Abstract

Afterpulsing arises from feedback in a photon detector. This means that each real signal pulse can be followed by an afterpulse at a later time. This effect is particularly troubling in photon correlation experiments. Few treatments of this effect have appeared in the literature, and few software programs to solve the problem have been written. We demonstrate the afterpulsing effect in fluorescence correlation spectroscopy by using different avalanche photodiodes. We prove theoretically that under simple and reasonable conditions afterpulsing in autocorrelation can be eliminated to the leading order; we have found it easy to program software for the correction. We compare our results with those from cross correlation. We also discuss some experimental parameters that may affect the afterpulsing.

© 2003 Optical Society of America

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References

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  1. D. Madge, E. Elson, W. W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
    [CrossRef]
  2. E. L. Elson, D. Madge, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
    [CrossRef]
  3. D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
    [CrossRef]
  4. R. Rigler, U. 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]
  5. D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
    [CrossRef] [PubMed]
  6. H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
    [CrossRef] [PubMed]
  7. P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
    [CrossRef] [PubMed]
  8. D. Madge, “Chemical kinetics and fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 35–47 (1976).
    [CrossRef] [PubMed]
  9. M. Ehrenberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–401 (1974).
    [CrossRef]
  10. A. G. I. Palmer, N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52, 257–270 (1987).
    [CrossRef] [PubMed]
  11. H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
    [CrossRef] [PubMed]
  12. J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
    [CrossRef]
  13. P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
    [CrossRef] [PubMed]
  14. E. Overbeck, C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
    [CrossRef]
  15. H. C. Burstyn, J. V. Sengers, “Time dependence of critical concentration fluctuations in a binary liquid,” Phys. Rev. A 27, 1071–1085 (1983).
    [CrossRef]
  16. J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
    [CrossRef] [PubMed]
  17. M. Hobel, J. Ricka, “Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum. 65, 2326–2336 (1994).
    [CrossRef]
  18. H. C. Burstyn, “Afterpulsing effects in photon correlation experiments,” Rev. Sci. Instrum. 51, 1431–1433 (1980).
    [CrossRef]

2000 (1)

P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
[CrossRef] [PubMed]

1998 (1)

E. Overbeck, C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
[CrossRef]

1995 (1)

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
[CrossRef]

1994 (1)

M. Hobel, J. Ricka, “Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum. 65, 2326–2336 (1994).
[CrossRef]

1993 (1)

R. Rigler, U. 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]

1992 (2)

H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

1990 (1)

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

1987 (1)

A. G. I. Palmer, N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52, 257–270 (1987).
[CrossRef] [PubMed]

1983 (1)

H. C. Burstyn, J. V. Sengers, “Time dependence of critical concentration fluctuations in a binary liquid,” Phys. Rev. A 27, 1071–1085 (1983).
[CrossRef]

1980 (1)

H. C. Burstyn, “Afterpulsing effects in photon correlation experiments,” Rev. Sci. Instrum. 51, 1431–1433 (1980).
[CrossRef]

1977 (1)

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

1976 (2)

D. Madge, “Chemical kinetics and fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 35–47 (1976).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

1974 (3)

E. L. Elson, D. Madge, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef]

M. Ehrenberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–401 (1974).
[CrossRef]

1972 (1)

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

Axelrod, D.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Barak, L. S.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

Burstyn, H. C.

H. C. Burstyn, J. V. Sengers, “Time dependence of critical concentration fluctuations in a binary liquid,” Phys. Rev. A 27, 1071–1085 (1983).
[CrossRef]

H. C. Burstyn, “Afterpulsing effects in photon correlation experiments,” Rev. Sci. Instrum. 51, 1431–1433 (1980).
[CrossRef]

Cluzel, P.

P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
[CrossRef] [PubMed]

Durian, D. J.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Ehrenberg, M.

M. Ehrenberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–401 (1974).
[CrossRef]

Elson, E.

D. Madge, 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.

H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

E. L. Elson, D. Madge, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef]

Fahey, P. F.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

Frieden, C.

H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
[CrossRef] [PubMed]

Hobel, M.

M. Hobel, J. Ricka, “Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum. 65, 2326–2336 (1994).
[CrossRef]

Kask, P.

R. Rigler, U. 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]

Koppel, D. E.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Leibler, S.

P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
[CrossRef] [PubMed]

Madge, D.

D. Madge, “Chemical kinetics and fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 35–47 (1976).
[CrossRef] [PubMed]

E. L. Elson, D. Madge, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef]

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

Mets, U.

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
[CrossRef]

R. Rigler, U. 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]

Müller, J.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Overbeck, E.

E. Overbeck, C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
[CrossRef]

Palmer, A. G. I.

A. G. I. Palmer, N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52, 257–270 (1987).
[CrossRef] [PubMed]

Pine, D. J.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Qian, H.

H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

Ricka, J.

M. Hobel, J. Ricka, “Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum. 65, 2326–2336 (1994).
[CrossRef]

Rigler, R.

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
[CrossRef]

R. Rigler, U. 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]

M. Ehrenberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–401 (1974).
[CrossRef]

Schlessinger, J.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

Sengers, J. V.

H. C. Burstyn, J. V. Sengers, “Time dependence of critical concentration fluctuations in a binary liquid,” Phys. Rev. A 27, 1071–1085 (1983).
[CrossRef]

Sinn, C.

E. Overbeck, C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
[CrossRef]

Surette, M.

P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
[CrossRef] [PubMed]

Thompson, N. L.

A. G. I. Palmer, N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52, 257–270 (1987).
[CrossRef] [PubMed]

Webb, W. W.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef]

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

Weitz, D. A.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Widengren, J.

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
[CrossRef]

R. Rigler, U. 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]

Wolf, D. E.

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

Zhu, J. X.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Biophys. J. (3)

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of fluorescence marker concentration as a probe of mobility,” Biophys. J. 16, 1315–1329 (1976).
[CrossRef] [PubMed]

H. Qian, E. L. Elson, C. Frieden, “Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads,” Biophys. J. 63, 1000–1010 (1992).
[CrossRef] [PubMed]

A. G. I. Palmer, N. L. Thompson, “Molecular aggregation characterized by high order autocorrelation in fluorescence correlation spectroscopy,” Biophys. J. 52, 257–270 (1987).
[CrossRef] [PubMed]

Biopolymers (2)

E. L. Elson, D. Madge, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

D. Madge, E. L. Elson, W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers 13, 29–61 (1974).
[CrossRef]

Chem. Phys. (1)

M. Ehrenberg, R. Rigler, “Rotational Brownian motion and fluorescence intensity fluctuations,” Chem. Phys. 4, 390–401 (1974).
[CrossRef]

Eur. Biophys. J. (1)

R. Rigler, U. 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]

J. Phys. Chem. (1)

J. Widengren, U. Mets, R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13,368–13,379 (1995).
[CrossRef]

Phys. Rev. A (1)

H. C. Burstyn, J. V. Sengers, “Time dependence of critical concentration fluctuations in a binary liquid,” Phys. Rev. A 27, 1071–1085 (1983).
[CrossRef]

Phys. Rev. Lett. (2)

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

D. Madge, 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 (1)

H. Qian, E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. USA 87, 5479–5483 (1990).
[CrossRef] [PubMed]

Q. Rev. Biophys. (1)

D. Madge, “Chemical kinetics and fluorescence correlation spectroscopy,” Q. Rev. Biophys. 9, 35–47 (1976).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (3)

M. Hobel, J. Ricka, “Dead-time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum. 65, 2326–2336 (1994).
[CrossRef]

H. C. Burstyn, “Afterpulsing effects in photon correlation experiments,” Rev. Sci. Instrum. 51, 1431–1433 (1980).
[CrossRef]

E. Overbeck, C. Sinn, “Silicon avalanche photodiodes as detectors for photon correlation experiments,” Rev. Sci. Instrum. 69, 3515–3523 (1998).
[CrossRef]

Science (2)

P. Cluzel, M. Surette, S. Leibler, “An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells,” Science 287, 1652–1655 (2000).
[CrossRef] [PubMed]

P. F. Fahey, D. E. Koppel, L. S. Barak, D. E. Wolf, E. L. Elson, W. W. Webb, “Lateral diffusion in planar lipid bilayers,” Science 195, 305–306 (1977).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic illustrations of two FCS setups. The sample is excited with the laser beam focused by the objective. (a) Emitted fluorescence is detected by one APD and then autocorrelated by a digital correlator. (b) Emitted light is directed into two APDs by a beam splitter; then the outputs of the APDs are cross correlated by the correlator.

Fig. 2
Fig. 2

(a) Result of fitting of the afterpulsing pattern of APD1 by the second-order exponential decay model. (b) Result of fitting of the afterpulsing pattern of APD2 by the exponential decay model.

Fig. 3
Fig. 3

(a) Correlation of fluorescence beads’ light intensity with the afterpulsing effect acquired with APD1. (b) Corrected data of (a) compared with cross correlation.

Fig. 4
Fig. 4

(a) Correlation of fluorescence beads’ light intensity with the afterpulsing acquired with APD2 at a relatively low count rate of 1 kHz. (b) Corrected data of (a) compared with cross correlation.

Fig. 5
Fig. 5

Corrected autocorrelation curves acquired with APD1 and APD2. APD2 still performs better than APD1 after correction.

Fig. 6
Fig. 6

Afterpulsing patterns of APD1 acquired at several count rates.

Fig. 7
Fig. 7

Afterpulsing patterns of APD1 at several supply voltages.

Equations (19)

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

αeffτ=n=1 n pn1-p0 ατ,
pn=μnn!exp-μ.
αeffτατμ1-exp-μ=ατ.
it=it+-t αt-titdt=it+0 αtit-tdt.
i=i1+A,
A=0 αtdt.
Gτ=itit+τ=i0iτ
Gτ=i0iτ=i0iτ+0 αtiτ-ti0dt+0 αtiτ+ti0dt+00 αt1αt2iτ-t1+t2i0dt1dt2.
iti0=i-ti0,
Gτ=i0iτ+Δtατi02+0τ-Δt/2 αtiτ-ti0dt+τ+Δt/2 αtit-τi0dt+0 αtit+τi0dt.
Gτ=Gτ+ΔtατG0+Gτ0τ αtdt+τ Gt-ταtdt+Gτ0 αtdt =Gτ1+2A+ΔtατG0,
gτ=i0iτi2=i2+δi0δiτi2=1+δi0δiτi2,
i2=i21+A2i21+2A.
gτ=Gτi2=gτ+Δtατ1+2Ai02i2.
i02i21+1i.
i02i21μ.
gτ=gτ+Δtμ ατ.
δi0δiτ=δi02τ=00τ0,
gτ=1+Δti ατ τ0

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