Abstract

A new development in angle measurement based on the internal-reflection effect (AMIRE) is described in which a pair of right-angle prisms is used to replace the previously used elongated critical-angle prisms, resulting in lower costs and a more compact size. Excellent linearity is achieved through careful alignment of the right-angle prisms. The measurement sensitivity and range can be selected through the use of light sources with different polarization states. Experiments with a prototype sensor demonstrated a measurement range of 1.6°, a resolution of 0.04 arcsec, and a nonlinearity error of ±0.1%. Both analytical and experimental results are presented.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).
  14. J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).
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    [CrossRef] [PubMed]
  16. P. S. Huang, “Laser optical measurement systems and their application to the on-line error compensation of coordinate measuring machines,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1993), pp. 131–135.
    [PubMed]

1993 (1)

1992 (2)

J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).

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]

1990 (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]

1988 (1)

1984 (1)

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

1983 (1)

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

1982 (1)

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[CrossRef]

1976 (1)

L. D. Hutcheson, “Practical electro-optic deflection measurements system,” Opt. Eng. 15, 61–63 (1976).

1975 (1)

1974 (1)

1970 (1)

1963 (1)

Chapman, G. D.

Chickvary, J. L.

Deslattes, R. D.

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

Duis, W.

W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).

Ennos, A. E.

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[CrossRef]

Harris, O.

Huang, P. S.

J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).

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]

P. S. Huang, “Laser optical measurement systems and their application to the on-line error compensation of coordinate measuring machines,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1993), pp. 131–135.
[PubMed]

Hutcheson, L. D.

L. D. Hutcheson, “Practical electro-optic deflection measurements system,” Opt. Eng. 15, 61–63 (1976).

Kamada, O.

Kiyono, S.

Luther, G. G.

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

Malacara, D.

Mross, M.

W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).

Ni, J.

J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).

Quenelle, R. C.

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J.34, 3–13 (1983).

Rohlin, J.

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.

Stijns, E.

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]

Trede, J.

W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).

Ulbrich, G.-J.

W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).

Virdee, M. S.

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[CrossRef]

Wu, S. M.

J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).

Wuerz, L. J.

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J.34, 3–13 (1983).

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)

ASME J. Eng. Ind. (1)

J. Ni, P. S. Huang, S. M. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” ASME J. Eng. Ind. 114, 362–369 (1992).

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. (1)

L. D. Hutcheson, “Practical electro-optic deflection measurements system,” Opt. Eng. 15, 61–63 (1976).

Precis. Eng. (1)

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[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]

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

Other (3)

W. Duis, J. Trede, G.-J. Ulbrich, M. Mross, “Design and performance of a high-resolution, high-accuracy automatic autocollimator,” in Precision Engineering and Optomechanics, D. Vakobratovich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1167, 297–304 (1989).

P. S. Huang, “Laser optical measurement systems and their application to the on-line error compensation of coordinate measuring machines,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1993), pp. 131–135.
[PubMed]

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J.34, 3–13 (1983).

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Figures (9)

Fig. 1
Fig. 1

Light traversing through a right-angle prism.

Fig. 2
Fig. 2

Optical layout of AMIRE with a pair of right-angle prisms.

Fig. 3
Fig. 3

Nonlinearity error plotted versus the initial angle of incidence.

Fig. 4
Fig. 4

Linearized reflectance plotted versus the angular displacement when θ0 is at the optimal angle.

Fig. 5
Fig. 5

Experimental setup for sensor calibration.

Fig. 6
Fig. 6

Sensor-calibration results (filled and open circles) compared with the theoretical calculations (solid curve).

Fig. 7
Fig. 7

Dependence of the angle sensitivity of the beam splitter on the angular displacement of the incident beams Ii1 and Ii2.

Fig. 8
Fig. 8

Noise-and-drift results of the sensor output over time.

Fig. 9
Fig. 9

Long-term drift of the sensor output.

Tables (1)

Tables Icon

Table 1 Optimal Angles, Measurement Sensitivities, and Measurement Ranges for the AMIRE

Equations (9)

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

R 1 = [ tan ( θ 1 - θ 2 ) tan ( θ 1 + θ 2 ) ] 2 ,
R 2 = [ tan ( θ 3 - θ 4 ) tan ( θ 3 + θ 4 ) ] 2 ,
R 3 = [ tan ( θ 5 - θ 6 ) tan ( θ 5 + θ 6 ) ] 2 ,
R = ( 1 - R 1 ) R 2 ( 1 - R 3 ) = ( 1 - R 1 ) 2 R 2 .
R l ( Δ θ ) = R ( Δ θ ) - R ( - Δ θ ) R ( Δ θ ) + R ( - Δ θ ) ,
R ( Δ θ ) = I 1 / I i ,
R ( - Δ θ ) = I 2 / I i ,
R l ( Δ θ ) = I 1 - I 2 I 1 + I 2 .
R l ( Δ θ ) = I 1 / I i 1 - I 2 / I i 2 I 1 / I i 1 + I 2 / I i 2 ,

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