.

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 327–332 (1988).
[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]

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]

Joenathan, C.

Jones, R.

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

Kuwamura, S.

Pfister, B.

Sirohi, R. S.

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

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 327–332 (1988).
[CrossRef]

Takeda, M.

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.

Wykes, C.

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

Yamaguchi, I.

Yamamoto, H.

Appl. Opt. (4)

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]

Other (5)

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. SPIE954, 327–332 (1988).
[CrossRef]

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 (Dekker, New York, 1993).

C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Methods for Testing, P. Rastogi, ed. (Artech House, London, 1997).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental arrangement of the Fourier-transform dual-beam speckle interferometric method for shape measurement. BS, beam splitter.

Fig. 2
Fig. 2

Schematic of the geometry of the in-plane motion and its relation to the height of the object.

Fig. 3
Fig. 3

The sign of the shape measurement depends on the location of the object: (a) The object is located in front of TP(0). (b) the reconstructed shape of the object that matches the object shape. (c) The object is located behind TP(0). (d) The reconstructed shape is reversed.

Fig. 4
Fig. 4

Experimental results with the flat plate inclined by 10 deg. (a) Slice of one horizontal line of pixel from each frame stacked together. (b) Two-dimensional Fourier transform of these data, showing that the frequency of the pixel intensity modulation generated is different because of the change in the height of the object point with respect to the tilt plane.

Fig. 5
Fig. 5

Results obtained for an object with step heights of 0.2, 0.4, and 0.8 mm. The top surface is inclined by 8.1 deg. The object was tilted at a rate of 0.1 deg/s and the placed 5.0 mm from TP(0). (a) 3-D plot of the three steps measured, showing the tilting of the object. (b) Slice showing the step height. The angle measured at the top was 8.0 deg.

Fig. 6
Fig. 6

Results obtained for a pyramid-shaped object. The object was rotated at a rate of 0.1 deg/s. The data were filtered with a 3 × 3 low-pass filter. (a) 3-D plot obtained for this object. (b) Contour plot generated from the 3-D plot.

Fig. 7
Fig. 7

3-D plot for a U.S. 25¢ coin placed at 4.0 mm in front of TP(0) and rotated at a rate of 0.4 deg/s. The size of observation is 23 mm × 17 mm. The data are filtered twice with a low-pass filter of kernel of 3 × 3.

Fig. 8
Fig. 8

Results for a bolt of dimension M12 placed at the tilt plane and rotated at a rate of 0.2 deg/s. The 3-D plot shown here is only spike filtered.

Equations (6)

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I x ,   y ,   t = I 0 x ,   y 1 + V   cos Φ 0 x ,   y + 2 π λ 2 U x ,   y ,   t sin   θ 1 .
f med x ,   y ,   t = 2 U x ,   y ,   t sin   θ λ t .
Φ x ,   y = 4 π U x ,   y sin   θ λ .
U x ,   y = 2 h x ,   y sin ω / 2 cos α x ,   y + ω / 2 cos α x ,   y .
h x ,   y Φ x ,   y λ 8 π   sin ω / 2 sin   θ .
N max = 2 σ   sin   θ λ .

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