Abstract

We examine the limit of spatial resolution achievable when a single optical fiber is used for excitation and collection of fluorescence from a bulk specimen. We calculate the probability of detecting a fluorescent particle as a function of its position relative to the fiber face, using excitation wavelength λ, radius a, numerical aperture N.A., and the particle’s fluorescence and absorbance spectra. Treating Rhodamine B as a model fluorescent analyte and using appropriate fiber parameters, we show that the maximum axial resolution (defined as the axial distance in a homogenous solution within which 50% of the detected signal originates) achievable is ∼10 μm. We experimentally measured the axial resolution for a 500-μM aqueous solution of Rhodamine B with λ = 543 nm, a = 1.31 μm, and a N.A. of 0.16 and found good qualitative agreement with the calculation.

© 2003 Optical Society of America

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References

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  1. O. S. Wolfbeis, “Fiber-optic chemical sensors and biosensors,” Anal. Chem. 72, 81R–89R (2000).
    [CrossRef]
  2. M. D. Marazuela, M. Cruz-Bondi, “Fiber-optic biosensors—an overview,” Anal. Bioanal. Chem. 372, 664–682 (2002).
    [CrossRef]
  3. A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
    [CrossRef]
  4. C. Ziegler, “Cell-based biosensors,” J. Anal. Chem. 366, 552–559 (2000).
    [CrossRef]
  5. J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
    [CrossRef]
  6. C. Liang, K. B. Sung, R. R. Richards-Kortum, M. R. Descour, “Fiber confocal reflectance microscope,” Opt. Express 9, 821–830 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  7. C. Liang, K. B. Sung, R. R. Richards-Kortum, M. R. Descour, “Design of a high-numerical-aperture miniature microscope objective for an endoscopic fiber confocal reflectance microscope,” Appl. Opt. 41, 4603–4610 (2002).
    [CrossRef] [PubMed]
  8. G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
    [CrossRef] [PubMed]
  9. C. Akcay, P. Parrein, J. P. Rolland, “Estimation of longitudinal resolution in optical coherence imaging,” Appl. Opt. 41, 5256–5262 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
    [CrossRef]
  12. U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
    [CrossRef]
  13. P. Sengupta, J. Balaji, S. Maiti, “Measuring diffusion in cell membranes by fluorescence correlation spectroscopy,” Methods 27, 374–387 (2002).
    [CrossRef] [PubMed]
  14. B. Eric, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
    [CrossRef]
  15. S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).
  16. D. M. Dinkel, F. E. Lytle, “Remote two-photon excited fluorescence sensing in a simulated fermentation broth,” Anal. Chim. Acta 263, 131–136 (1992).
    [CrossRef]
  17. G. P. Agarwal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  18. D. Marcuse, “Gaussian approximation of the fundamental modes of graded index fibers,” J. Opt. Soc. Am. 68, 103–109 (1978).
    [CrossRef]
  19. H. M. Antia, Numerical Methods for Scientists and Engineers, 2nd ed. (Hindustan Book Agency, New Delhi, 2002).
  20. J. B. Pawley, ed., Handbook of Biological Confocal Microscopy, 2nd ed. (Plenum, New York, 1995).

2002 (4)

2001 (2)

C. Liang, K. B. Sung, R. R. Richards-Kortum, M. R. Descour, “Fiber confocal reflectance microscope,” Opt. Express 9, 821–830 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

2000 (2)

C. Ziegler, “Cell-based biosensors,” J. Anal. Chem. 366, 552–559 (2000).
[CrossRef]

O. S. Wolfbeis, “Fiber-optic chemical sensors and biosensors,” Anal. Chem. 72, 81R–89R (2000).
[CrossRef]

1998 (1)

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

1997 (3)

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
[CrossRef]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

1996 (1)

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

1992 (2)

B. Eric, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef]

D. M. Dinkel, F. E. Lytle, “Remote two-photon excited fluorescence sensing in a simulated fermentation broth,” Anal. Chim. Acta 263, 131–136 (1992).
[CrossRef]

1978 (1)

1972 (1)

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuation in a reaction system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Agarwal, G. P.

G. P. Agarwal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Akcay, C.

Anderson, G. P.

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

Antia, H. M.

H. M. Antia, Numerical Methods for Scientists and Engineers, 2nd ed. (Hindustan Book Agency, New Delhi, 2002).

Balaji, J.

P. Sengupta, J. Balaji, S. Maiti, “Measuring diffusion in cell membranes by fluorescence correlation spectroscopy,” Methods 27, 374–387 (2002).
[CrossRef] [PubMed]

Boppart, S. A.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Bouma, B. E.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Brezinski, M. E.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Buess, G.

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Cruz-Bondi, M.

M. D. Marazuela, M. Cruz-Bondi, “Fiber-optic biosensors—an overview,” Anal. Bioanal. Chem. 372, 664–682 (2002).
[CrossRef]

Descour, M. R.

Dinkel, D. M.

D. M. Dinkel, F. E. Lytle, “Remote two-photon excited fluorescence sensing in a simulated fermentation broth,” Anal. Chim. Acta 263, 131–136 (1992).
[CrossRef]

Elson, E.

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuation in a reaction system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Eric, B.

B. Eric, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef]

Fujimoto, J. G.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Gaeta, A. L.

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

Haupts, U.

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
[CrossRef]

King, K. D.

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

Knittel, J.

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Liang, C.

Ligler, F. S.

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

Linda, A. T.

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

Lytle, F. E.

D. M. Dinkel, F. E. Lytle, “Remote two-photon excited fluorescence sensing in a simulated fermentation broth,” Anal. Chim. Acta 263, 131–136 (1992).
[CrossRef]

Magde, D.

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuation in a reaction system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Maiti, S.

P. Sengupta, J. Balaji, S. Maiti, “Measuring diffusion in cell membranes by fluorescence correlation spectroscopy,” Methods 27, 374–387 (2002).
[CrossRef] [PubMed]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
[CrossRef]

Marazuela, M. D.

M. D. Marazuela, M. Cruz-Bondi, “Fiber-optic biosensors—an overview,” Anal. Bioanal. Chem. 372, 664–682 (2002).
[CrossRef]

Marcuse, D.

Messerschmidt, B.

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Parrein, P.

Pitris, C.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Possner, T.

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Ranka, J. K.

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

Richards-Kortum, R. R.

Rolland, J. P.

Schnieder, L.

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Schwille, P.

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

Sengupta, P.

P. Sengupta, J. Balaji, S. Maiti, “Measuring diffusion in cell membranes by fluorescence correlation spectroscopy,” Methods 27, 374–387 (2002).
[CrossRef] [PubMed]

Southern, F. J.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Sung, K. B.

Tearney, G. J.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Trautman, J. K.

B. Eric, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef]

Webb, W. W.

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
[CrossRef]

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuation in a reaction system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Wolfbeis, O. S.

O. S. Wolfbeis, “Fiber-optic chemical sensors and biosensors,” Anal. Chem. 72, 81R–89R (2000).
[CrossRef]

Ziegler, C.

C. Ziegler, “Cell-based biosensors,” J. Anal. Chem. 366, 552–559 (2000).
[CrossRef]

Anal. Bioanal. Chem. (1)

M. D. Marazuela, M. Cruz-Bondi, “Fiber-optic biosensors—an overview,” Anal. Bioanal. Chem. 372, 664–682 (2002).
[CrossRef]

Anal. Biochem. (1)

A. T. Linda, K. D. King, G. P. Anderson, F. S. Ligler, “Quantitating staphylococcal enterotoxin B in diverse media using a portable fiber optic biosensor,” Anal. Biochem. 233, 50–57 (1996).
[CrossRef]

Anal. Chem. (1)

O. S. Wolfbeis, “Fiber-optic chemical sensors and biosensors,” Anal. Chem. 72, 81R–89R (2000).
[CrossRef]

Anal. Chim. Acta (1)

D. M. Dinkel, F. E. Lytle, “Remote two-photon excited fluorescence sensing in a simulated fermentation broth,” Anal. Chim. Acta 263, 131–136 (1992).
[CrossRef]

Appl. Opt. (2)

Biophys. J. (1)

S. Maiti, J. K. Ranka, A. L. Gaeta, W. W. Webb, “Multiphoton fluorescence spectroscopy through optical fibers,” Biophys. J. 72, A-217 (1997).

J. Anal. Chem. (1)

C. Ziegler, “Cell-based biosensors,” J. Anal. Chem. 366, 552–559 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Methods (1)

P. Sengupta, J. Balaji, S. Maiti, “Measuring diffusion in cell membranes by fluorescence correlation spectroscopy,” Methods 27, 374–387 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Knittel, L. Schnieder, G. Buess, B. Messerschmidt, T. Possner, “Endoscope-compatible confocal microscope using a gradient index-lens system,” Opt. Commun. 188, 267–273 (2001).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (1)

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuation in a reaction system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11,753–11,757 (1997).
[CrossRef]

U. Haupts, S. Maiti, P. Schwille, W. W. Webb, “Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 95, 13,573–13,578 (1998).
[CrossRef]

Science (2)

B. Eric, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, F. J. Southern, J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276, 2037–2039 (1997).
[CrossRef] [PubMed]

Other (3)

G. P. Agarwal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

H. M. Antia, Numerical Methods for Scientists and Engineers, 2nd ed. (Hindustan Book Agency, New Delhi, 2002).

J. B. Pawley, ed., Handbook of Biological Confocal Microscopy, 2nd ed. (Plenum, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

Geometry of photon collection by a fiber from an arbitrary point P(r, z). α is the acceptance angle and a is the radius of the fiber core. The solid angle subtended by the shaded area at P is proportional to the probability that a photon emitted from P will be collected by the fiber. θ and ϕ are the integration variables used for the solid-angle calculation. The partial annulus represents the integration area element.

Fig. 2
Fig. 2

Contour plot of normalized detectivity function D(r, z) [from Eq. (3)]. Contours are drawn at D values of 0.9–0.2 in increments of 0.1, with the darkest area representing 0.9. The fiber tip, with a core radius of 1.31 μm, is shown in white. The negative r quadrant is a reflection of the positive r quadrant.

Fig. 3
Fig. 3

Total fluorescence collected by a single-mode fiber as a function of the thickness of the fluorescent specimen (500-μM Rhodamine B solution) placed in front of it. Open circles, experimentally measured values. Values calculated neglecting absorption (solid curve), incorporating absorption of the excitation (short-dashed curve), and incorporating absorption of both the excitation and the fluorescence (long-dashed curve) by the specimen are also shown.

Equations (6)

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

Ir, z=2/πω2zexp-2r2/ω2z,
Ωr, z=2π 0γ1sin θdθ+γ1γ2sin θdθ 02π-2δdϕarΩr, z=γ1γ2sin θdθ 02π-2δdϕa<r, 
Dr, z=Ir, zΩr, z.
FZ=0Zdz 0 2πrDr, zdr.
Tλ, r, z=10-λcr2+z2,
Dcr, z=Ir, zTλex, r, zΩr, z×λ1λ2 ψRbλTλ, r, zdλ,

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