Abstract

An optical approach for angular displacement measurement (ADM) based on the attenuated total reflection technique is presented. As a laser beam is incident upon a planar optical waveguide, an m line is obtained by scanning the incident angle. Theoretical analysis shows that the m line sharply shifts with a tiny variation of the thickness of the waveguided layer. And the specific schemes for ADM, which are based on the angular interrogation and the intensity measurement, are analyzed. The calculated result of sensitivity demonstrates that the intensity measurement is more efficient than the angular interrogation. Furthermore, small incident angles indicate higher sensitivity to the angular displacement than relatively large incident angles for the intensity measurement.

© 2005 Optical Society of America

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References

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  1. W. D. Zhou, L. L. Cai, “Interferometer for small-angle measurement based on total internal reflection,” Appl. Opt. 37, 5957–5963 (1998).
    [CrossRef]
  2. S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
    [CrossRef]
  3. B. H. De, “Experiments relating to the gravitational constant,” in Precision Measurement and Fundamental Constants, B. N. Taylor, W. D. Philips, eds. (U.S. Government Printing Office, 1984), pp. 561–572.
  4. V. Iafolla, S. Nozzoli, “Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘BepiColombo’ ESA CORNERSTONE,” Planet. Space Sci. 45, 1–2 (2001).
  5. S. Z. Zhang, S. Kiyono, Y. Uda, “Nanoradian angle sensor and in situ self-calibration,” Appl. Opt. 37, 4154–4159 (1998).
    [CrossRef]
  6. 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]
  7. M. H. Chiu, D. C. Su, “Improved technique for measuring small angles,” Appl. Opt. 36, 7104–7106 (1997).
    [CrossRef]
  8. P. S. Huang, “Use of thin films for high-sensitivity angle measurement,” Appl. Opt. 38, 4831–4836 (1999).
    [CrossRef]
  9. Y. Jiang, Z. Q. Cao, Q. S. Shen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17, 805–808 (2000).
    [CrossRef]
  10. Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).
  11. 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]
  12. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 1, pp. 64–70.
  13. J. Homola, S. S. Yee, G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
    [CrossRef]
  14. J. Villatoro, A. Garcia-Valenzuela, “Sensitivity of optical sensors based on laser-excited surface-plasmon waves,” Appl. Opt. 38, 4837–4844 (1999).
    [CrossRef]

2003 (1)

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

2001 (1)

V. Iafolla, S. Nozzoli, “Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘BepiColombo’ ESA CORNERSTONE,” Planet. Space Sci. 45, 1–2 (2001).

2000 (2)

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17, 805–808 (2000).
[CrossRef]

1999 (3)

1998 (2)

1997 (2)

1992 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 1, pp. 64–70.

Cai, L. L.

Cao, Z. Q.

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17, 805–808 (2000).
[CrossRef]

Chiu, M. H.

De, B. H.

B. H. De, “Experiments relating to the gravitational constant,” in Precision Measurement and Fundamental Constants, B. N. Taylor, W. D. Philips, eds. (U.S. Government Printing Office, 1984), pp. 561–572.

Fan, S. H.

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

Garcia-Valenzuela, A.

Gauglitz, G.

J. Homola, S. S. Yee, G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[CrossRef]

Homola, J.

J. Homola, S. S. Yee, G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[CrossRef]

Huang, P. S.

Huang, Y.

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

Iafolla, V.

V. Iafolla, S. Nozzoli, “Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘BepiColombo’ ESA CORNERSTONE,” Planet. Space Sci. 45, 1–2 (2001).

Jiang, Y.

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17, 805–808 (2000).
[CrossRef]

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).

Kamada, O.

Kiyono, S.

Luo, J.

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

Mannoni, A.

Margheri, G.

Nozzoli, S.

V. Iafolla, S. Nozzoli, “Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘BepiColombo’ ESA CORNERSTONE,” Planet. Space Sci. 45, 1–2 (2001).

Quercioli, F.

Shen, Q. S.

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17, 805–808 (2000).
[CrossRef]

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).

Su, D. C.

Uda, Y.

Villatoro, J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 1, pp. 64–70.

Wu, S. C.

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

Yee, S. S.

J. Homola, S. S. Yee, G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[CrossRef]

Zhang, S. Z.

Zhou, W. D.

Acta Opt. Sin. (1)

Y. Jiang, Z. Q. Cao, Q. S. Shen, “Determination of the complex dielectric coefficient and thickness of absorbing films using guided waves,” Acta Opt. Sin. 20, 642–646 (2000).

Appl. Opt. (7)

Chin. Phys. Lett. (1)

S. C. Wu, Y. Huang, S. H. Fan, J. Luo, “Measurement of the floor tilt in experimental determination of the gravitational constant,” Chin. Phys. Lett. 20, 1210–1213 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Planet. Space Sci. (1)

V. Iafolla, S. Nozzoli, “Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘BepiColombo’ ESA CORNERSTONE,” Planet. Space Sci. 45, 1–2 (2001).

Sens. Actuators B (1)

J. Homola, S. S. Yee, G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999).
[CrossRef]

Other (2)

B. H. De, “Experiments relating to the gravitational constant,” in Precision Measurement and Fundamental Constants, B. N. Taylor, W. D. Philips, eds. (U.S. Government Printing Office, 1984), pp. 561–572.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 1, pp. 64–70.

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Figures (7)

Fig. 1
Fig. 1

Optical layout for ADM based on the ATR technique. A detector is used to monitor the light reflected from the interface between the prism coupler and metal film 2 (MF2). The vertical dashed line represents the rest position of the oscillator, and the horizontal dashed–dotted line indicates the normal orientation to the hypotenuse face of the prism.

Fig. 2
Fig. 2

Typical ATR curve is obtained with ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 6←2.8 nm, ɛ3 = 3.0, h1 = 3 μm, and d2 = 43 nm.

Fig. 3
Fig. 3

Sensitive response of the ATR curve to the thickness variation of a waveguided layer. The solid curve represents the absorbing dig of the guided mode obtained with ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 632.8 nm, ɛ3 = 3.0, h1 = 1.0 mm, and d2 = 40 nm. (b) The dotted curve represents the absorbing dig of the guided mode obtained with ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 632.8 nm, ɛ3 = 3.0, h1 = 1.0 mm + 1.0 nm, and d2 = 40 nm.

Fig. 4
Fig. 4

S2 versus the incident angle θi and the thickness of waveguided layer (AG) h1. The curves noted by 1, 2, 3, 4 are obtained with parameters h1 = 10, 20, 50, and 120 μm, respectively.

Fig. 5
Fig. 5

S1 versus the incident angle θi. The sensitivity curve is obtained with the parameters ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 632.8 nm, ɛ3 = 3.0, h1 = 10 μm, and d2 = 40 nm.

Fig. 6
Fig. 6

S versus the incident angle θi with ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 632.8 nm, ɛ3 = 3.0, h1 = 10 μm, and d2 = 40 nm.

Fig. 7
Fig. 7

S versus d2, ɛ1 = 1.0, ɛ0 = ɛ2 = −16 + 0.6i at 632.8 nm, ɛ3 = 3.0, and h1 = 10 μm.

Equations (17)

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R ( θ i ) = | B 3 A 3 | 2 = [ γ 23 + B 2 / A 2 exp ( i 2 α 2 d 2 ) 1 + γ 23 B 2 / A 2 exp ( i 2 α 2 d 2 ) ] 2 ,
{ B 2 / A 2 = γ 12 + B 1 / A 1 exp ( i 2 α 1 h 1 ) 1 + γ 2 B 1 / A 1 exp ( i 2 α 1 h 1 ) B 1 / A 1 = γ 01 .
α j = β 2 - k 0 2 ɛ j ,             ( j = 0 ,     1 ,     2 ,     3 ) ,
β = k 0 ɛ 1 sin θ 1 ,
h 1 = h 10 + l θ ,
S = d R d θ = ( R θ i ) θ = θ 0 ( θ i θ ) = S 1 S 2 ,
κ h 1 - tan - 1 ( ɛ 1 ɛ 0 p κ ) - tan - 1 ( ɛ 1 ɛ 2 q κ ) = m π ( m = 0 ,     1 ,     ) ,
p = β 2 - k 0 2 ɛ 2 ,
q = β 2 - k 0 2 ɛ 0 ,
κ = k 0 2 ɛ 1 - β 2 ,
d κ d h 1 = - κ h eff ,
h eff = h 1 + 2 p ɛ 1 ( κ 2 + p 2 ɛ 1 2 / ɛ 2 2 ) ɛ 2 ,
d κ d h 1 = - k 0 ɛ 3 sin θ i cos θ i l ɛ 1 - ɛ 3 sin 2 θ i d θ i d θ .
S 2 = l h eff ɛ 1 - ɛ 3 sin 2 θ i ɛ 3 sin θ i cos θ i .
Δ ν min = 1.0 × 10 - 4 π 180 1 S 2 ,
S 1 = R k + 1 - R k θ i k + 1 - θ i k             ( k = 0 ,     1 ,     2 ,     ,     N - 1 ) ,
Δ θ min = 2.0 × 10 - 3 S .

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