Abstract

A high-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry is proposed that uses a new technique with two right-angle prisms. Interestingly, the technique provides a novel method for designing small-angle sensors with high sensitivity and high resolution. Its theoretical resolution can reach 1.2×107 rad over the measurement range of 0.15°θ0.15°. The method has some merits, e.g., a simple optical setup, easy operation, high resolution, high sensitivity, and rapid measurement. Its feasibility is demonstrated.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. P. S. Huang and J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl. Opt. 35, 2239-2241 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. 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, 5438-5442 (2004).
    [CrossRef] [PubMed]
  8. W. Zhou and L. Cai, "Interferometer for small-angle measurement based on total internal reflection," Appl. Opt. 37, 5957-5963 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. G. Margheri, A. Mannoni, and F. Quercioli, "High-resolution angular and displacement sensing based on the excitation of surface plasma waves," Appl. Opt. 36, 4521-4525 (1997).
    [CrossRef] [PubMed]
  17. S. Shen, T. Liu, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
    [CrossRef]
  18. J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
    [CrossRef]
  19. E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
    [CrossRef]
  20. Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
    [CrossRef]
  21. H. E. de Bruijn, R. P. H. Kooyman, and J. Greve, "Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment," Appl. Opt. 29, 1974-1978 (1990).
    [CrossRef]
  22. C. C. Lee and Y. J. Jen, "Influence of surface roughness on the calculation of optical constants of a metallic film by attenuated total reflection," Appl. Opt. 38, 6029-6033 (1999).
    [CrossRef]

2004

2001

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

2000

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

1999

1998

1997

1996

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

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

1995

1993

1990

1989

1988

1983

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

1971

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Aldinger, U.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Bartholomew, D. U.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Cai, L.

Carr, R.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Chang, R. S.

Cheng, Y. C.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Chiu, M. H.

de Bruijn, H. E.

Deng, W.

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Diekmann, S.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Elkind, J.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Fullerton, E.

Furlong, C.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Greve, J.

Guo, J.

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

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Haojuan, W.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Hong, J.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Huang, P. S.

Jen, Y. J.

Kooyman, R. P. H.

Kretshmann, E.

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

Kukanskis, K.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Lee, C. C.

Lequn, Z.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Lévesque, L.

Lieberg, B.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Liou, J. H.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Liu, T.

Lundström, I.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Mannoni, A.

Margheri, G.

Melendez, H.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Ni, J.

Nylander, C.

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Paton, B. E.

Pfeifer, P.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Quercioli, F.

Robertson, W. M.

Schwotzer, G.

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Shen, S.

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

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Shi, P.

Stijns, E.

Su, D. C.

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

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

Su, W. K.

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Wang, S. F.

Woodbury, R.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Xinglong, Y.

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

Yee, S.

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Zhou, W.

Zhu, Z.

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Appl. Opt.

P. Shi and E. Stijns, "Improving the linearity of the Mechelson interferometric angular measurement by a parameter-compensation method," Appl. Opt. 32, 44-51 (1993).
[CrossRef] [PubMed]

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

P. S. Huang, "Use of thin films for high-sensitivity angle measurement," Appl. Opt. 38, 4831-4836 (1999).
[CrossRef]

M. H. Chiu and D. C. Su, "Improved technique for measuring small angles," Appl. Opt. 36, 7104-7106 (1997).
[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, 5438-5442 (2004).
[CrossRef] [PubMed]

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

P. Shi and E. Stijns, "New optical method for measuring small-angle rotations," Appl. Opt. 27, 4342-4346 (1988).
[CrossRef] [PubMed]

L. Lévesque and B. E. Paton, "Detection of defects in multiple-layer structures by using surface plasmon resonance," Appl. Opt. 36, 7199-7203 (1997).
[CrossRef]

G. Margheri, A. Mannoni, and 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, and J. Guo, "Optical phase-shift detection of surface plasmon resonance," Appl. Opt. 37, 1747-1751 (1998).
[CrossRef]

H. E. de Bruijn, R. P. H. Kooyman, and J. Greve, "Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment," Appl. Opt. 29, 1974-1978 (1990).
[CrossRef]

C. C. Lee and Y. J. Jen, "Influence of surface roughness on the calculation of optical constants of a metallic film by attenuated total reflection," Appl. Opt. 38, 6029-6033 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

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

J. Guo, Z. Zhu, W. Deng, and S. Shen, "Angle measurement using surface-plasmon-resonance heterodyne interferometry: a new method," Opt. Eng. 37, 2998-3001 (1998).
[CrossRef]

Y. C. Cheng, W. K. Su, and J. H. Liou, "Application of a liquid sensor based on surface plasmon wave excitation to distinguish methyl alcohol from ethyl alcohol," Opt. Eng. 39, 311-314 (2000).
[CrossRef]

Sens. Actuators

B. Lieberg, C. Nylander, and I. Lundström, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Sens. Actuators B

H. Melendez, R. Carr, D. U. Bartholomew, K. Kukanskis, J. Elkind, S. Yee, C. Furlong, and R. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212-216 (1996).
[CrossRef]

Y. Xinglong, Z. Lequn, J. Hong, and W. Haojuan, "Immunosensor based on optical heterodyne phase detection," Sens. Actuators B 76, 199-202 (2001).
[CrossRef]

P. Pfeifer, U. Aldinger, G. Schwotzer, and S. Diekmann, "Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy," Sens. Actuators B 54, 166-175 (1999).
[CrossRef]

Z. Phys.

E. Kretshmann, "Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen," Z. Phys. 241, 313-324 (1971).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Kretchmann's configuration for the generation of surface plasmon resonance. n 1 is the refractive index of the prism, n 2 is the refractive index of the Ti metal, n 3 is the refractive index of the Au metal, n 4 is the refractive index of air, and d 2 and d 3 are the thicknesses of Ti and Au, respectively.

Fig. 2
Fig. 2

Plot of the reflectivity of p polarizatin versus the incident angle α.

Fig. 3
Fig. 3

Phase difference ϕ as a function of the incident angle α for different d 2 at a constant wavelength of λ = 632.8   nm (only one prism is used).

Fig. 4
Fig. 4

Experimental setup (AN1 and AN2, analyzers; D1 and D2, photodetectors; P1 and P2, right-angle prisms).

Fig. 5
Fig. 5

Geometric relations between θ and α 1 or α 2 .

Fig. 6
Fig. 6

Experimental and theoretical curves of Δ ϕ versus Δ θ for d 2 = 2   nm and d 3 = 43.1   nm at a constant wavelength of λ = 632.8   nm .

Fig. 7
Fig. 7

Resolution versus Δ θ .

Fig. 8
Fig. 8

Sensitivity S versus Δ θ .

Fig. 9
Fig. 9

Phase difference Δ ϕ versus the rotation angle Δ θ for a different thickness d 2 of the Ti metal in the measurement range of ± 0.05 ° .

Fig. 10
Fig. 10

Relative error (%) versus the rotation angle Δ θ .

Equations (15)

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

r 1234 t = r 12 t + r 234 t e i 2 k z 2 d 2 1 + r 12 t r 234 t e i 2 k z 2 d 2 ,
r 234 t = r 23 t + r 34 t e i 2 k z 3 d 3 1 + r 23 t r 34 t e i 2 k z 3 d 3 ,
E I t = { n I 2 / k zI , t = p k zI , t = s , I = i , j ; i , j = 1 , 2 , 3 , 4.
k z i ( j ) = k 0 [ n i ( j ) 2 n 1 2 sin 2 α ] ,
r 1234 p = | r 1234 p | e i ϕ p , r 1234 s = | r 1234 s | e i ϕ s ,
ϕ = ϕ p ϕ s .
α = 45 ° + sin - 1 ( n 4 sin θ i n 1 ) ,
θ 0 = sin 1 [ n 1 sin ( 45 ° θ sp ) n 4 ] 1.742 ° .
α 1 = 45 ° sin - 1 [ n 4 sin ( θ 0 Δ θ ) n 1 ] ,
α 2 = 45 ° sin - 1 [ n 4 sin ( θ 0 + Δ θ ) n 1 ] .
I 1 = I 10 [ 1 + V 1 cos ( 2 π Δ f t + ϕ 1 ) ] ,
I 2 = I 20 [ 1 + V 2 cos ( 2 π Δ f t + ϕ 2 + ϕ BS ) ] ,
ϕ = ϕ 1 ϕ 2 ϕ BS .
A resolution = δ θ δ ϕ Δ ϕ ,
S = d ϕ d θ ,

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