Abstract

We describe a new method for angle measurement based on the internal-reflection effect and heterodyne interferometry. A novel prism assembly is designed that can always parallel retroreflect the incoming light beams so the optical configuration is compact. As a differential common-path optical configuration is integrated into the design, the linearity of the method is greatly improved. Details of theoretical analysis of the method and experimental verification of the principle are presented. The resolution can be better than 0.3 arc sec. The experimental results and further improvements of the proposed method are also addressed.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  7. Pan Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 44–51 (1993).
    [CrossRef] [PubMed]
  8. G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
    [CrossRef]
  9. T. Takano, S. Yonehara, “Basic investigation on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
    [CrossRef]
  10. Renishaw Laser Measurement System Users’ Manual, PC 10 version (Renishaw Transducer Systems, Limited, Old Town, Wotton-under-Edge, Gloucestershire GL12 7DH, UK, 1988).
  11. Laser and optics users’ manuals (Hewlett-Packard Company, 5301 Stevens Creek Boulevard, Santa Clara, Calif., 1996).
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    [CrossRef] [PubMed]
  15. M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
    [CrossRef]
  16. M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

1997 (2)

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

1996 (1)

1995 (1)

1993 (1)

1992 (1)

1990 (1)

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

1988 (1)

1984 (1)

G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

1983 (1)

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

1975 (1)

1974 (1)

1970 (1)

1963 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

Chapman, G. D.

Chickvary, J. L.

Chiu, M.-H.

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

Deslattes, R. D.

G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Harris,

Huang, P. S.

Kamada, O.

Kiyono, S.

Luther, G. G.

G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Malacara, D.

Ni, J.

Rohlin, J.

Schlesinger, E. R.

Shi, Pan

Shuda, F. J.

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

Stijns, E.

Su, D.-C.

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

M.-H. Chiu, D.-C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[CrossRef]

Takano, T.

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

Towler, W. R.

G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

Yoder, P. R.

Yonehara, S.

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

Appl. Opt. (10)

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

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

Opt. Eng. (1)

M.-H. Chiu, D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

Rev. Sci. Instrum. (2)

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

G. G. Luther, R. D. Deslattes, W. R. Towler, “Single axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Other (3)

Renishaw Laser Measurement System Users’ Manual, PC 10 version (Renishaw Transducer Systems, Limited, Old Town, Wotton-under-Edge, Gloucestershire GL12 7DH, UK, 1988).

Laser and optics users’ manuals (Hewlett-Packard Company, 5301 Stevens Creek Boulevard, Santa Clara, Calif., 1996).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 47–50.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the prism assembly.

Fig. 2
Fig. 2

Optical path difference introduced by the rotation of a glass plate.

Fig. 3
Fig. 3

Theoretical curve of φ versus θ.

Fig. 4
Fig. 4

Curves of sensitivity k and measurement range θMax versus refractive index n.

Fig. 5
Fig. 5

Schematic diagram of the experiment setup.

Fig. 6
Fig. 6

Experimental setup for angle measurement.

Fig. 7
Fig. 7

Details of the prism assembly.

Fig. 8
Fig. 8

Experimental curve of φ versus θ.

Equations (16)

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θ i 1 = π / 4 + sin - 1 sin   θ n ,
θ i 2 = π / 4 - sin - 1 sin   θ n ,
φ = φ 0 + 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 1 n 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 1 n 2 cos   θ i 2 + 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 cos   θ i 2 + Δ φ ,
OPD = n AC ¯ - n AB ¯ - BE ¯ ,
AB ¯ = t , AC ¯ = t 1 - 1 n 2 sin 2   θ 1 / 2 , BE ¯ = AC ¯ cos θ - θ - t , sin   θ = n   sin   θ .
OPD θ = n 2 t - t   cos   θ n 2 - sin 2   θ 1 / 2 - t   sin 2   θ n 2 - sin 2   θ 1 / 2 - n - 1 t ,
Δ φ = 2 π λ Δ f f OPD θ = n 2 t - t   cos   θ n 2 - sin 2   θ 1 / 2 - t   sin 2   θ n 2 - sin 2   θ 1 / 2 - n - 1 t Δ f f 2 π λ ,
φ = φ 0 + 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 1 n 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 1 n 2 cos   θ i 2 + 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 cos   θ i 2 + n 2 t - t   cos   θ n 2 - sin 2   θ 1 / 2 - t   sin 2   θ n 2 - sin 2   θ 1 / 2 - n - 1 t Δ f f 2 π λ .
φ = 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 1 n 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 1 n 2 cos   θ i 2 + 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 cos   θ i 2 .
θ Max = sin - 1 n   sin π 4 - sin - 1 1 n .
Δ φ = Δ f f 2 π λ   t   n - 1 n θ 2 2 .
φ = φ 0 + 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 1 n 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 1 - 1 n 2 1 / 2 cos   θ i 1 - 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 1 n 2 cos   θ i 2 + 2   tan - 1 - sin 2   θ i 2 - 1 n 2 1 / 2 cos   θ i 2 .
φ θ = φ 0 + φ 0 + φ 0 θ + 1 / 2 ! φ 0 θ 2 + 1 / 3 ! φ 0 θ 3 + ,
φ 0 = 0 , φ 0 = 4 3 - n 2 n 2 - 1 n 2 - 2 .
φ θ φ 0 + φ 0 + φ 0 θ = φ 0 + 4 3 - n 2 n 2 - 1 n 2 - 2   θ = φ 0 + k θ ,
k = 4 3 - n 2 n 2 - 1 n 2 - 2 ,

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