Abstract

Based on the idea of measuring small rotation angles with a parallel interference pattern (PIP), a method is developed to measure large rotation angles accurately. Two parallel PIP’s that have different periods are used to measure a rotation angle of an object. The measurement made with a small-period PIP provides a high accuracy, and the measurement made with a large-period PIP provides a wide range. An accurate measurement for wide-range angles is made by combining the two measured values. The accuracy of the phase detection is determined by the periods of two PIP’s. Rotation angles from approximately -30 to 30 arc min can be measured with an accuracy of 0.2 arc sec. Analytical results are supported by experimental results.

© 1997 Optical Society of America

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References

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  1. X. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, “Measurement of small rotation angles by using a parallel interference pattern,” Appl. Opt. 34, 6380–6388 (1995).
    [CrossRef] [PubMed]
  2. J. G. Marzolf, “Angle measuring interferometer,” Rev. Sci. Instrum. 35, 1212–1215 (1964).
    [CrossRef]
  3. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [CrossRef] [PubMed]
  4. T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
    [CrossRef]
  5. P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
    [CrossRef] [PubMed]
  6. P. R. Yoder, E. R. Schlesinger, J. L. Chickvary, “Active annular-beam laser auto-collimator system,” Appl. Opt. 14, 1890–1895 (1975).
    [CrossRef] [PubMed]
  7. F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
    [CrossRef]
  8. P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef] [PubMed]
  9. B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
    [CrossRef]
  10. Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4541 (1984).
    [CrossRef] [PubMed]
  11. O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase-modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
    [CrossRef] [PubMed]
  12. O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
    [CrossRef]

1995 (1)

1992 (2)

P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[CrossRef] [PubMed]

B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
[CrossRef]

1991 (1)

1990 (2)

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

1988 (1)

1984 (1)

1983 (1)

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
[CrossRef]

1975 (1)

1974 (1)

1964 (1)

J. G. Marzolf, “Angle measuring interferometer,” Rev. Sci. Instrum. 35, 1212–1215 (1964).
[CrossRef]

Chapman, G. D.

Cheng, Y. Y.

Chickvary, J. L.

Chitnis, V. T.

B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
[CrossRef]

Dai, X.

Greivenkamp, J. E.

Huang, P. S.

Kamada, O.

Kiyono, S.

Marzolf, J. G.

J. G. Marzolf, “Angle measuring interferometer,” Rev. Sci. Instrum. 35, 1212–1215 (1964).
[CrossRef]

Sasaki, O.

Sasazaki, H.

Schlesinger, E. R.

Schuda, F. J.

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
[CrossRef]

Shi, P.

Singh, B. P.

B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
[CrossRef]

Stijns, E.

Suzuki, T.

Takahashi, K.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Takano, T.

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Varadan, K.

B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
[CrossRef]

Wyant, J. C.

Yoder, P. R.

Yonehara, S.

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Aerosp. Electron. Syst. (1)

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Opt. Eng. (2)

B. P. Singh, K. Varadan, V. T. Chitnis, “Measurement of small angular displacement by a modified moiré technique,” Opt. Eng. 31, 2665–2667 (1992).
[CrossRef]

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Rev. Sci. Instrum. (2)

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
[CrossRef]

J. G. Marzolf, “Angle measuring interferometer,” Rev. Sci. Instrum. 35, 1212–1215 (1964).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

PIP’s of two different periods reflected by an optical surface.

Fig. 2
Fig. 2

Fundamental configuration to measure a rotation angle.

Fig. 3
Fig. 3

Experimental setup; OSC, oscillator.

Fig. 4
Fig. 4

Relationship between the rotation angle and the error in phase detection.

Fig. 5
Fig. 5

Measurement of rotation angles by our method and an autocollimator: (a) measurement results of Nm, (b) measurement results of θ1m.

Fig. 6
Fig. 6

Measurement results of Nm for wide-range rotation angles.

Tables (1)

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Table 1 Measurement Results of Small Rotation Angles

Equations (20)

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S2=mS1,
αi0=αiB-αiA,
d0=nS1+α102πS1,
d0=α202πS2.
α20=2πn+α10m.
tan β=z0/d0,
αi=αib-αia,
d=cosβ-2θcos βd0.
θ=d-d0/2z0.
d=nS1+α1/2πS1,
θ=NS1/2z0+θ1,
θ1=α1-α10S1/4πz0.
σθ1=S12 σ/4πz0,
θ1 max=S12z0.
θ=Nθ1 max+θ1.
θ2=α2-α20S2/4πz0.
N=α2-α20m-α1-α10/2π.
σN=σ2m2+1/2π.
-nNm-n-1.
-mθ1 max/2θmθ1 max/2.

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