Abstract

Based on the total-internal-reflection effect and heterodyne interferometry, an improved technique for measuring small angles is proposed. This technique not only expands the measurement range but it also improves measurement performances. Its validity is demonstrated.

© 1997 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. P. Shi, E. Stijns, “New optical methods for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
    [CrossRef] [PubMed]
  5. P. Shi, E. Stijns, “Improving the linearity of the Mechelson interferometric angular measurement by a parameter-compensation method,” Appl. Opt. 32, 44–51 (1993).
    [CrossRef] [PubMed]
  6. 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]
  7. G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
    [CrossRef]
  8. 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]
  9. 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]
  10. D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

1996 (1)

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

1988 (1)

1984 (1)

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

1974 (1)

1970 (1)

1963 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

Chapman, G. D.

Chen, C. D.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chiu, M. H.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Deslattes, R. D.

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

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.

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.

Ni, J.

Rohlin, J.

Shi, P.

Stijns, E.

Su, D. C.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

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]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

Appl. Opt. (7)

Precis. Eng. (2)

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

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. (1)

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

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram for measuring small angles: PL, polarizer; EOM, electro-optical modulator; AN, analyzer.

Fig. 2
Fig. 2

Geometric relations between θ and α1 or α2.

Fig. 3
Fig. 3

Calculated curves of ϕ versus θ, (ϕ1 - ϕ2), and ϕBS.

Fig. 4
Fig. 4

Experimental curves of ϕ versus θ.

Fig. 5
Fig. 5

Relation curves of Δθ versus θ.

Equations (11)

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I1=I101+V1 cos2πft+ϕ1+ϕBS,
I2=I201+V2 cos2πft+ϕ2,
ϕ1=2 tan-1sin2 α1-1/np21/2tan α1 sin α1,
ϕ2=2 tan-1sin2 α2-1/np21/2tan α2 sin α2,
ϕBS=tan-1bc-adbd+ac,
a=2v cos β, b=cos2 β-u2-v2, c=2v cos βn2-k2-2u2, d=n2+k22×cos2β-u2+v2, 2u2=n2-k2-sin2 β+n2-k2-sin2 β2+4n2k21/2, 2v2=-m2-k2-sin2 β+n2-k2-sin2 β2+4n2k21/2, β=45°+θ.
α1=45°+sin-1sin θnp,
α2=45°-sin-1sin θnp.
ϕ=ϕ1-ϕ2+ϕBS.
θmax=sin-1np sin45°-sin-11np.
Δθ=1dϕ1-dϕ2/dθ+dϕBS/dθ)Δϕ,

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