Abstract

We present a fluorescence correlation spectroscopy setup based on a software correlator. The setup can process autocorrelation curves in real-time at countrate as high as 8MHz, with time resolution of 1µs. It uses the F2Cor autocorrelation algorithm, a low cost counting board and a desktop computer. Symmetrical normalization, which improves the signal to noise ratio of the FCS curve for large values of the lag-time, is adapted to the F2Cor algorithm. A new acquisition mode, which we call oscilloscope-mode, is presented. It takes advantage of the flexibility F2Cor, and proves to be very useful for optical setup adjustment. As an application of this setup, we performed FCS measurements on a reference tetramethylrhodamine solution at high concentration, up to 2.5µM, which extend to the micromolar range the concentration applicable in FCS, using a conventional optical setup. At such high countrates the FCS curves need to be corrected for dead-time of the photo-detector, which was done successfully.

© 2013 Optical Society of America

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References

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  1. E. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers13(1), 1–27 (1974).
    [CrossRef]
  2. D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
    [CrossRef] [PubMed]
  3. P. Schwille and J. Ries, “Principles and applications of fluorescence correlation spectroscopy (FCS),” in Biophotonics: Spectroscopy, Imaging, Sensing, and Manipulation (Springer, 2011), pp. 63–85.
  4. ALV-5000 multiple tau digital correlator reference manual (ALV gmbh, 1993).
  5. T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett.31(6), 829–831 (2006).
    [CrossRef] [PubMed]
  6. D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt.40(24), 4011–4021 (2001).
    [CrossRef] [PubMed]
  7. D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum.74(2), 1135–1144 (2003).
    [CrossRef]
  8. M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Express11(26), 3583–3591 (2003).
    [CrossRef] [PubMed]
  9. L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
    [CrossRef] [PubMed]
  10. K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B42, 193–213 (1987).
    [CrossRef]
  11. W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).
  12. J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
    [CrossRef]
  13. E. Schaub, “F2Cor: fast 2-stage correlation algorithm for FCS and DLS,” Opt. Express20(3), 2184–2195 (2012).
    [CrossRef] [PubMed]
  14. DMA Performance Improvements for TIO-based Devices,” http://digital.ni.com/public.nsf/allkb/1B64310FAE9007C086256A1D006D9BBF .
  15. S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
    [CrossRef] [PubMed]
  16. K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
    [CrossRef]
  17. T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
    [CrossRef] [PubMed]
  18. D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A10(6), 1938–1945 (1974).
    [CrossRef]
  19. L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
    [CrossRef] [PubMed]
  20. J. Wenger, D. Gérard, P. F. Lenne, H. Rigneault, J. Dintinger, T. W. Ebbesen, A. Boned, F. Conchonaud, and D. Marguet, “Dual-color fluorescence cross-correlation spectroscopy in a single nanoaperture : towards rapid multicomponent screening at high concentrations,” Opt. Express14(25), 12206–12216 (2006).
    [CrossRef] [PubMed]
  21. Z. Petrasek and P. Schwille, “Scanning fluorescence correlation spectroscopy,” in Single Molecules and Nanotechnology (Springer, 2008), pp. 83–105.

2012 (1)

2010 (1)

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

2009 (1)

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

2008 (1)

W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).

2007 (1)

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

2006 (2)

2003 (2)

D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum.74(2), 1135–1144 (2003).
[CrossRef]

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Express11(26), 3583–3591 (2003).
[CrossRef] [PubMed]

2001 (2)

D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt.40(24), 4011–4021 (2001).
[CrossRef] [PubMed]

T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
[CrossRef] [PubMed]

2000 (1)

J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
[CrossRef]

1988 (1)

K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
[CrossRef]

1987 (1)

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B42, 193–213 (1987).
[CrossRef]

1974 (3)

E. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers13(1), 1–27 (1974).
[CrossRef]

D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
[CrossRef] [PubMed]

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A10(6), 1938–1945 (1974).
[CrossRef]

Boned, A.

Chang, Y. R.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Conchonaud, F.

Dintinger, J.

Drewel, M.

K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
[CrossRef]

Ebbesen, T. W.

Eid, J. S.

J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
[CrossRef]

Elson, E.

E. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers13(1), 1–27 (1974).
[CrossRef]

Elson, E. L.

D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
[CrossRef] [PubMed]

Enderlein, J.

Fallica, G.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Fann, W.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Ferri, F.

D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum.74(2), 1135–1144 (2003).
[CrossRef]

D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt.40(24), 4011–4021 (2001).
[CrossRef] [PubMed]

Fore, S.

Gérard, D.

Gratton, E.

J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
[CrossRef]

Gregor, I.

Heinze, K. G.

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

Hsu, K. H.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Huser, T.

Kim, S. A.

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

Koppel, D. E.

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A10(6), 1938–1945 (1974).
[CrossRef]

Laurence, T. A.

Lee, H. Y.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Lenne, P. F.

Lin, X. Y.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Liu, W.

W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).

Magatti, D.

D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum.74(2), 1135–1144 (2003).
[CrossRef]

D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt.40(24), 4011–4021 (2001).
[CrossRef] [PubMed]

Magde, D.

D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
[CrossRef] [PubMed]

E. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers13(1), 1–27 (1974).
[CrossRef]

Marguet, D.

Mazzillo, M.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Muller, J. D.

J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
[CrossRef]

Musumeci, F.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Neri, L.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Patting, M.

Rigler, R.

T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
[CrossRef] [PubMed]

Rigneault, H.

Schätzel, K.

K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
[CrossRef]

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B42, 193–213 (1987).
[CrossRef]

Schaub, E.

Schwille, P.

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

Scordino, A.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Shen, J.

W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).

Stimac, S.

K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
[CrossRef]

Sun, X.

W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).

Tudisco, S.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Vogel, H.

T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
[CrossRef] [PubMed]

Wahl, M.

Wang, M. K.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Webb, W. W.

D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
[CrossRef] [PubMed]

Wenger, J.

White, J. D.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Wohland, T.

T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
[CrossRef] [PubMed]

Yang, L. L.

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

Zimbone, M.

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B42, 193–213 (1987).
[CrossRef]

Biophys. J. (1)

T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J.80(6), 2987–2999 (2001).
[CrossRef] [PubMed]

Biopolymers (2)

E. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers13(1), 1–27 (1974).
[CrossRef]

D. Magde, E. L. Elson, and W. W. Webb, “Fluorescence correlation spectroscopy. II. An experimental realization,” Biopolymers13(1), 29–61 (1974).
[CrossRef] [PubMed]

Design of multiple-tau photon correlation system implemented by FPGA (1)

W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” Software and Systems, 410-414 (2008).

J. Microsc. (1)

L. L. Yang, H. Y. Lee, M. K. Wang, X. Y. Lin, K. H. Hsu, Y. R. Chang, W. Fann, and J. D. White, “Real-time data acquisition incorporating high-speed software correlator for single-molecule spectroscopy,” J. Microsc.234(3), 302–310 (2009).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

K. Schätzel, M. Drewel, and S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt.35(4), 711–718 (1988).
[CrossRef]

Nat. Methods (1)

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A10(6), 1938–1945 (1974).
[CrossRef]

Rev. Sci. Instrum. (3)

L. Neri, S. Tudisco, F. Musumeci, A. Scordino, G. Fallica, M. Mazzillo, and M. Zimbone, “Note: Dead time causes and correction method for single photon avalanche diode devices,” Rev. Sci. Instrum.81(8), 086102–086103 (2010).
[CrossRef] [PubMed]

D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum.74(2), 1135–1144 (2003).
[CrossRef]

J. S. Eid, J. D. Muller, and E. Gratton, “Data acquisition card for fluctuation correlation spectroscopy allowing full access to the detected photon sequence,” Rev. Sci. Instrum.71(2), 361–368 (2000).
[CrossRef]

Other (4)

DMA Performance Improvements for TIO-based Devices,” http://digital.ni.com/public.nsf/allkb/1B64310FAE9007C086256A1D006D9BBF .

P. Schwille and J. Ries, “Principles and applications of fluorescence correlation spectroscopy (FCS),” in Biophotonics: Spectroscopy, Imaging, Sensing, and Manipulation (Springer, 2011), pp. 63–85.

ALV-5000 multiple tau digital correlator reference manual (ALV gmbh, 1993).

Z. Petrasek and P. Schwille, “Scanning fluorescence correlation spectroscopy,” in Single Molecules and Nanotechnology (Springer, 2008), pp. 83–105.

Supplementary Material (2)

» Media 1: AVI (1978 KB)     
» Media 2: AVI (4998 KB)     

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Figures (8)

Fig. 1
Fig. 1

Optical setup. The 561nm laser beam is focused into the dye solution using a 1.2NA water immersion x60 objective. The fluorescence signal is collected by the same objective. It is transmitted by the acousto-optic beam splitter (AOBS) and it is focused onto the confocal pinhole. The fluorescence passes trough a 570-625 nm band-pass interference filter. It is focused onto the core of a multimode optical fiber and detected by a single photon avalanche photodiode (SPAD).

Fig. 2
Fig. 2

Diagram of the acquisition chain. It contains a single photon avalanche diode (SPAD), and a computer equipped with a PCI counter board (NI PCI6602). LabVIEW manages the acquisition and the user interface and uses the F2Cor library to compute the autocorrelation function (ACF).

Fig. 3
Fig. 3

(Media 1). ACF curve. In this example the countrate is about 8.4 MHz. The first point of the ACF (1µs lag time) is lower because of the dead-time of the SPAD, which cannot be neglected at such a high countrate. Media 1 shows the real-time FCS curve display at high countrate, and the subsequent fitting of the curve.

Fig. 4
Fig. 4

Effect of the symmetrical normalization on the ACF of simulated shot noise signals (countrate of 1MHz, signal duration of 10s). (a) ACF of 3 simulations without symmetrical normalization. (b) ACF of 3 simulations with symmetrical normalization. (c) Standard deviation obtained from 10 simulations without symmetrical normalization (yellow) and with symmetrical normalization (white). (d) Improvement of the signal-to-noise ratio provided by the symmetrical normalization, expressed as the ratio between the standard deviation of the ACF with symmetrical normalization to that without symmetrical normalization.

Fig. 5
Fig. 5

(Media 2). Brightness display of the user interface operating in the oscilloscope mode, which shows the fluctuations of the molecular brightness while adjusting the correction collar. Media 2 shows the real-time optimization procedure by adjusting the correction collar and the pinhole diameter. The curves are refreshed every 0.1s, and the ACF is calculated over a 2s sliding window.

Fig. 6
Fig. 6

FCS measurements of TMR solutions in water for a concentration range of 0.5-2.5µM. The excitation power is 4µW at the sample and the measurement time is 60s. To normalize the ACF with respect to the number of molecules in the observation volume, the ACF is multiplied by the concentration. The curves don't superimpose because of the dead-time of the SPAD. The inset shows the correlation time which is constant as a function of the concentration.

Fig. 7
Fig. 7

Measured countrate as a function of the concentration of the TMR dye solutions.

Fig. 8
Fig. 8

FCS measurements of TMR with correction for the dead-time effect. All curves superimpose. The curve for 2.5µM slightly deviates from the average because the validity condition of the correction is not well respected. The inset shows the particle number as a function of the concentration before (⬜) and after (⬛) dead-time correction. In this latter case the dependency is linear.

Equations (18)

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

{ τ n } n=1,,8 k max +15 ={ 2 k l| l{ 1,2,,15 } for k=0 l{ 8,9,,15 } for 1k k max }={ 1,2,,15, 16,18,,30, 32,36,,60, , 8× 2 k max ,,15× 2 k max },
2 k mΔ t 0 t< 2 k ( m+1 )Δ t 0 . I k,m = i=0 2 k 1 I( 2 k m+i ) .
G B&M ( τ= 2 k l )= 1 L/ 2 k l m=0 L/ 2 k l1 I k,m I k,m+l ,
G Tr ( τ= 2 k l )= G 0 ( τ )+ i=1 2 k 1 2 k i 2 k ( G 0 ( τi )+ G 0 ( τ+i ) ) ,
g( τ )= I( n )I( n+τ ) I( n ) 2 .
g ^ sym ( τ )= 1 Lτ i=0 Lτ1 I( i )I( i+τ ) ( 1 Lτ i=0 Lτ1 I( i ) )( 1 Lτ i=0 Lτ1 I( i+τ ) ) .
g ^ B&M ( τ= 2 k l )= G B&M ( τ ) M dir ( τ ) M del ( τ ) ,
M dir ( τ= 2 k l )=( 1 L/ 2 k l m=0 L/ 2 k l1 I k,m ) M del ( τ= 2 k l )=( 1 L/ 2 k l m=0 L/ 2 k l1 I k,m+l ).
g ^ Tr ( τ= 2 k l )= ( 2 k /( Lτ ) ) G Tr ( τ ) M dir ( τ ) M del ( τ ) .
g ^ ( τ= 2 k l )={ g ^ Tr ( τ ) for k<K g ^ B&M ( τ ) for kK .
g ^ ΔT ( τ= 2 k l )= 1 L/ 2 k ( LΔT )/ 2 k m= ( LΔT )/ 2 k l L/ 2 k l1 I k,m I k,m+l ( m= ( LΔT )/ 2 k l L/ 2 k l1 I k,m L/ 2 k ( LΔT )/ 2 k )( m= ( LΔT )/ 2 k l L/ 2 k l1 I k,m+l L/ 2 k ( LΔT )/ 2 k ) .
Let G ΔT,Tr ( τ )= G ΔT,0 ( τ )+ i=1 2 k 1 2 k i 2 k ( G ΔT,0 ( τi )+ G ΔT,0 ( τ+i ) ) ,
G ΔT,Tr ( τ )= G Tr ( τ,L ) G Tr ( τ,Lτ ).
R( τ= 2 k l,L )={ 2 k ( L/ 2 k ( LΔT )/ 2 k ) ΔT G Tr ( τ,L )if k<K m=0 L/ 2 k l1 I k,m I k,m+l if kK S dir ( τ= 2 k l,L )= m=0 L/ 2 k l1 I k,m . S del ( τ= 2 k l,L )= m=0 L/ 2 k l1 I k,m+l
g ^ ΔT ( τ= 2 k l )= ( L/ 2 k ( LΔT )/ 2 k )( R( τ,L )R( τ,LΔT ) ) ( S dir ( τ,L ) S dir ( τ,LΔT ) )( S del ( τ,L ) S del ( τ,LΔT ) ) .
G( τ )( 1 2 t dd n Δ t 0 ) G ideal ( τ ),
m = n 1+ n t dd .
m = αC 1+αC t dd

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