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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Rohlin, “An interferometer for precision angle measurement,” Appl. Opt. 2, 762–763 (1963).
    [CrossRef]
  2. D. Malacara, O. Harris, “Interferometric measurement of angles,” Appl. Opt. 9, 1630–1633 (1970).
    [CrossRef] [PubMed]
  3. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [CrossRef] [PubMed]
  4. R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J.34, 3–13 (1983).
  5. P. Shi, E. Stijns, “New optical methods for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
    [CrossRef] [PubMed]
  6. T. Takano, S. Yonehara, “Basic investigations on an angle-measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
    [CrossRef]
  7. P. 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. P. R. Yoder, E. R. Schlesinger, J. L. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
    [CrossRef] [PubMed]
  9. L. D. Hutcheson, “Practical electro-optic deflection measurements system,” Opt. Eng. 15, 61–63 (1976).
  10. 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]
  11. F. J. Schuda, “High-precision, wide-range, dual-axis, angle-monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
    [CrossRef]
  12. G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
    [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).
  15. 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]
  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

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]

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).

1990

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

1984

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

1983

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

1982

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

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

1975

1974

1970

1963

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.

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]

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, “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.

ASME J. Eng. Ind.

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.

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.

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

Precis. Eng.

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.

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

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).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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 ,

Metrics