Abstract

A new method of angle measurement based on the internal reflection effect is proposed that uses a single right-angle prism. We measure the angular displacement between a laser beam and the prism by detecting the changes in reflectance as a function of the angle of incidence. We achieve high linearity of measurement by taking the inverse of reflectance as the output. The inverse of reflectance is obtained from the intensities of the reflected and the transmitted beams measured by two photodiodes. Experiments with a prototype device have demonstrated that angle measurement with a range of ±500 arc sec, a nonlinearity error of ±0.1%, and a resolution of 0.1 arc sec can be readily achieved. The measurement range can be further increased with some sacrifice of linearity.

© 1998 Optical Society of America

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References

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    [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).
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    [CrossRef]
  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).
    [PubMed]
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    [CrossRef] [PubMed]
  9. L. D. Hutcheson, “Practical electro-optic deflection measurements system,” Opt. Eng. 15, 61–63 (1976).
    [CrossRef]
  10. A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 4, 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. SPIE1167, 297–304 (1989).
    [CrossRef]
  14. 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]
  15. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
    [CrossRef] [PubMed]
  16. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef] [PubMed]
  17. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and its application in measurement of geometric errors of machine tools,” presented at the American Society for Precision Engineering Annual Meeting, Seattle, Wash., 7–12 November 1993.
  18. P. S. Huang, X. Xu, “Optical probe for surface profiling of aspherical mirrors,” presented at the American Society for Precision Engineering Annual Meeting, Austin, Tex., 15–20 October 1995.

1996 (1)

1995 (1)

1993 (1)

1992 (1)

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 (2)

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

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

1982 (1)

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 4, 5–8 (1982).
[CrossRef]

1976 (1)

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

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. SPIE1167, 297–304 (1989).
[CrossRef]

Ennos, A. E.

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 4, 5–8 (1982).
[CrossRef]

Harris, O.

Huang, P. S.

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef] [PubMed]

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
[CrossRef] [PubMed]

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, J. Ni, “Angle measurement based on the internal-reflection effect and its application in measurement of geometric errors of machine tools,” presented at the American Society for Precision Engineering Annual Meeting, Seattle, Wash., 7–12 November 1993.

P. S. Huang, X. Xu, “Optical probe for surface profiling of aspherical mirrors,” presented at the American Society for Precision Engineering Annual Meeting, Austin, Tex., 15–20 October 1995.

Hutcheson, L. D.

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

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. SPIE1167, 297–304 (1989).
[CrossRef]

Ni, J.

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef] [PubMed]

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
[CrossRef] [PubMed]

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and its application in measurement of geometric errors of machine tools,” presented at the American Society for Precision Engineering Annual Meeting, Seattle, Wash., 7–12 November 1993.

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, Pan

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. SPIE1167, 297–304 (1989).
[CrossRef]

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. SPIE1167, 297–304 (1989).
[CrossRef]

Virdee, M. S.

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 4, 5–8 (1982).
[CrossRef]

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).

Xu, X.

P. S. Huang, X. Xu, “Optical probe for surface profiling of aspherical mirrors,” presented at the American Society for Precision Engineering Annual Meeting, Austin, Tex., 15–20 October 1995.

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. (9)

Hewlett-Packard J. (1)

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

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).
[CrossRef]

Precis. Eng. (1)

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation,” Precis. Eng. 4, 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. SPIE1167, 297–304 (1989).
[CrossRef]

P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect and its application in measurement of geometric errors of machine tools,” presented at the American Society for Precision Engineering Annual Meeting, Seattle, Wash., 7–12 November 1993.

P. S. Huang, X. Xu, “Optical probe for surface profiling of aspherical mirrors,” presented at the American Society for Precision Engineering Annual Meeting, Austin, Tex., 15–20 October 1995.

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Figures (10)

Fig. 1
Fig. 1

Inverse of reflectance versus the angle of incidence for s-polarized light.

Fig. 2
Fig. 2

Inverse of reflectance versus the angle of incidence for p-polarized light.

Fig. 3
Fig. 3

First derivative of the inverse of reflectance with respect to the angle of incidence for s-polarized light.

Fig. 4
Fig. 4

First derivative of the inverse of reflectance with respect to the angle of incidence for p-polarized light.

Fig. 5
Fig. 5

Inverse of reflectance and nonlinearity error versus the angle of incidence for p-polarized light. Optimal initial angle, θ0 = 41.028°.

Fig. 6
Fig. 6

Optical layout of the prototype sensor.

Fig. 7
Fig. 7

Electronic circuit for signal processing.

Fig. 8
Fig. 8

Calibration results.

Fig. 9
Fig. 9

Residuals of linear regression analysis on the calibration curve.

Fig. 10
Fig. 10

Noise and drift of the sensor output.

Tables (1)

Tables Icon

Table 1 Optimal Initial Angle, Measurement Range, and Sensitivity

Equations (18)

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

R s = sin θ i - θ t sin θ i + θ t 2 ,
R p = tan θ i - θ t tan θ i + θ t 2 ,
d R s d θ i = 4   tan   θ t R s
d 1 / R s d θ i = - 4   tan   θ t R s .
d R p d θ i = 4   tan   θ t u R p ,
d 1 / R p d θ i = - 4   tan   θ t uR p ,
u = - cos θ i - θ t cos θ i + θ t .
d 2 1 / R s d θ i 2 = 4 - n i   cos   θ i   sec 3   θ t + 4   tan 2   θ t / R s ,
d 2 1 / R p d θ i 2 = 4 u 2 - n i u   cos   θ i   sec 3   θ t + 1 + n i 2 × sin   2 θ i   tan   θ t + 4   tan 2   θ t / R p .
I r = 1 - R 1 1 - R 3 R 2 I i = 1 - R 1 2 R 2 I i ,
I t = 1 - R 1 1 - R 2 I i ,
R = I r I i I r I r + I t = 1 - R 1 1 - R 2 R 1 R 2 R 2 .
S = I i I r I r + I t I r = 1 + I t I r .
θ t = arc   sin 1.51377   sin   41.028 ° = 83.555 ° ,
S 0 = 1 R p = tan θ i + θ t tan θ i - θ t 2 = 2.501 ,
Δ S = S - S 0 = 1 + I t I r - 2.501 = I t I r - 1.501 .
W = 10 Z 2 - Z 1 X 1 - X 2 + Y 1 ,
W = 5 I t / I r - 7.505 ,

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