F2Cor: fast 2-stage correlation algorithm for FCS and DLS |
Optics Express, Vol. 20, Issue 3, pp. 2184-2195 (2012)
http://dx.doi.org/10.1364/OE.20.002184
Acrobat PDF (851 KB)
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
1. Introduction
3. K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987). [CrossRef]
4. 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]
5. 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]
6. 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]
7. 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]
8. 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]
9. 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]
10. 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]
11. 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]
12. 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]
13. 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]
15. 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]
16. D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 74(2), 1135–1144 (2003). [CrossRef]
17. 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]
18. T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett. 31(6), 829–831 (2006). [CrossRef] [PubMed]
19. 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]
13. 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]
16. D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 74(2), 1135–1144 (2003). [CrossRef]
2. Theory
13. 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]
19. 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]
3. Results
3.1 Results on simulated data
3.2 Results on real photon records
4. Discussion and prospects
4.1 Discussion
17. 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]
4.2 Prospects
- - While our current algorithm is very fast, it could be even faster. Indeed, in our current implementation, while our computer is a multi-core computer, only one of them is used. In the future, we plan to parallelize our algorithm. The fact that our algorithm is dual stage makes it particularly suitable for parallelization. Indeed, it is interesting to notice that, according to Eq. (4) the computation time of both SCH and B&M stages are exactly the same. Then one core could process the SCH stage while a second one could be used for the B&M stage.
- - At present time, our software correlator can only process autocorrelations, but all principles exposed in this paper would apply to cross-correlation.
- - The tau sampling we have used follows a quasi geometric progression. In some cases, it could result in aliasing, as in the case of circular correlation [21,22
21. Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008). [CrossRef] [PubMed]
] or dual focus FCS [1022. J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005). [CrossRef] [PubMed]
]. A future work could be to make our current algorithm more flexible in term of tau sampling as in [1810. 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]
], while maintaining its rapidity.18. T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett. 31(6), 829–831 (2006). [CrossRef] [PubMed]
- - Another development would be the adaptation of F2Cor to Fluorescence Lifetime Correlation Spectroscopy [23].
23. P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007). [CrossRef] [PubMed]
Conclusion
References and links
1. | B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, 1976). |
2. | 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. |
3. | K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987). [CrossRef] |
4. | 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] |
5. | 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] |
6. | 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] |
7. | 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] |
8. | 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] |
9. | 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] |
10. | 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] |
11. | 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] |
12. | 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] |
13. | 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] |
14. | D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic, 2002), p. 90. |
15. | 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] |
16. | D. Magatti and F. Ferri, “25 ns software correlator for photon and fluorescence correlation spectroscopy,” Rev. Sci. Instrum. 74(2), 1135–1144 (2003). [CrossRef] |
17. | 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] |
18. | T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett. 31(6), 829–831 (2006). [CrossRef] [PubMed] |
19. | 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] |
20. | ALV-5000 Multiple Tau Digital Correlator Reference Manual (ALV gmbh, 1993). |
21. | Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008). [CrossRef] [PubMed] |
22. | J. P. Skinner, Y. Chen, and J. D. Müller, “Position-sensitive scanning fluorescence correlation spectroscopy,” Biophys. J. 89(2), 1288–1301 (2005). [CrossRef] [PubMed] |
23. | P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007). [CrossRef] [PubMed] |
OCIS Codes
(070.4550) Fourier optics and signal processing : Correlators
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(170.2520) Medical optics and biotechnology : Fluorescence microscopy
(070.7145) Fourier optics and signal processing : Ultrafast processing
ToC Category:
Fourier Optics and Signal Processing
History
Original Manuscript: November 21, 2011
Revised Manuscript: January 5, 2012
Manuscript Accepted: January 7, 2012
Published: January 17, 2012
Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics
Citation
Emmanuel Schaub, "F2Cor: fast 2-stage correlation algorithm for FCS and DLS," Opt. Express 20, 2184-2195 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2184
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References
- B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, 1976).
- 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.
- K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B Photophys. Laser Chem. 42(4), 193–213 (1987). [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]
- 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]
- 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]
- 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]
- 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. 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]
- 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]
- 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]
- D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic, 2002), p. 90.
- 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]
- 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]
- T. A. Laurence, S. Fore, and T. Huser, “Fast, flexible algorithm for calculating photon correlations,” Opt. Lett. 31(6), 829–831 (2006). [CrossRef] [PubMed]
- 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]
- ALV-5000 Multiple Tau Digital Correlator Reference Manual (ALV gmbh, 1993).
- 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]
- P. Kapusta, M. Wahl, A. Benda, M. Hof, and J. Enderlein, “Fluorescence lifetime correlation spectroscopy,” J. Fluoresc. 17(1), 43–48 (2007). [CrossRef] [PubMed]
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