Abstract

We present an alternative method for diffusion measurements of fluorescent species in solution by use of confocal microscopy and fluorescence correlation spectroscopy techniques. It consists of making a time and spatial dual correlation in which one detects the fluorescence signals from two nearby separate confocal volumes and cross correlates them. To improve the spatial discrimination between the two confocal volumes we propose filtering of fluorescence photocounts by rejecting the fluorescence background, which corresponds to particles located far from the center of the detection volumes.

© 2006 Optical Society of America

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References

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  1. R. Rigler and E. Elson, eds., Fluorescence Correlation Spectroscopy, Theory and Applications (Springer-Verlag, 2001).
  2. R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
    [CrossRef]
  3. J. Mertz, C. Xu, and W. Webb, "Single molecule detection by two-photon excited fluorescence," Opt. Lett. 20, 2532-2534 (1995).
  4. L. Edman, "Theory of fluorescence correlation spectroscopy on single molecules," J. Phys. Chem. A 104, 6165-6170 (2000).
    [CrossRef]
  5. N. L. Thompson, Fluorescence Correlation Spectroscopy, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1991).
  6. O. Krichevsky and G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep. Prog. Phys. 65, 251-297 (2002).
    [CrossRef]
  7. U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).
  8. K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).
  9. K. Bacia and P. Schwille, "A dynamics view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy," Methods 29, 74-85 (2002).
    [CrossRef]
  10. A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
    [CrossRef]
  11. M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
    [CrossRef]
  12. P. Dittrich and P. Schwille, "Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures," Anal. Chem. 74, 4472-4479 (2002).
    [CrossRef]
  13. H. Blom, M. Johansson, A.-S. Hedman, L. Lundberg, A. Hanning, S. Hard, and R. Rigler, "Parallel fluorescence detection of single biomolecules in microarrays by a diffractive-optical-designed 2 × 2 fan-out element," Appl. Opt. 41, 3336-3342 (2002).
  14. H. Blom, M. Johansson, M. Gosch, T. Sigmundsson, J. Holm, S. Hard, and R. Rigler, "Parallel flow measurements in microstructures by use of a multifocal 4 × 1 diffractive optical fan-out element," Appl. Opt. 41, 6614-6620 (2002).
  15. S. T. Hess and W. W. Webb, "Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy," Biophys. J. 83, 2300-2317 (2002).
  16. T. Wilson, "Fluorescence imaging modes in fibre-optic based confocal scanning microscopes," Opt. Commun. 96, 133-141 (1993).
    [CrossRef]
  17. T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).
  18. S. Aragon and R. Pecora, "Fluorescence correlation spectroscopy as a probe of molecular dynamics," J. Chem. Phys. 64, 1791-1803 (1976).
    [CrossRef]
  19. T. Wilson and A. Carlini, "Size of the detector in confocal imaging systems," Opt. Lett. 12, 227-229 (1987).
  20. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  21. H. Qian and E. Elson, "Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy," Appl. Opt. 30, 1185-1195 (1991).
  22. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980).
  23. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system." Proc. R. Soc. London Ser. A 253, 349-379 (1959).
  24. C. Sheppard and H. Matthews, "Imaging in high-aperture optical systems," J. Opt. Soc. Am. A 4, 1354-1360 (1987).
  25. R. Juskaitis and T. Wilson, "The measurement of the amplitude point spread function of microscope objective lenses," J. Microsc. 189, 8-11 (1998).
    [CrossRef]
  26. B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).
  27. B. Saleh, Photoelectron Statistics (Springer-Verlag, 1978).
  28. Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).
  29. J. Muller, "Cumulant analysis in fluorescence fluctuation spectroscopy," Biophys. J. 86, 3981-3992 (2004).
    [CrossRef]
  30. A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
    [CrossRef]
  31. L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
    [CrossRef]

2005 (1)

L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef]

2004 (3)

B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).

J. Muller, "Cumulant analysis in fluorescence fluctuation spectroscopy," Biophys. J. 86, 3981-3992 (2004).
[CrossRef]

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

2002 (8)

O. Krichevsky and G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep. Prog. Phys. 65, 251-297 (2002).
[CrossRef]

K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).

K. Bacia and P. Schwille, "A dynamics view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy," Methods 29, 74-85 (2002).
[CrossRef]

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

P. Dittrich and P. Schwille, "Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures," Anal. Chem. 74, 4472-4479 (2002).
[CrossRef]

H. Blom, M. Johansson, A.-S. Hedman, L. Lundberg, A. Hanning, S. Hard, and R. Rigler, "Parallel fluorescence detection of single biomolecules in microarrays by a diffractive-optical-designed 2 × 2 fan-out element," Appl. Opt. 41, 3336-3342 (2002).

H. Blom, M. Johansson, M. Gosch, T. Sigmundsson, J. Holm, S. Hard, and R. Rigler, "Parallel flow measurements in microstructures by use of a multifocal 4 × 1 diffractive optical fan-out element," Appl. Opt. 41, 6614-6620 (2002).

S. T. Hess and W. W. Webb, "Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy," Biophys. J. 83, 2300-2317 (2002).

2001 (1)

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).

2000 (1)

L. Edman, "Theory of fluorescence correlation spectroscopy on single molecules," J. Phys. Chem. A 104, 6165-6170 (2000).
[CrossRef]

1999 (3)

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

1998 (1)

R. Juskaitis and T. Wilson, "The measurement of the amplitude point spread function of microscope objective lenses," J. Microsc. 189, 8-11 (1998).
[CrossRef]

1995 (1)

1993 (2)

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

T. Wilson, "Fluorescence imaging modes in fibre-optic based confocal scanning microscopes," Opt. Commun. 96, 133-141 (1993).
[CrossRef]

1991 (1)

1987 (2)

1976 (1)

S. Aragon and R. Pecora, "Fluorescence correlation spectroscopy as a probe of molecular dynamics," J. Chem. Phys. 64, 1791-1803 (1976).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system." Proc. R. Soc. London Ser. A 253, 349-379 (1959).

Amediek, A.

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

Aragon, S.

S. Aragon and R. Pecora, "Fluorescence correlation spectroscopy as a probe of molecular dynamics," J. Chem. Phys. 64, 1791-1803 (1976).
[CrossRef]

Bacia, K.

K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).

K. Bacia and P. Schwille, "A dynamics view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy," Methods 29, 74-85 (2002).
[CrossRef]

Biben, T.

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

Blom, H.

Bonnet, G.

O. Krichevsky and G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep. Prog. Phys. 65, 251-297 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980).

Brinkmeier, M.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

Carlini, A.

Chen, Y.

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

Delon, A.

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

Derouard, J.

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

Dittrich, P.

P. Dittrich and P. Schwille, "Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures," Anal. Chem. 74, 4472-4479 (2002).
[CrossRef]

Dörre, K.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

Edman, L.

L. Edman, "Theory of fluorescence correlation spectroscopy on single molecules," J. Phys. Chem. A 104, 6165-6170 (2000).
[CrossRef]

Eggeling, C.

L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef]

Eigen, M.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

Elson, E.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gosch, M.

Gratton, E.

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

Hanning, A.

Hard, S.

Haustein, E.

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

Hedman, A.-S.

Hell, S.

L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef]

Hess, S. T.

S. T. Hess and W. W. Webb, "Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy," Biophys. J. 83, 2300-2317 (2002).

Holm, J.

Huang, B.

B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).

Johansson, M.

Juskaitis, R.

R. Juskaitis and T. Wilson, "The measurement of the amplitude point spread function of microscope objective lenses," J. Microsc. 189, 8-11 (1998).
[CrossRef]

Kask, P.

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

Kastrup, L.

L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef]

Krichevsky, O.

O. Krichevsky and G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep. Prog. Phys. 65, 251-297 (2002).
[CrossRef]

Lundberg, L.

Majoul, I.

K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).

Matthews, H.

Mertz, J.

Meseth, U.

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

Mets, U.

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

Muller, J.

J. Muller, "Cumulant analysis in fluorescence fluctuation spectroscopy," Biophys. J. 86, 3981-3992 (2004).
[CrossRef]

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

Pecora, R.

S. Aragon and R. Pecora, "Fluorescence correlation spectroscopy as a probe of molecular dynamics," J. Chem. Phys. 64, 1791-1803 (1976).
[CrossRef]

Perroud, T.

B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).

Qian, H.

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system." Proc. R. Soc. London Ser. A 253, 349-379 (1959).

Rigler, R.

H. Blom, M. Johansson, M. Gosch, T. Sigmundsson, J. Holm, S. Hard, and R. Rigler, "Parallel flow measurements in microstructures by use of a multifocal 4 × 1 diffractive optical fan-out element," Appl. Opt. 41, 6614-6620 (2002).

H. Blom, M. Johansson, A.-S. Hedman, L. Lundberg, A. Hanning, S. Hard, and R. Rigler, "Parallel fluorescence detection of single biomolecules in microarrays by a diffractive-optical-designed 2 × 2 fan-out element," Appl. Opt. 41, 3336-3342 (2002).

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

Saleh, B.

B. Saleh, Photoelectron Statistics (Springer-Verlag, 1978).

Scherfeld, D.

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

Schwille, P.

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

P. Dittrich and P. Schwille, "Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures," Anal. Chem. 74, 4472-4479 (2002).
[CrossRef]

K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).

K. Bacia and P. Schwille, "A dynamics view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy," Methods 29, 74-85 (2002).
[CrossRef]

Sheppard, C.

Sigmundsson, T.

So, P.

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

Souchier, C.

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

Stephan, J.

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

Thompson, N. L.

N. L. Thompson, Fluorescence Correlation Spectroscopy, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1991).

Usson, Y.

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

Vogel, H.

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

Webb, W.

Webb, W. W.

S. T. Hess and W. W. Webb, "Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy," Biophys. J. 83, 2300-2317 (2002).

Wilson, T.

R. Juskaitis and T. Wilson, "The measurement of the amplitude point spread function of microscope objective lenses," J. Microsc. 189, 8-11 (1998).
[CrossRef]

T. Wilson, "Fluorescence imaging modes in fibre-optic based confocal scanning microscopes," Opt. Commun. 96, 133-141 (1993).
[CrossRef]

T. Wilson and A. Carlini, "Size of the detector in confocal imaging systems," Opt. Lett. 12, 227-229 (1987).

Windengren, J.

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

Wohland, T.

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system." Proc. R. Soc. London Ser. A 253, 349-379 (1959).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980).

Xu, C.

Zare, R.

B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).

Anal. Chem. (2)

M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, "Two-beam cross-correlation: a method to characterize transport phenomena in Micrometer-sized structures," Anal. Chem. 71, 609-616 (1999).
[CrossRef]

P. Dittrich and P. Schwille, "Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures," Anal. Chem. 74, 4472-4479 (2002).
[CrossRef]

Appl. Opt. (3)

Biophys. J. (6)

Y. Chen, J. Muller, P. So, and E. Gratton, "The photon counting histogramme in fluorescence fluctuation spectroscopy," Biophys. J. 77, 553-567 (1999).

J. Muller, "Cumulant analysis in fluorescence fluctuation spectroscopy," Biophys. J. 86, 3981-3992 (2004).
[CrossRef]

S. T. Hess and W. W. Webb, "Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy," Biophys. J. 83, 2300-2317 (2002).

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

K. Bacia, I. Majoul, and P. Schwille, "Probing the endocytic pathway in live cells using dual-color fluorescence cross-correlation analysis," Biophys. J. 83, 1184-1193 (2002).

Chem. Phys. Chem. (1)

B. Huang, T. Perroud, and R. Zare, "Photon counting histogram: one-photon excitation," Chem. Phys. Chem. 5, 1523-1531 (2004).

Eur. Biophys. J. (1)

R. Rigler, U. Mets, J. Windengren, and P. Kask, "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion," Eur. Biophys. J. 22, 169-175 (1993).
[CrossRef]

J. Chem. Phys. (1)

S. Aragon and R. Pecora, "Fluorescence correlation spectroscopy as a probe of molecular dynamics," J. Chem. Phys. 64, 1791-1803 (1976).
[CrossRef]

J. Fluoresc. (1)

A. Delon, Y. Usson, J. Derouard, T. Biben, and C. Souchier, "Photobleaching, mobility and compartmentalisation: inferences in fluorescence correlation spectroscopy," J. Fluoresc. 14, 255-267 (2004).
[CrossRef]

J. Microsc. (1)

R. Juskaitis and T. Wilson, "The measurement of the amplitude point spread function of microscope objective lenses," J. Microsc. 189, 8-11 (1998).
[CrossRef]

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

J. Phys. Chem. A (1)

L. Edman, "Theory of fluorescence correlation spectroscopy on single molecules," J. Phys. Chem. A 104, 6165-6170 (2000).
[CrossRef]

Methods (1)

K. Bacia and P. Schwille, "A dynamics view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy," Methods 29, 74-85 (2002).
[CrossRef]

Opt. Commun. (1)

T. Wilson, "Fluorescence imaging modes in fibre-optic based confocal scanning microscopes," Opt. Commun. 96, 133-141 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

L. Kastrup, H. Blom, C. Eggeling, and S. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system." Proc. R. Soc. London Ser. A 253, 349-379 (1959).

Rep. Prog. Phys. (1)

O. Krichevsky and G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep. Prog. Phys. 65, 251-297 (2002).
[CrossRef]

Single Mol. (1)

A. Amediek, E. Haustein, D. Scherfeld, and P. Schwille, "Scanning dual-color cross-correlation analysis for dynamic co-colalization studies of immobile molecules," Single Mol. 3, 201-210 (2002).
[CrossRef]

Other (5)

N. L. Thompson, Fluorescence Correlation Spectroscopy, Vol. 1 of Topics in Fluorescence Spectroscopy, J. R. Lakowicz, ed. (Plenum, New York, 1991).

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

R. Rigler and E. Elson, eds., Fluorescence Correlation Spectroscopy, Theory and Applications (Springer-Verlag, 2001).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980).

B. Saleh, Photoelectron Statistics (Springer-Verlag, 1978).

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Figures (11)

Fig. 1
Fig. 1

Experimental setup for sFCCS.

Fig. 2
Fig. 2

Evolution of illumination I(uo , 0) and I(0, vo ) along the optical axis and in the lateral direction, respectively. All curves are normalized to unity. The maximum of illumination is 1.0 at the geometrical focal point (uo = 0, vo = 0). The value of underfilling fraction β is given for each curve. The dashed curves correspond to incident plane waves (large β). ou, optical units.

Fig. 3
Fig. 3

Optical geometry for sFCCS; a is the lateral shift between the two detection volumes, which are approximated by two ellipsoids in this representation.

Fig. 4
Fig. 4

cef(uo , vo ) pattern for two different pinhole radii: (a) si = 3.2 ou, (b) si = 4.0 ou. The amplitude is displayed on a log-base-10 gray-level scale. ou, optical units.

Fig. 5
Fig. 5

Comparison of several normalized W(u o, v o) profile images. All calculations used cef(u o, v o) and illumination I(u o, v o) as described in the text: (a) a filled illuminated configuration (β = 1), (b)–(d) an underfilled illuminated configuration (β = 0.1). For (c) and (d) we introduce lateral pinhole offsets of v o = 6 ou and 10 ou, respectively. The amplitude is displayed in a log base = 10 gray-level scale. ou, optical units.

Fig. 6
Fig. 6

Typical fluorescence photon counts recorded with one detector channel from a dilute solution of nanobeads.

Fig. 7
Fig. 7

Autocorrelation curves corresponding to the photon stream recorded with one of the two shifted pinholes as a function of thresholding frequency CR T : (a) initial signal without thresholding; (b) CR T = 10 kHz, (c) CR T = 20 kHz, (d) CR T = 40 kHz, (e) CR T = 80 kHz. The error bars are the standard error of the mean calculated from five different acquisitions. The superimposed solid curves are the result of least-square fits. The inset magnifies the autocorrelation curve without thresholding.

Fig. 8
Fig. 8

Thresholded number of molecules 〈N′〉 as a function of thresholding frequency CR T . Solid curve with small vertical error bars, values obtained by fitting the experimental autocorrelations curves (such as shown in Fig. 7). Dashed curve, result of the simulation that takes into account the discretization effect through the horizontal error bars. Inset, variation of the diffusion time obtained by fitting the experimental autocorrelation curves (such as shown in Fig. 7). For 〈N′〉 the error bars are sometimes smaller than the size of the data points.

Fig. 9
Fig. 9

Count rate CR′ as a function of thresholding frequency CR T . Solid curve with small vertical error bars, experimental data. Dashed curve with large horizontal error bars (discretization effect), result of the simulation. Inset, count rate per molecule (CRM) obtained by dividing experimental count rate CR′ by the number of molecules 〈N′〉 (obtained by fitting the experimental autocorrelation curves).

Fig. 10
Fig. 10

Cross-correlation curves for several values of thresholding CR T : (a) initial signal, (b) 20 kHz, (c) 40 kHz, (d) 60 kHz, (e) 120 kHz, (f) 200 kHz.

Fig. 11
Fig. 11

Fitting results for the cross-correlation curve according to threshold level CRT = 200 kHz. Solid curve, the experimental GCC (τ) curve. Filled circles, the total fit according to Eq. (25).

Equations (27)

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G A C ( τ ) = F ( t ) F ( t + τ ) F ( t ) 2 = δ F ( t ) δ F ( t + τ ) F 2 + 1 ,
G C C ( τ ) = F 1 ( r , z , t ) F 2 ( r , z , t + τ ) F 1 ( r , z , t ) F 2 ( r , z , t ) = δ F 1 ( r , z , t ) δ F 2 ( r , z , t + τ ) F 1 ( r , z ) F 2 ( r , z ) + 1.
F ( t ) = D i d Ω i P ( r i ) f i ( r i , z i , t ) = D i d Ω i P ( r i ) ( f o P S F ) ( r i , z i , t ) ,
f o ( r o , z o , t ) = κ I ( r o , z o ) C ( r o , z o , t ) ,
F ( t ) = κ S o d Ω o I ( r o , z o ) C ( r o , z o , t ) c e f ( r o , z o ) = κ S o d Ω o W ( r o , z o ) C ( r o , z o , t ) ,
c e f ( r o , z o ) = D i d Ω i P ( r i ) P S F ( r i r o , z i z o ) .
u o = 8 π λ n ( sin 2 θ 2 ) z o , u i = 8 π λ n ( sin 2 θ 2 ) z i M ,
v o = 2 π λ n ( sin θ ) r o , v i = 2 π λ n ( sin θ ) r i M ,
h ( u o , v o ) = C n    0 1 J 0 ( ρ v o ) exp ( 1 2 i u o ρ 2 ) × exp ( - ρ 2 β 2 ) ρ d ρ ,
c e f ( u o , v o ) = + 0 + 0 2 π v i d u i d v i | h ( u i u o , v i v o ) | 2 δ ( u i ) circ s i ( v i )
= 0 s i 0 2 π | h [ u o , ( v i     2 + v o     2 2 v i v o cos φ ) 1 / 2 ] | v i 2 d v i ,
Δ F 2 F 2 = Δ N 2 N 2 = 1 N .
Δ F 2 F F T 2 = Δ F 2 F 2 [ 1 - ( F T / F )] 2 = Δ F 2 F 2 .
N = N ( 1 F T F ) 2 .
P N ( N ) = N N N ! exp ( N ) .
P ε N ( k ) = ε N k k ! exp ( ε N ) .
P N , ε ( k ) = N = 0 P N ( N ) P ε N ( k ) .
N = k 2 Δ k 2 k .
P N , ε ( k > 0 ) = P N , ε ( k T + k ) ,
P N , ε ( k = 0 ) = k = 0 k T P N , ε ( k ) .
C R = k δ t ,
N = k 2 Δ k 2 k .
CR i = n i / ( Δ t i 1 , i + Δ t i , i + 1 2 ) .
CR i CR T n i = 0 ,
CR i > CR T n i = n i CR T Δ t i 1 , i + Δ t i , i + 1 2 .
G A C ( τ ) = 1 + 1 N ( 1 + τ τ d ) 1 ( 1 + τ S 2 τ d ) 1 / 2 [ 1 + T e q 1 T e q exp ( τ τ T ) ] .
G C C ( τ ) = 1 + 1 N [ P ( 1 + τ τ a c ) 3 / 2 + ( 1 P ) ( 1 + τ τ d ) 1 ( 1 + τ S 2 τ d ) 1 / 2     exp { a 2 ω o     2 ( 1 + τ τ d ) 1 } ] .

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