Abstract

A new, to our knowledge, optical method for small-angle measurement based on surface-plasmon resonance (SPR) is presented. In this method the high sensitivity of the phase of SPR to the angle of incidence is employed to improve the resolution of the measurement of the angle. Small-angle measurement is performed by the monitoring of the phase shift resulting from the minute change of the angle of incidence with the use of magneto-optical modulation. The validity of this method is demonstrated, and a measurement resolution of 0.2 arc sec is achieved experimentally.

© 1999 Optical Society of America

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References

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  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. P. Shi, E. Stijins, “New optical methods for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
    [CrossRef] [PubMed]
  5. P. Shi, E. Stijins, “Improving the linearity of the Michelson interferometric angular measurement by a parameter-compensation method,” Appl. Opt. 32, 44–51 (1993).
    [CrossRef] [PubMed]
  6. P. R. Yoder, E. R. Schlesinger, J. L. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
    [CrossRef] [PubMed]
  7. A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasiconical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
    [CrossRef]
  8. F. J. Schuda, “High-precision, wide range, dual-axis, angle-monitoring system,” Rev. Sci. Instrum. 54, 1648–1652 (1983).
    [CrossRef]
  9. G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
    [CrossRef]
  10. 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]
  11. 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]
  12. P. S. Huang, J. Ni, “Angle measurement based on the internal-reflection effect using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
    [CrossRef] [PubMed]
  13. M. H. Chiu, D. C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
    [CrossRef]
  14. M. H. Chiu, D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
    [CrossRef]
  15. G. Margheri, A. Mannoni, F. Quercioli, “High-resolution angular and displacement sensing based on the excitation of surface plasma waves,” Appl. Opt. 36, 4521–4525 (1997).
    [CrossRef] [PubMed]
  16. S. Shen, T. Liu, J. Guo, “Optical phase-shift detection of surface plasmon resonance,” Appl. Opt. 37, 1747–1751 (1998).
    [CrossRef]
  17. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  18. G. J. Kovacs, “Optical excitation of surface plasmon-polaritons in layered media,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 143–200.
  19. M. Abraamowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 361.

1998 (1)

1997 (3)

1996 (1)

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]

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 quasiconical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[CrossRef]

1975 (1)

1974 (1)

1970 (1)

1963 (1)

Abraamowitz, M.

M. Abraamowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 361.

Chapman, G. D.

Chickvary, J. L.

Chiu, M. H.

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

M. H. Chiu, D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
[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 quasiconical mirror surface by laser autocollimation,” Precis. Eng. 5, 5–8 (1982).
[CrossRef]

Guo, J.

Harris, O.

Huang, P. S.

Kamada, O.

Kiyono, S.

Kovacs, G. J.

G. J. Kovacs, “Optical excitation of surface plasmon-polaritons in layered media,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 143–200.

Liu, T.

Luther, G. G.

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

Malacara, D.

Mannoni, A.

Margheri, G.

Ni, J.

Quercioli, F.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

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]

Shen, S.

Shi, P.

Stegun, I. A.

M. Abraamowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 361.

Stijins, E.

Su, D. C.

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

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

Virdee, M. S.

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

Yoder, P. R.

Appl. Opt. (12)

J. Rohlin, “An interferometer for precision angle measurement,” Appl. Opt. 2, 762–763 (1963).
[CrossRef]

D. Malacara, O. Harris, “Interferometric measurement of angles,” Appl. Opt. 9, 1630–1633 (1970).
[CrossRef] [PubMed]

G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
[CrossRef] [PubMed]

P. Shi, E. Stijins, “New optical methods for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
[CrossRef] [PubMed]

P. Shi, E. Stijins, “Improving the linearity of the Michelson interferometric angular measurement by a parameter-compensation method,” Appl. Opt. 32, 44–51 (1993).
[CrossRef] [PubMed]

P. R. Yoder, E. R. Schlesinger, J. L. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
[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 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 using elongated critical-angle prisms,” Appl. Opt. 35, 2239–2241 (1996).
[CrossRef] [PubMed]

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

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

S. Shen, T. Liu, J. Guo, “Optical phase-shift detection of surface plasmon resonance,” Appl. Opt. 37, 1747–1751 (1998).
[CrossRef]

Opt. Eng. (1)

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

Precis. Eng. (1)

A. E. Ennos, M. S. Virdee, “High accuracy profile measurement of quasiconical 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)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

G. J. Kovacs, “Optical excitation of surface plasmon-polaritons in layered media,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 143–200.

M. Abraamowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 361.

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Figures (8)

Fig. 1
Fig. 1

ATR configuration.

Fig. 2
Fig. 2

Theoretical curves of SPR for a gold film. The solid curve represents ρ ∼ θ, and the dashed curve represents ϕ ∼ θ.

Fig. 3
Fig. 3

Theoretical curves for Q ∼ θ at different thicknesses of the gold film.

Fig. 4
Fig. 4

Schematic of the setup for angular sensing: L, laser diode; P, polarizer; A, analyzer; M, magneto-optical modulator; S, SPR device; C, phase compensator; D, p-i-n–field-effect-transistor detector; O, signal source and power driver; K, lock-in amplifier; R, analog-to-digital converter; T, personal computer.

Fig. 5
Fig. 5

Theoretical curves for γ ∼ θ at different thicknesses of the gold film.

Fig. 6
Fig. 6

Output voltage plotted versus the rotation angle. The filled squares represent the measured data, and the solid curve represents a linear regression.

Fig. 7
Fig. 7

Results of the noise and the drift of the output over time.

Fig. 8
Fig. 8

Long-term drift of the output.

Equations (20)

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ksp=k0mdm+d1/2,
ksp=kx=k0p sin θsp,
rq=r01q+r12q exp2ik1zd1+r01qr12q exp2ik1zd,  q=p, s,
rijq=Ziq-ZjqZiq+Zjq, Ziq=i/kizq=pkizq=s,  kiz=k0i-0 sin2 θ1/2,
rp=|rp|expjϕp,  rs=|rs|expjϕs,
ρ expjϕ001
ρ expjϕ=rprs,  ρ=|rp||rs|,
Mp=cos2 psin p cos psin p cos psin2 p, Mc=expjϕc001, Ma=cos2 asin a cos asin a cos asin2 a.
Ms=ρ expjϕ001,  Mm=cos φ-sin φsin φcos φ,
E0=MaMcMsMmEi,
Ei=cos psin p
Id  |E0|2=12cos2p+2φρ2 cos2 a-sin2 a+12 ρ sin 2a sin 2p+φcosϕ+ϕc+12ρ2 cos2 a+sin2 a.
cosz sin θ=J0z+2 m=1 J2mzcos 2mθ, sinz sin θ=2 m=0 J2m+1zsin2m+1θ.
Iω  ρ sin2acosϕ+ϕcJ12φ0sin ωt.
U  ρ sin2acosϕ+ϕcJ12φ0.
U  ρ sin2aJ12φ0Δ.
U  ρQ sin2aJ12φ0δθ.
α=δθ/np,
U  ρQ1/npsin2aJ12φ0α.
γ=ρQ=ρϕθ

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