Abstract

We present a new multiple-tau correlation algorithm which is the fastest to date. The resulting curve is identical to that obtained with the conventional multiple-tau algorithm, but the calculation time is much shorter. It combines two approaches. For short values of the lag-time a very simple correlation histogram is used, while for higher lag-time values the traditional multiple-tau bin-and-multiply approach is used. The lag-time limit between these two stages depends on the count rate. The computation time scales linearly with the count rate and is as fast as 0.1µs/photon.

© 2012 OSA

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2010 (2)

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[CrossRef] [PubMed]

R. A. Colyer, G. Scalia, I. Rech, A. Gulinatti, M. Ghioni, S. Cova, S. Weiss, and X. Michalet, “High-throughput FCS using an LCOS spatial light modulator and an 8 × 1 SPAD array,” Biomed. Opt. Express 1(5), 1408–1431 (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)

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[CrossRef] [PubMed]

2007 (2)

P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007).
[CrossRef] [PubMed]

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005).
[CrossRef] [PubMed]

2004 (1)

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

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. Express 11(26), 3583–3591 (2003).
[CrossRef] [PubMed]

2001 (1)

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]

1999 (2)

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

P. Kask, K. Palo, D. Ullmann, and K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96(24), 13756–13761 (1999).
[CrossRef] [PubMed]

1997 (1)

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72(4), 1878–1886 (1997).
[CrossRef] [PubMed]

1990 (2)

H. Qian and E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57(2), 375–380 (1990).
[CrossRef] [PubMed]

H. Qian and E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. U.S.A. 87(14), 5479–5483 (1990).
[CrossRef] [PubMed]

1987 (1)

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987).
[CrossRef]

Benda, A.

P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007).
[CrossRef] [PubMed]

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]

Chemla, D. S.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

Chen, Y.

J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005).
[CrossRef] [PubMed]

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

Colyer, R. A.

Cova, S.

Dertinger, T.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

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. L.

H. Qian and E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. U.S.A. 87(14), 5479–5483 (1990).
[CrossRef] [PubMed]

H. Qian and E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57(2), 375–380 (1990).
[CrossRef] [PubMed]

Enderlein, J.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007).
[CrossRef] [PubMed]

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Express 11(26), 3583–3591 (2003).
[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.

Gall, K.

P. Kask, K. Palo, D. Ullmann, and K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96(24), 13756–13761 (1999).
[CrossRef] [PubMed]

Ghioni, M.

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]

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

Gregor, I.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Express 11(26), 3583–3591 (2003).
[CrossRef] [PubMed]

Gulinatti, A.

Hartmann, R.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

Hof, M.

P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (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.

Kapanidis, A. N.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

Kapusta, P.

P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007).
[CrossRef] [PubMed]

Kask, P.

P. Kask, K. Palo, D. Ullmann, and K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96(24), 13756–13761 (1999).
[CrossRef] [PubMed]

Kong, X. X.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

Laurence, T. A.

T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett. 31(6), 829–831 (2006).
[CrossRef] [PubMed]

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

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]

Likhtman, A. E.

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[CrossRef] [PubMed]

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]

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]

Meyer-Almes, F. J.

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72(4), 1878–1886 (1997).
[CrossRef] [PubMed]

Michalet, X.

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]

Müller, J. D.

J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005).
[CrossRef] [PubMed]

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

Pacheco, V.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

Palo, K.

P. Kask, K. Palo, D. Ullmann, and K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96(24), 13756–13761 (1999).
[CrossRef] [PubMed]

Patting, M.

Petrášek, Z.

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[CrossRef] [PubMed]

Qian, H.

H. Qian and E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. U.S.A. 87(14), 5479–5483 (1990).
[CrossRef] [PubMed]

H. Qian and E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57(2), 375–380 (1990).
[CrossRef] [PubMed]

Ramírez, J.

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[CrossRef] [PubMed]

Rech, I.

Rigler, R.

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72(4), 1878–1886 (1997).
[CrossRef] [PubMed]

Scalia, G.

Schätzel, K.

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987).
[CrossRef]

Schwille, P.

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[CrossRef] [PubMed]

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72(4), 1878–1886 (1997).
[CrossRef] [PubMed]

Skinner, J. P.

J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005).
[CrossRef] [PubMed]

So, P. T. C.

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

Sukumaran, S. K.

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[CrossRef] [PubMed]

Ullmann, D.

P. Kask, K. Palo, D. Ullmann, and K. Gall, “Fluorescence-intensity distribution analysis and its application in biomolecular detection technology,” Proc. Natl. Acad. Sci. U.S.A. 96(24), 13756–13761 (1999).
[CrossRef] [PubMed]

von der Hocht, I.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

Vorselaars, B.

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[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]

Weiss, S.

R. A. Colyer, G. Scalia, I. Rech, A. Gulinatti, M. Ghioni, S. Cova, S. Weiss, and X. Michalet, “High-throughput FCS using an LCOS spatial light modulator and an 8 × 1 SPAD array,” Biomed. Opt. Express 1(5), 1408–1431 (2010).
[CrossRef] [PubMed]

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, “Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions,” J. Phys. Chem. B 108(9), 3051–3067 (2004).
[CrossRef]

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]

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]

Appl. Opt. (1)

Appl. Phys. B Photophys. Laser Chem. (1)

K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987).
[CrossRef]

Biomed. Opt. Express (1)

Biophys. J. (5)

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[CrossRef] [PubMed]

J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005).
[CrossRef] [PubMed]

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77(1), 553–567 (1999).
[CrossRef] [PubMed]

H. Qian and E. L. Elson, “On the analysis of high order moments of fluorescence fluctuations,” Biophys. J. 57(2), 375–380 (1990).
[CrossRef] [PubMed]

P. Schwille, F. J. Meyer-Almes, and R. Rigler, “Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution,” Biophys. J. 72(4), 1878–1886 (1997).
[CrossRef] [PubMed]

ChemPhysChem (1)

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements,” ChemPhysChem 8(3), 433–443 (2007).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

J. Ramírez, S. K. Sukumaran, B. Vorselaars, and A. E. Likhtman, “Efficient on the fly calculation of time correlation functions in computer simulations,” J. Chem. Phys. 133(15), 154103 (2010).
[CrossRef] [PubMed]

J. Fluoresc. (1)

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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).
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J. Phys. Chem. B (1)

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Opt. Express (1)

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Figures (6)

Fig. 1
Fig. 1

Simple correlation histogram algorithm (SCH), which is used for lower value of the lag-time.

Fig. 2
Fig. 2

Computation Time normalized to the Record Time for a 100ns resolution system as a function of the bin-and-multiply (B&M) start level for average count rates ranging from 1kHz to 10MHz (10−4 to 1 photon/resolution time). The points correspond to the experimental results. The black solid curves are a global fit according to Eq. (4), resulting in A = 0.267 and B = 0.760, that is 0.09µs/photon according to Eq. (6). The rectilinear dash line joins the optimum B&M start level values.

Fig. 3
Fig. 3

Computation Time normalized to the Record Time as a function of the average count rate ranging from 1kHz to 10MHz for a 100ns time resolution system. Conventional B&M algorithm, i.e. K = 0 (circle). B&M start level = 13 (triangle), which is the maximum B&M start level allowed by our software, and which behaves approximately the same as SCH, except for very low count rates. Fast 2-stage Correlation algorithm, F2Cor (square). Speedup of F2Cor (diamond), calculated as the min(conventional B&M, SCH) to F2Cor ratio, demonstrating a dramatic calculation speed improvement in the 10kHz-3MHz count rate range .

Fig. 4
Fig. 4

Normalized autocorrelation of a 100nM 5-Carboxytetramethylrhodamine solution computed for a B&M start level value K of 0, 9 and of 13, and for an average excitation power of 13% at 850nm.

Fig. 5
Fig. 5

Normalized autocorrelation computed by F2Cor of a 100nM 5-Carboxytetramethylrhodamine solution at excitation power of 3, 13 and 72% of the maximum power, with average count rate of 22.8, 104 and 309kHz.

Fig. 6
Fig. 6

Comparison of the dependence of the computation time on the count rate between Whal et al. algorithm (circle, ref [17], Athlon 1.5GHz) and F2Cor (square, Pentium I7 1.6GHz).

Tables (1)

Tables Icon

Table 1 . Computation speed for TMR 100nM, for three different excitation powers.

Equations (11)

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{ τ n } n ={ 8,9,,15, 16,18,,30, 2 k max ×8, 2 k max ×9,, 2 k max ×15 }
C v,B&M = 1 2 k L σ μ
V SCH =A 2 K n 2 L,
V B&M = BL / 2 K ,
V= V SCH + V B&M =( A n 2 2 K + B 2 K )L
K opt = ln( 1 n B A ) ln2
V F2Cor =2 n L AB
G Tr ( τ n )= G 0 ( τ n )+ i=1 2 k 1 2 k i 2 k ( G 0 ( τ n i )+ G 0 ( τ n i ) ) .
μ G Tr =Lμ+2 i=1 2 k 1 2 k i 2 k Lμ= 2 k Lμ
σ G Tr 2 =L σ 2 +2 i=1 2 k 1 ( 2 k i 2 k ) 2 L σ 2 =L σ 2 M k 2 ,with M k = 2× 2 2k +1 3× 2 2k .
C v,SCH = 1 2 k L σ μ M k

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