Abstract

A simple method is presented for the measurement of in-plane rotation (angle and sign) of an object by use of the conventional in-plane sensitive electronic speckle pattern interferometry technique combined with the two-wavelength laser diode method. The advantage of this method is that it can be used to measure the angle of rotation in a simple way by determination of fringe tilt. The experimental setup is described, and results are presented.

© 1999 Optical Society of America

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References

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  1. C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).
    [CrossRef]
  2. J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Meas. Control 4, 349–354 (1971).
  3. O. J. Lokberg, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16–22 (1980).
    [CrossRef]
  4. O. J. Lokberg, G. A. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), pp. 455–504.
  5. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
    [CrossRef]
  6. Y. Ishii, J. Chen, K. Murata, “Digital phase-measuring interferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 (1987).
    [CrossRef] [PubMed]

1987

1982

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).
[CrossRef]

1980

O. J. Lokberg, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16–22 (1980).
[CrossRef]

1971

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Meas. Control 4, 349–354 (1971).

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Meas. Control 4, 349–354 (1971).

Chen, J.

Ishii, Y.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Meas. Control 4, 349–354 (1971).

Lokberg, O. J.

O. J. Lokberg, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16–22 (1980).
[CrossRef]

O. J. Lokberg, G. A. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), pp. 455–504.

Murata, K.

Slettemoen, G. A.

O. J. Lokberg, G. A. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), pp. 455–504.

Wykes, C.

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Meas. Control

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Meas. Control 4, 349–354 (1971).

Opt. Eng.

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).
[CrossRef]

Opt. Lett.

Phys. Technol.

O. J. Lokberg, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16–22 (1980).
[CrossRef]

Other

O. J. Lokberg, G. A. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), pp. 455–504.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Optical setup for in-plane sensitive ESPI. BS, beam splitter; M’s, mirrors.

Fig. 2
Fig. 2

(a), (b) Tilted two-wavelength fringes when the surface is rotated +0.03° and -0.03°, respectively; (c), (d) horizontal one-wavelength fringes when the surface is rotated +0.03° and -0.03°, respectively.

Fig. 3
Fig. 3

Wrapped phase image obtained with the one-wavelength method. The surface is rotated +0.03°.

Equations (5)

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

I1x, y=I1x, y+I2x, y+2I1I2 cosψ1x, y, ψ1x, y=φs+4πλ1 x sin θ,
I2x, y=I1x, y+I2x, y+2I1I2 cosψ2x, y, ψ2x, y=φs+4πλ2 x sin θ-4πλ2 yΔα sin θ,
ΔIx, ysin2πΔλλ12 x sin θ-2πλ2 yΔα sin θ.
Λ=Λx sin χ=Λy cos χ.
cotχ=ΛxΛy=λ1ΔλΔα.

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