Abstract

Fluorescence correlation spectroscopy is a valuable tool in many scientific disciplines. In particular, such a spectroscopic technique has received a great deal of attention because of its remarkable potential for single-molecule detection. It is understood, however, that quantitative measurements can be considered reliable as long as molecular photophysics has been well characterized. To that end, molecular saturation and probe volume effects, which can worsen experimental accuracy, are treated here. These phenomena are adequately incorporated into the well-known three-dimensional Gaussian approximation by a novel method applied to interpret saturated fluorescence signals [Opt. Lett. 28, 2016 (2003)]. Comparisons with literature data are given to show the improvements of the suggested method compared with other approaches.

© 2004 Optical Society of America

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References

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  1. W. Demtröder, Laser Spectroscopy (Springer-Verlag, Berlin, 2003).
    [CrossRef]
  2. R. Rigler, E. S. Elson, eds., Fluorescence Correlation Spectroscopy (Springer-Verlag, Berlin, 2001).
    [CrossRef]
  3. W. E. Moerner, M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
    [CrossRef] [PubMed]
  4. N. L. Thompson, “Fluorescence correlation spectroscopy,” in Techniques, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York1991).
  5. D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system: measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
    [CrossRef]
  6. S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
    [CrossRef] [PubMed]
  7. S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
    [CrossRef] [PubMed]
  8. J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon-excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
    [CrossRef] [PubMed]
  9. Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
    [CrossRef] [PubMed]
  10. D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
    [CrossRef] [PubMed]
  11. W. W. Webb, “Fluorescence correlation spectroscopy: inception, biophysical experimentations, and prospectus,” Appl. Opt. 40, 3969–3983 (2001).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989).
  13. R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1983).
  14. R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
    [CrossRef]
  15. J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
    [CrossRef]
  16. T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
    [CrossRef]
  17. J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
    [CrossRef]
  18. J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4, 149–157 (1996).
    [CrossRef]
  19. Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
    [CrossRef]
  20. J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D 3, 53–66 (1998).
    [CrossRef]
  21. D. L. Burden, J. J. Kasianowicz, “Diffusion bias and photophysical dynamics of single molecules in unsupported lipid bilayer membranes probed with confocal microscopy,” J. Phys. Chem. B 104, 6103–6107 (2000).
    [CrossRef]
  22. P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–837 (2001).
    [CrossRef]
  23. K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
    [CrossRef] [PubMed]
  24. K. Berland, G. Shen, “Excitation saturation in two-photon fluorescence correlation spectroscopy,” Appl. Opt. 42, 5566–5576 (2003).
    [CrossRef] [PubMed]
  25. H. Qian, E. L. Elson, “Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy,” Appl. Opt. 30, 1185–1195 (1991).
    [CrossRef] [PubMed]
  26. In principle K = 0, but some authors have considered a nonvanishing background in their fitting routines.17 To keep the formalism as general as possible, the constant K has been used here.
  27. M. Marrocco, “Spatial laser-wing suppression in saturated laser-induced fluorescence without spatial discrimination,” Opt. Lett. 28, 2016–2018 (2003).
    [CrossRef] [PubMed]
  28. J. W. Daily, “Saturation of fluorescence in flames with a Gaussian laser beam,” Appl. Opt. 17, 225–229 (1978).
    [CrossRef] [PubMed]
  29. G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
    [CrossRef]
  30. Note that the modified Bessel function is usually written as In(x), where n denotes the order. But the notation Ben(x) has been adopted in the text to prevent confusion with laser intensity I0.
  31. S. Wolfram, ed., The Mathematica Book, 3rd ed. (Cambridge U. Press, Cambridge, 1996), pp. 872–879.

2003 (3)

2002 (2)

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

2001 (3)

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–837 (2001).
[CrossRef]

Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
[CrossRef] [PubMed]

W. W. Webb, “Fluorescence correlation spectroscopy: inception, biophysical experimentations, and prospectus,” Appl. Opt. 40, 3969–3983 (2001).
[CrossRef]

2000 (1)

D. L. Burden, J. J. Kasianowicz, “Diffusion bias and photophysical dynamics of single molecules in unsupported lipid bilayer membranes probed with confocal microscopy,” J. Phys. Chem. B 104, 6103–6107 (2000).
[CrossRef]

1999 (1)

W. E. Moerner, M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

1998 (1)

J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D 3, 53–66 (1998).
[CrossRef]

1997 (2)

Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
[CrossRef]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[CrossRef] [PubMed]

1996 (1)

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4, 149–157 (1996).
[CrossRef]

1995 (3)

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon-excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
[CrossRef] [PubMed]

1994 (1)

J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
[CrossRef]

1993 (1)

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

1991 (1)

1990 (1)

G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
[CrossRef]

1978 (1)

1972 (1)

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

Benecchi, S.

G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
[CrossRef]

Berland, K.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989).

Burden, D. L.

D. L. Burden, J. J. Kasianowicz, “Diffusion bias and photophysical dynamics of single molecules in unsupported lipid bilayer membranes probed with confocal microscopy,” J. Phys. Chem. B 104, 6103–6107 (2000).
[CrossRef]

Cignoli, F.

G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
[CrossRef]

Daily, J. W.

Demel, U.

Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
[CrossRef] [PubMed]

Demtröder, W.

W. Demtröder, Laser Spectroscopy (Springer-Verlag, Berlin, 2003).
[CrossRef]

Dittrich, P. S.

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–837 (2001).
[CrossRef]

Elson, E.

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

Elson, E. L.

Földes-Papp, Z.

Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
[CrossRef] [PubMed]

Haupts, U.

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[CrossRef] [PubMed]

Heikal, A. A.

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

Heinze, K. G.

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

Hess, S. T.

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

Huang, S.

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

Jahnz, M.

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

Kasianowicz, J. J.

D. L. Burden, J. J. Kasianowicz, “Diffusion bias and photophysical dynamics of single molecules in unsupported lipid bilayer membranes probed with confocal microscopy,” J. Phys. Chem. B 104, 6103–6107 (2000).
[CrossRef]

Kask, P.

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Keller, S.

D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1983).

Lumma, D.

D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
[CrossRef] [PubMed]

Magde, D.

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

Maiti, S.

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[CrossRef] [PubMed]

Marrocco, M.

Mertz, J.

J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D 3, 53–66 (1998).
[CrossRef]

J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon-excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
[CrossRef] [PubMed]

Mets, Ü.

Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
[CrossRef]

J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
[CrossRef]

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Moerner, W. E.

W. E. Moerner, M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

Orrit, M.

W. E. Moerner, M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

Palm, V.

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

Plakhotnik, T.

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

Qian, H.

Rädler, J. R.

D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
[CrossRef] [PubMed]

Rarbach, M.

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

Rigler, R.

Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
[CrossRef]

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4, 149–157 (1996).
[CrossRef]

J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
[CrossRef]

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Schwille, P.

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–837 (2001).
[CrossRef]

Shen, G.

Thompson, N. L.

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Techniques, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York1991).

Tilz, G. P.

Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
[CrossRef] [PubMed]

Vilgis, T.

D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
[CrossRef] [PubMed]

Webb, W. W.

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

W. W. Webb, “Fluorescence correlation spectroscopy: inception, biophysical experimentations, and prospectus,” Appl. Opt. 40, 3969–3983 (2001).
[CrossRef]

S. Maiti, U. Haupts, W. W. Webb, “Fluorescence correlation spectroscopy: diagnostics for sparse molecules,” Proc. Natl. Acad. Sci. USA 94, 11753–11757 (1997).
[CrossRef] [PubMed]

J. Mertz, C. Xu, W. W. Webb, “Single-molecule detection by two-photon-excited fluorescence,” Opt. Lett. 20, 2532–2534 (1995).
[CrossRef] [PubMed]

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

Widengren, J.

Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
[CrossRef]

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4, 149–157 (1996).
[CrossRef]

J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
[CrossRef]

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Wild, U. P.

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989).

Xu, C.

Zizak, G.

G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (2)

G. Zizak, F. Cignoli, S. Benecchi, “A complete treatment of a steady-state 4-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric-pressure flames,” Appl. Phys. B 51, 67–70 (1990).
[CrossRef]

P. S. Dittrich, P. Schwille, “Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and two-photon excitation,” Appl. Phys. B 73, 829–837 (2001).
[CrossRef]

Biochemistry (1)

S. T. Hess, S. Huang, A. A. Heikal, W. W. Webb, “Biological and chemical applications of fluorescence correlation spectroscopy: a review,” Biochemistry 41, 697–705 (2002).
[CrossRef] [PubMed]

Bioimaging (1)

J. Widengren, R. Rigler, “Mechanisms of photobleaching investigated by fluorescence correlation spectroscopy,” Bioimaging 4, 149–157 (1996).
[CrossRef]

Biophys. J. (1)

K. G. Heinze, M. Rarbach, M. Jahnz, P. Schwille, “Two-photon fluorescence coincidence analysis: rapid measurements of enzyme kinetics,” Biophys. J. 83, 1671–1681 (2002).
[CrossRef] [PubMed]

Chem. Phys. (1)

Ü. Mets, J. Widengren, R. Rigler, “Application of the antibunching in dye fluorescence: measuring the excitation rates in solution,” Chem. Phys. 218, 191–198 (1997).
[CrossRef]

Eur. Biophys. J. (1)

R. Rigler, Ü. Mets, J. Widengren, P. Kask, “Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169–175 (1993).
[CrossRef]

Eur. Phys. J. D (1)

J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D 3, 53–66 (1998).
[CrossRef]

J. Fluoresc. (1)

J. Widengren, R. Rigler, Ü. Mets, “Triplet-state monitoring by fluorescence correlation spectroscopy,” J. Fluoresc. 4, 255–258 (1994).
[CrossRef]

J. Phys. Chem. (1)

J. Widengren, Ü. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995).
[CrossRef]

J. Phys. Chem. B (1)

D. L. Burden, J. J. Kasianowicz, “Diffusion bias and photophysical dynamics of single molecules in unsupported lipid bilayer membranes probed with confocal microscopy,” J. Phys. Chem. B 104, 6103–6107 (2000).
[CrossRef]

Opt. Commun. (1)

T. Plakhotnik, W. E. Moerner, V. Palm, U. P. Wild, “Single molecule spectroscopy: maximum emission rate and saturation intensity,” Opt. Commun. 114, 83–88 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

D. Lumma, S. Keller, T. Vilgis, J. R. Rädler, “Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 90, 218301 (2003).
[CrossRef] [PubMed]

D. Magde, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting 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, 11753–11757 (1997).
[CrossRef] [PubMed]

Z. Földes-Papp, U. Demel, G. P. Tilz, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. USA 98, 11509–11514 (2001).
[CrossRef] [PubMed]

Science (1)

W. E. Moerner, M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

Other (8)

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Techniques, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York1991).

W. Demtröder, Laser Spectroscopy (Springer-Verlag, Berlin, 2003).
[CrossRef]

R. Rigler, E. S. Elson, eds., Fluorescence Correlation Spectroscopy (Springer-Verlag, Berlin, 2001).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989).

R. Loudon, The Quantum Theory of Light (Oxford U. Press, New York, 1983).

In principle K = 0, but some authors have considered a nonvanishing background in their fitting routines.17 To keep the formalism as general as possible, the constant K has been used here.

Note that the modified Bessel function is usually written as In(x), where n denotes the order. But the notation Ben(x) has been adopted in the text to prevent confusion with laser intensity I0.

S. Wolfram, ed., The Mathematica Book, 3rd ed. (Cambridge U. Press, Cambridge, 1996), pp. 872–879.

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Figures (9)

Fig. 1
Fig. 1

Relative deviation R as obtained from Eq. (21). The horizontal scale has been adjusted to match the horizontal scale of Fig. 9 of Ref. 20.

Fig. 2
Fig. 2

Power dependence of the two-photon induced fluorescence as predicted by standard theory, Ref. 24 [or Eq. (17) in this paper], and this work.

Fig. 3
Fig. 3

Surface plots of the emission function for standard TPE FCS (n = 2): (a) φGL(r, z) in Eq. (7) but with no contribution of pinhole function CEF(r, z) and (b) φ3DG(r, z) in Eq. (9). The parameters are z 0/w 0 = 2 and z 1 = 1.7z 0. The two surfaces are very similar, which demonstrates the goodness of the 3DG approximation.

Fig. 4
Fig. 4

Surface plots of (a) φGL sat(r, z), (b) φ3DG sat(r, z), and (c) φBS(r, z) for TPE FCS when I 0 = I th. The parameters are taken from Fig. 3.

Fig. 5
Fig. 5

Surface plots of (a) φGL sat(r, z), (b) φ3DG sat(r, z), and (c) φBS(r, z) for TPE FCS when I 0 = 5I th. The parameters are taken from Fig. 3.

Fig. 6
Fig. 6

Fig. 6. G sat(τ)/G D (τ) as a function of t = τ/τ D for OPE FCS (n = 1). Values of parameter μ (=I 0/I th) are shown.

Fig. 7
Fig. 7

Fig. 7. G sat(τ)/G D (τ) as a function of t = τ/τ D for TPE FCS (n = 2). Values of parameter μ (=I 0/I th) are shown.

Fig. 8
Fig. 8

Coincidence between G sat(τ) in Eq. (24) and G WMR(τ) in Eq. (14). Standard correlation G D (τ) given in Eq. (11), i.e., without corrections for volume effects, is shown as well for OPE FCS (n = 1). The amplitude of G D (τ) was arbitrarily chosen and determines the normalization of G sat(τ) drawn for μ = 1. One reaches the coincidence between G sat(τ) and G WMR(τ) by varying the fitting parameters in G WMR(τ). Additionally, many combinations of these parameters are found to reproduce the behavior of G sat(τ).

Fig. 9
Fig. 9

Comparison of G sat(τ) given in Eq. (24) with G BS(τ) shown in Eq. (18). The physical parameters are taken from Fig. 4.

Equations (35)

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Gτ=δFt+τδFtFt2,
δFt=Ft-F=k  δCr, tφrdr,
Gτ= δCr, t+τδCr, tφrφrdrdrC  φrdr2,
Veff= φrdr2 φ2rdr.
φr=CEFrEr,
Ir=I0exp-2r2/w2z1+z/z02,
φGLr, z=I0nCEFr, zexp-2nr2/w2z1+z/z02n,
Ir, zI3DGr, z=I0 exp-2r2/w02+z2/z12.
φGLr, zφ3DGr, z=I0n exp-2nr2/w02+z2/z12.
δCr, t+τδCr, t=C4πDτ-3/2×exp-r-r2/4πDτ,
GDτ=GD011+τ/τD11+w0/z12τ/τD1/2,
GD0=1/N,
Gτ=GDτΓτ+K,
GWMRτ=GD0A 11+τ/τ1D11+w0/z12τ/τ1D1/2+1-A11+τ/τ2D11+w0/z12τ/τ2D1/2,
φBSr, z=I02 exp-4r2/w02+z2/z12-Is2 exp-4r2/ws2+z2/zs2.
α=Is2I02=ws2w02=zs2z02=I02-Ith2I02,
F=kCI02V3DGI0IthkCI02V3DG1-α5/2I0>Ith,
GBSτ=GD01-α5/2211+τ/τD1+w0/z12τ/τD1/2+α7/21+τ/ατD1+w0/z12τ/ατD1/2-42α1+1/α+2τ/ατD1+1/α+2w0/z12τ/ατD1/2.
dFdI0=πkCw022I0-zinfzsup φ0, zdz,
F=F0 log1+I0/Ithn,
R=log1+I0/Ith2I0/Ith2.
φ3DGsatr, z=I0nexp-2nr2/w02+z2/z121+I0/Ithn exp-2nr2/w02.
φGLsatr, z=I0nexp-2nr2/w2z/1+z/z02n1+I0/Ithn exp-2nr2/w2z/1+z/z02n.
Gsatτ=n3/2π3/2w02z1Cμ-n/tlog21+μnMnμ, tt1+tw02/z121/2,
Mnμ, t=0μn0μnx11/2t1+x1x21/2t1+x2 Be0logx1μ-nlogx2μ-n1/2/tdx1dx2,
Gsatτ=GDτ1+ttμ-n/tlog21+μnMnμ, t.
F=kC  φrdr=2πkC 0rmax-zinfzsup φr, zrdrdz,
F=π2 kCw020I0-zinfzsupΦψζzψdψdz,
dFdI0=πkCw022I0-zinfzsup ΦI0ζzdz,
φ0, z=φ3DG0, z=I0n exp-2nz2/z12,
FlowI0=π2n3/2kCw02z1I0n=kCI0nV3DG,
FhighI0=πkCw02β logI0/Ith,
F=0 I0=0, F=FlowI0 I0  Ith, F=FhighI0 I0  Ith,
F=πkCw02βn log1+I0/Ithn,
F=π/2n3/2kCw02z1Ith2log1+I0/Ithn,

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