Abstract

A novel angular probe using the Fabry-Perot etalon and angular scanning technique is proposed for absolute angular displacement determinations in this paper. The measurement theory is first derived, a setup constructed to implement the angular probe is then introduced and analyzed, and the experimental results from the uses of the setup are finally presented. The setup analyses reveal that the probe is with high measurement resolution and sensitivity. The experimental results not only confirm the validity, stability, accuracy, and repeatability, but also show an application of the angular probe.

©2010 Optical Society of America

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References

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  1. D. Malacara, Optical shop testing (John Wily & Sons, 1978), Chap. 15.
  2. F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54(12), 1648–1652 (1983).
    [Crossref]
  3. P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34(22), 4976–4981 (1995).
    [Crossref] [PubMed]
  4. P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35(13), 2239–2241 (1996).
    [Crossref] [PubMed]
  5. M. H. Chiu and D. C. Su, “Angle measurement using total-internal reflection heterodyne interferometry,” Opt. Eng. 36(6), 1750–1753 (1997).
    [Crossref]
  6. M. H. Chiu and D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36(28), 7104–7106 (1997).
    [Crossref]
  7. W. Zhou and L. Cai, “Interferometer for small-angle measurement based on total internal reflection,” Appl. Opt. 37(25), 5957–5963 (1998).
    [Crossref]
  8. P. S. Huang and Y. Li, “Small-angle measurement by use of a single prism,” Appl. Opt. 37(28), 6636–6642 (1998).
    [Crossref]
  9. W. Zhou and L. Cai, “Improved angle interferometer based on total internal reflection,” Appl. Opt. 38(7), 1179–1185 (1999).
    [Crossref]
  10. A. Zhang and P. S. Huang, “Total internal reflection for precision small-angle measurement,” Appl. Opt. 40(10), 1617–1622 (2001).
    [Crossref]
  11. M. H. Chiu, S. F. Wang, and R. S. Chang, “Instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry,” Appl. Opt. 43(29), 5438–5442 (2004).
    [Crossref] [PubMed]
  12. G. Margheri, A. Mannoni, and F. Quercioli, “High-resolution angular and displacement sensing based on the excitation of surface plasma waves,” Appl. Opt. 36(19), 4521–4525 (1997).
    [Crossref] [PubMed]
  13. F. Chen, Z. Cao, Q. Shen, and Y. Feng, “Optical approach to angular displacement measurement based on attenuated total reflection,” Appl. Opt. 44(26), 5393–5397 (2005).
    [Crossref] [PubMed]
  14. S. T. Lin and W. J. Syu, “Heterodyne Angular Interferometer Using a Square Prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
    [Crossref]
  15. Agilent 5529A Dynamic Calibrator: http://cp.literature.agilent.com/litweb/pdf/5968-0111E.pdf .
  16. S. T. Lin, S. L. Yeh, and C. W. Chang, “Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique,” Opt. Lett. 33(20), 2344–2346 (2008).
    [Crossref] [PubMed]
  17. S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
    [Crossref]
  18. E. Hecht, Optics (Addison Wesley, 4th ed.), Chap. 9.

2009 (1)

S. T. Lin and W. J. Syu, “Heterodyne Angular Interferometer Using a Square Prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

2008 (2)

S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
[Crossref]

S. T. Lin, S. L. Yeh, and C. W. Chang, “Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique,” Opt. Lett. 33(20), 2344–2346 (2008).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2001 (1)

1999 (1)

1998 (2)

1997 (3)

1996 (1)

1995 (1)

1983 (1)

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54(12), 1648–1652 (1983).
[Crossref]

Cai, L.

Cao, Z.

Chang, C. W.

S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
[Crossref]

S. T. Lin, S. L. Yeh, and C. W. Chang, “Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique,” Opt. Lett. 33(20), 2344–2346 (2008).
[Crossref] [PubMed]

Chang, R. S.

Chen, F.

Chiu, M. H.

Feng, Y.

Huang, P. S.

Li, Y.

Lin, S. T.

S. T. Lin and W. J. Syu, “Heterodyne Angular Interferometer Using a Square Prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
[Crossref]

S. T. Lin, S. L. Yeh, and C. W. Chang, “Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique,” Opt. Lett. 33(20), 2344–2346 (2008).
[Crossref] [PubMed]

Mannoni, A.

Margheri, G.

Ni, J.

Quercioli, F.

Schuda, F. J.

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54(12), 1648–1652 (1983).
[Crossref]

Shen, Q.

Su, D. C.

M. H. Chiu and D. C. Su, “Angle measurement using total-internal reflection heterodyne interferometry,” Opt. Eng. 36(6), 1750–1753 (1997).
[Crossref]

M. H. Chiu and D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36(28), 7104–7106 (1997).
[Crossref]

Syu, W. J.

S. T. Lin and W. J. Syu, “Heterodyne Angular Interferometer Using a Square Prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

Wang, S. F.

Yeh, S. L.

S. T. Lin, S. L. Yeh, and C. W. Chang, “Low-coherent light-source angular interferometer using a square prism and the angular-scanning technique,” Opt. Lett. 33(20), 2344–2346 (2008).
[Crossref] [PubMed]

S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
[Crossref]

Zhang, A.

Zhou, W.

Appl. Opt. (10)

G. Margheri, A. Mannoni, and F. Quercioli, “High-resolution angular and displacement sensing based on the excitation of surface plasma waves,” Appl. Opt. 36(19), 4521–4525 (1997).
[Crossref] [PubMed]

M. H. Chiu and D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36(28), 7104–7106 (1997).
[Crossref]

W. Zhou and L. Cai, “Interferometer for small-angle measurement based on total internal reflection,” Appl. Opt. 37(25), 5957–5963 (1998).
[Crossref]

P. S. Huang and Y. Li, “Small-angle measurement by use of a single prism,” Appl. Opt. 37(28), 6636–6642 (1998).
[Crossref]

W. Zhou and L. Cai, “Improved angle interferometer based on total internal reflection,” Appl. Opt. 38(7), 1179–1185 (1999).
[Crossref]

P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect and the use of right-angle prisms,” Appl. Opt. 34(22), 4976–4981 (1995).
[Crossref] [PubMed]

P. S. Huang and J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35(13), 2239–2241 (1996).
[Crossref] [PubMed]

A. Zhang and P. S. Huang, “Total internal reflection for precision small-angle measurement,” Appl. Opt. 40(10), 1617–1622 (2001).
[Crossref]

M. H. Chiu, S. F. Wang, and R. S. Chang, “Instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry,” Appl. Opt. 43(29), 5438–5442 (2004).
[Crossref] [PubMed]

F. Chen, Z. Cao, Q. Shen, and Y. Feng, “Optical approach to angular displacement measurement based on attenuated total reflection,” Appl. Opt. 44(26), 5393–5397 (2005).
[Crossref] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

S. T. Lin, S. L. Yeh, and C. W. Chang, “Absolute angular displacement determination using Mach-Zehnder interferometer,” J. Opt. A, Pure Appl. Opt. 10(9), 095304 (2008).
[Crossref]

Opt. Eng. (1)

M. H. Chiu and D. C. Su, “Angle measurement using total-internal reflection heterodyne interferometry,” Opt. Eng. 36(6), 1750–1753 (1997).
[Crossref]

Opt. Lasers Eng. (1)

S. T. Lin and W. J. Syu, “Heterodyne Angular Interferometer Using a Square Prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

F. J. Schuda, “High-precision, wide-range, dual-axis, angle monitoring system,” Rev. Sci. Instrum. 54(12), 1648–1652 (1983).
[Crossref]

Other (3)

D. Malacara, Optical shop testing (John Wily & Sons, 1978), Chap. 15.

Agilent 5529A Dynamic Calibrator: http://cp.literature.agilent.com/litweb/pdf/5968-0111E.pdf .

E. Hecht, Optics (Addison Wesley, 4th ed.), Chap. 9.

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Figures (8)

Fig. 1
Fig. 1 The Fabry-Perot etalon
Fig. 2
Fig. 2 Schematic diagrams of (a) the proposed angular probe and (b) the control and signal processing system
Fig. 3
Fig. 3 The etalon module
Fig. 4
Fig. 4 The calculated and measured Airy functions of beam L1
Fig. 5
Fig. 5 The least squares line of the measured S-curve
Fig. 6
Fig. 6 The result of the stability test of the proposed angular probe
Fig. 7
Fig. 7 The result of the validity test of the proposed angular probe
Fig. 8
Fig. 8 The result of the applicability test of the proposed angular probe

Equations (13)

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

I t I t max = 1 1 + F sin 2 ( ϕ / 2 ) = A ( θ ) .
ϕ = 4 π λ n d cos θ t .
sin θ = n sin θ t .
θ 1 = θ c + γ 2 + Δ θ
θ 2 = θ c γ 2 + Δ θ ,
A 1 = A ( θ c + γ / 2 + Δ θ ) = A ( θ c + γ / 2 ) + d A ( θ ) d θ | θ = θ c + γ / 2 Δ θ
A 2 = A ( θ c γ / 2 + Δ θ ) = A ( θ c γ / 2 ) + d A ( θ ) d θ | θ = θ c γ / 2 Δ θ .
d A ( θ ) d θ = 4 π λ F sin ( φ / 2 ) cos ( φ / 2 ) [ 1 + F sin 2 ( φ / 2 ) ] 2 d tan θ t cos θ .
d A ( θ ) d θ | θ = θ c ± γ / 2 = π d F θ c n λ .
A 2 A 1 = 2 π d F θ c n λ Δ θ ,
I t 2 I t 1 I t 2 + I t 1 = 2 π d F θ c n λ Δ θ ,
S = K Δ θ .
K = 2 π d F θ c n λ .

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