Abstract

The effect of numerical aperture on signal level from fluorescent substances or solutions in the evanescent zone of a cylindrical waveguide is analyzed. The analysis applies to the case in which the fluorescence is excited by the evanescent wave of a fiber and the fluorescence signal is that which tunnels back into the same fiber. The analysis is for two cases: bulk fluorescence and fluorescence of a thin film layer. Experimental results are also presented.

© 1987 Optical Society of America

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References

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  1. M. J. Block, T. B. Hirschfeld, “Assay Apparatus and Method,” U.S. Patent4,558,014 (1984).
  2. T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Employing Optical Fiber in Capillary Tube,” U.S. Patent4,447,546 (1984).
  3. M. J. Block, T. B. Hirschfeld, “Apparatus Including Optical Fiber for Fluorescence Immunoassay,” U.S. Patent4,582,809 (1986).
  4. M. N. Kronick, W. A. Little, “A New Fluorescent Immunoassay,” Bull. Am. Phys. Soc. 18, 782 (1973).
  5. M. N. Kronick, W. A. Little, “A New Immunoassay Based on Fluorescence Excitation by Internal Reflection Spectroscopy,” J. Immunol. Methods 8, 235 (1975).
    [CrossRef] [PubMed]
  6. R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
    [CrossRef]
  7. J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
    [CrossRef]
  8. R. M. Sutherland, C. Dahne, “Optical Detection of Antibody-Antigen reactions at a Glass Liquid Interface,” Clin. Chem. NY 30, 1533 (1984).
  9. T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Using Optical Fibers and Antibodies Immobilized on Surfaces,” at FACSS Eleventh Annual Meeting, 16 Sept. 1984.
  10. T. B. Hirschfeld, “Total Reflection Fluorescence,” J. Can. Spectrosc. 126 (Nov.1965).
  11. E. H. Lee, R. E. Benner, J. B. Fenn, R. K. Chang, “Angular Distribution of Fluorescence from Liquids and Monodispersed Spheres by Evanescent Wave Excitation,” Appl. Opt. 18, 862 (1976).
    [CrossRef]
  12. C. K. Carniglia, L. Mandel, H. Drexhage, “Absorption and Emission of Evanescent Photons,” J. Opt. Soc. Am. 62, 479 (1972).
    [CrossRef]
  13. W. R. Holland, D. G. Hall, “Waveguide Mode Enhancement of Molecular Fluroescence,” Opt. Lett. 10, 414 (1985).
    [CrossRef] [PubMed]
  14. N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. 2.
  15. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 5.
  16. T. B. Hirschfeld, “Apparatus for Improving the Numerical Aperture at the Input of A Fiber Optics Device” U.S. Patent4,654,532 (1987).

1985

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

W. R. Holland, D. G. Hall, “Waveguide Mode Enhancement of Molecular Fluroescence,” Opt. Lett. 10, 414 (1985).
[CrossRef] [PubMed]

1984

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

R. M. Sutherland, C. Dahne, “Optical Detection of Antibody-Antigen reactions at a Glass Liquid Interface,” Clin. Chem. NY 30, 1533 (1984).

1976

1975

M. N. Kronick, W. A. Little, “A New Immunoassay Based on Fluorescence Excitation by Internal Reflection Spectroscopy,” J. Immunol. Methods 8, 235 (1975).
[CrossRef] [PubMed]

1973

M. N. Kronick, W. A. Little, “A New Fluorescent Immunoassay,” Bull. Am. Phys. Soc. 18, 782 (1973).

1972

1965

T. B. Hirschfeld, “Total Reflection Fluorescence,” J. Can. Spectrosc. 126 (Nov.1965).

Andrade, J. D.

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

Benner, R. E.

Block, M. J.

M. J. Block, T. B. Hirschfeld, “Assay Apparatus and Method,” U.S. Patent4,558,014 (1984).

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Using Optical Fibers and Antibodies Immobilized on Surfaces,” at FACSS Eleventh Annual Meeting, 16 Sept. 1984.

M. J. Block, T. B. Hirschfeld, “Apparatus Including Optical Fiber for Fluorescence Immunoassay,” U.S. Patent4,582,809 (1986).

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Employing Optical Fiber in Capillary Tube,” U.S. Patent4,447,546 (1984).

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 5.

Carniglia, C. K.

Chang, R. K.

Dahne, C.

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

R. M. Sutherland, C. Dahne, “Optical Detection of Antibody-Antigen reactions at a Glass Liquid Interface,” Clin. Chem. NY 30, 1533 (1984).

Drexhage, H.

Fenn, J. B.

Gregonis, D. E.

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

Hall, D. G.

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. 2.

Hirschfeld, T. B.

T. B. Hirschfeld, “Total Reflection Fluorescence,” J. Can. Spectrosc. 126 (Nov.1965).

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Employing Optical Fiber in Capillary Tube,” U.S. Patent4,447,546 (1984).

T. B. Hirschfeld, “Apparatus for Improving the Numerical Aperture at the Input of A Fiber Optics Device” U.S. Patent4,654,532 (1987).

M. J. Block, T. B. Hirschfeld, “Assay Apparatus and Method,” U.S. Patent4,558,014 (1984).

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Using Optical Fibers and Antibodies Immobilized on Surfaces,” at FACSS Eleventh Annual Meeting, 16 Sept. 1984.

M. J. Block, T. B. Hirschfeld, “Apparatus Including Optical Fiber for Fluorescence Immunoassay,” U.S. Patent4,582,809 (1986).

Holland, W. R.

Kronick, M. N.

M. N. Kronick, W. A. Little, “A New Immunoassay Based on Fluorescence Excitation by Internal Reflection Spectroscopy,” J. Immunol. Methods 8, 235 (1975).
[CrossRef] [PubMed]

M. N. Kronick, W. A. Little, “A New Fluorescent Immunoassay,” Bull. Am. Phys. Soc. 18, 782 (1973).

Lee, E. H.

Lin, J. N.

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

Little, W. A.

M. N. Kronick, W. A. Little, “A New Immunoassay Based on Fluorescence Excitation by Internal Reflection Spectroscopy,” J. Immunol. Methods 8, 235 (1975).
[CrossRef] [PubMed]

M. N. Kronick, W. A. Little, “A New Fluorescent Immunoassay,” Bull. Am. Phys. Soc. 18, 782 (1973).

Mandel, L.

Newby, K.

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

Place, J. F.

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

Ringrose, A. R.

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

Sutherland, R. M.

R. M. Sutherland, C. Dahne, “Optical Detection of Antibody-Antigen reactions at a Glass Liquid Interface,” Clin. Chem. NY 30, 1533 (1984).

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

Van Wagenan, R. A.

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

Appl. Opt.

Bull. Am. Phys. Soc.

M. N. Kronick, W. A. Little, “A New Fluorescent Immunoassay,” Bull. Am. Phys. Soc. 18, 782 (1973).

Clin. Chem. NY

R. M. Sutherland, C. Dahne, “Optical Detection of Antibody-Antigen reactions at a Glass Liquid Interface,” Clin. Chem. NY 30, 1533 (1984).

IEEE Trans. Electron Devices

J. D. Andrade, R. A. Van Wagenan, D. E. Gregonis, K. Newby, J. N. Lin, “Remote Fibre-optic Biosensors Based on Evanescent-Excited Fluoro-Immunoassay: Concept and Progress,” IEEE Trans. Electron Devices ED-32, 1175 (1985).
[CrossRef]

J. Can. Spectrosc.

T. B. Hirschfeld, “Total Reflection Fluorescence,” J. Can. Spectrosc. 126 (Nov.1965).

J. Immunol. Methods

M. N. Kronick, W. A. Little, “A New Immunoassay Based on Fluorescence Excitation by Internal Reflection Spectroscopy,” J. Immunol. Methods 8, 235 (1975).
[CrossRef] [PubMed]

R. M. Sutherland, C. Dahne, J. F. Place, A. R. Ringrose, “Immunoassays at a Quartz-Liquid Interface: Theory, Instrumentation and Preliminary Application to the Fluorescent Immunoassay of Human Immunoglobulin G,” J. Immunol. Methods 74, 235 (1984).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Using Optical Fibers and Antibodies Immobilized on Surfaces,” at FACSS Eleventh Annual Meeting, 16 Sept. 1984.

M. J. Block, T. B. Hirschfeld, “Assay Apparatus and Method,” U.S. Patent4,558,014 (1984).

T. B. Hirschfeld, M. J. Block, “Fluorescent Immunoassay Employing Optical Fiber in Capillary Tube,” U.S. Patent4,447,546 (1984).

M. J. Block, T. B. Hirschfeld, “Apparatus Including Optical Fiber for Fluorescence Immunoassay,” U.S. Patent4,582,809 (1986).

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. 2.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 5.

T. B. Hirschfeld, “Apparatus for Improving the Numerical Aperture at the Input of A Fiber Optics Device” U.S. Patent4,654,532 (1987).

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Figures (7)

Fig. 1
Fig. 1

Fiber-optic evanescent fluorosensor geometry. The fluorescor is excited by the evanescent wave associated with the total internal reflection of the exciting ray (heavy line). A fraction of the fluorescence (light line) tunnels back into the fiber and is available for detection.

Fig. 2
Fig. 2

Arbitrary ray entering the fiber.

Fig. 3
Fig. 3

Arbitrary ray impinging on a reflection point 0 on the fiber surface. The fiber axis is parallel to the z axis, the x axis is normal to the fiber surface, and the y axis is tangential to the fiber surface.

Fig. 4
Fig. 4

Path length of a ray in a fiber may be easily calculated from the ray longitudinal angle α and fiber length ρ.

Fig. 5
Fig. 5

Schematic of the optical system used in experiments.

Fig. 6
Fig. 6

Theory (solid line) and experimental (asterisks) points for the case of a bulk sample.

Fig. 7
Fig. 7

Theory (solid line) and experimental (asterisks) points for the case of a thin layer.

Equations (27)

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ϕ = ( π / 2 ) - sin - 1 [ ( r / a ) sin β ] .
sin η = cos ( π / 2 - α ) sin ϕ = sin α sin ϕ ,
d = ρ / cos ( α ) .
c = 2 a cos ( ξ ) = 2 a 1 - ( r / a ) 2 sin 2 β .
m = ρ tan ( α ) 2 a 1 - ( r / a ) 2 sin 2 β ,
m = ( ρ / 2 a ) tan α .
S = k A θ E c ,
( d / d ) = [ 4 n 1 n 2 cos θ ( n 1 2 - n 3 2 ) ] ,
( d / d ) = ( d / d ) f ( θ ) ,
f ( θ ) = [ 1 + ( n 3 / n 2 ) 4 ] sin 2 θ - ( n 3 / n 1 ) 2 [ 1 + ( n 3 / n 1 ) 2 ] sin 2 θ - ( n 3 / n 1 ) 2 .
( d av / d ) = 2 n 2 n 1 [ 1 + f ( θ ) ] cos θ n 1 2 - n 3 2 .
P i 0 α max 0 a 2 π r sin α cos α d r d α = π a 2 ( n 1 / n 0 ) 2 sin 2 α max ,
A e L 0 a 0 2 π 0 a max 2 π r sin α cos α d av m d α d β d r .
A e L 0 a 0 2 π 0 α max 2 π r sin 3 α d α d β d r
A e L ( 2 3 + cos α max 3 + cos α max ) .
d e = n 3 n 1 λ cos θ [ 1 + g ( θ ) ] 2 π ( n 1 2 - n 3 2 ) sin 2 θ - ( n 3 / n 1 ) 2 ,
g ( θ ) = 2 n 1 2 sin 2 θ - n 3 2 ( n 1 2 + n 3 2 ) sin 2 θ - n 3 2 .
A e B 0 a 0 2 π 0 α max 2 π r sin α cos α d e m d α β d r .
A e B 0 a 0 2 π 0 α max r sin 3 α d α d β d r 1 - ( n 3 / n 1 ) 2 - [ 1 - ( r / a ) 2 sin 2 β ] sin 2 α .
A e B 0 2 π 0 α max [ [ 1 - ( n 3 / n 1 ) 2 ] sin 2 α - sin 4 α sin 4 β + sin 4 α sin 2 β ] 1 / 2 d α d β - 0 2 π 0 α max [ [ 1 - ( n 3 / n 1 ) 2 ] sin 2 α - sin 4 α sin 4 β ] 1 / 2 d α d β .
( E av / E ) 2 = 2 cos 2 θ 1 - ( n 3 / n 1 ) 2 [ 1 + f ( θ ) ] ,
E c 0 a 0 2 π 0 α max ( E av / E ) 2 m d α d β d r ,
E c C 2 [ - sin 2 α max 2 - ln ( cos α max ) ] ,
C 2 = 0 a 0 2 π 1 - ( r / a ) 2 sin 2 β d β d r
S F n 2 n 1 3 n 0 2 ( n 1 2 - n 3 2 ) 2 ( 2 + cos 3 α max 3 - cos α max ) E c ,
S B ( A e B ) E c ,
cos α max = 1 - ( N . A . / n 1 ) 2 .

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