Abstract

The multiplexing of fluorescence correlation spectroscopy (FCS), especially in imaging FCS using fast, sensitive array detectors, requires the handling of large amounts of data. One can easily collect in excess of 100,000 FCS curves a day, too many to be treated manually. Therefore, ImFCS, an open-source software which relies on standard image files was developed and provides a wide range of options for the calculation of spatial and temporal auto- and cross-correlations, as well as differences in Cross-Correlation Functions (ΔCCF). ImFCS permits fitting of standard models to correlation functions and provides optimized histograms of fitted parameters. Applications include the measurement of diffusion and flow with Imaging Total Internal Reflection FCS (ITIR-FCS) and Single Plane Illumination Microscopy FCS (SPIM-FCS) in biologically relevant samples. As a compromise between ITIR-FCS and SPIM-FCS, we extend the applications to Imaging Variable Angle-FCS (IVA-FCS) where sub-critical oblique illumination provides sample sectioning close to the cover slide.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
    [CrossRef] [PubMed]
  2. M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
    [CrossRef] [PubMed]
  3. B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
    [CrossRef] [PubMed]
  4. M. Burkhardt and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).
    [CrossRef] [PubMed]
  5. D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
    [CrossRef] [PubMed]
  6. B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
    [CrossRef] [PubMed]
  7. L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
    [CrossRef] [PubMed]
  8. J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
    [CrossRef] [PubMed]
  9. T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
    [CrossRef] [PubMed]
  10. M. Matsumoto, T. Sugiura, and K. Minato, “Spatially resolved fluorescence correlation spectroscopy based on electron multiplying CCD - art. no. 663017,” in Confocal, Multiphoton, and Nonlinear Microscopic Imaging III, T. Wilson, and A. Periasamy, eds. (2007), pp. 63017–63017.
  11. M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
    [CrossRef]
  12. D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
    [CrossRef] [PubMed]
  13. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
    [CrossRef] [PubMed]
  14. R. Rigler, H. Vogel, Z. Petrášek, and P. Schwille, “Scanning Fluorescence Correlation Spectroscopy,” in Single Molecules and Nanotechnology (Springer Berlin Heidelberg, 2008), pp. 83–105.
  15. “Tiff 6.0 specification,” http://partners.adobe.com/public/developer/en/tiff/TIFF6.pdf .
  16. W. S. Rasband, “ImageJ,” (U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/ , 1997–2009).
  17. K. Schaetzel, and R. Peters, “Noise on multiple-tau photon correlation data,” S. S. Kenneth, ed., (SPIE, 1991), pp. 109–115.
  18. T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80(6), 2987–2999 (2001).
    [CrossRef] [PubMed]
  19. X. Shi, and T. Wohland, “Fluorescence Correlation Spectroscopy,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy A. Diaspro, ed. (CRC Press, 2010).
  20. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).
  21. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
    [CrossRef] [PubMed]
  22. B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “A study of Gaussian approximations of fluorescence microscopy PSF models - art. no. 60900K,” in Conference on Three-Dimensional and Multidimensional Microscopy - Image Acquisition and Processing XIII, J. A. Conchello, C. J. Cogswell, and T. Wilson, eds., (SPIE, San Jose, CA, 2006), pp. K900–K900.
  23. J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
    [CrossRef] [PubMed]
  24. D. Freedman and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields 57, 453–476 (1981).
  25. C. A. Konopka and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).
    [CrossRef]
  26. M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
    [CrossRef] [PubMed]
  27. M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
    [CrossRef]
  28. J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
    [CrossRef] [PubMed]

2010

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
[CrossRef]

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

2009

D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
[CrossRef] [PubMed]

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

2008

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
[CrossRef] [PubMed]

C. A. Konopka and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).
[CrossRef]

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[CrossRef] [PubMed]

M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
[CrossRef]

2007

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[CrossRef] [PubMed]

2006

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

M. Burkhardt and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).
[CrossRef] [PubMed]

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[CrossRef] [PubMed]

2004

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

2001

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

1999

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

1981

D. Freedman and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields 57, 453–476 (1981).

Ahmed, S.

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

Anhut, T.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Arevalo, R.

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[CrossRef] [PubMed]

Bayer, M.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

Bednarek, S. Y.

C. A. Konopka and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).
[CrossRef]

Besse, P. A.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Blom, H.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Brinkmeier, M.

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

Burkhardt, M.

M. Burkhardt and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).
[CrossRef] [PubMed]

Csúcs, G.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Diaconis, P.

D. Freedman and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields 57, 453–476 (1981).

Ding, J. L.

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

Dirkx, R.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

Dorre, K.

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

Eigen, M.

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

Ewers, H.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

Freedman, D.

D. Freedman and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields 57, 453–476 (1981).

Gösch, M.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Graves, C.

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[CrossRef] [PubMed]

Guo, L.

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

Har, J. Y.

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

Hong, Y. M.

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Imamoto, N.

M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
[CrossRef]

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[CrossRef] [PubMed]

Kannan, B.

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

Konopka, C. A.

C. A. Konopka and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).
[CrossRef]

Kraut, R.

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

Lasser, T.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Liu, P.

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

Manna, M.

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

Maruyama, I.

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

Matsumoto, M.

M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
[CrossRef]

McAllister, R.

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[CrossRef] [PubMed]

Minato, K.

M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
[CrossRef]

Mitchison, T. J.

D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
[CrossRef] [PubMed]

Needleman, D. J.

D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
[CrossRef] [PubMed]

Olivo-Marin, J.-C.

B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[CrossRef] [PubMed]

Petrov, E. P.

J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
[CrossRef] [PubMed]

Popovic, R. S.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Ries, J.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
[CrossRef] [PubMed]

Rigler, R.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[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]

Rochas, A.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Sakata-Sogawa, K.

M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
[CrossRef]

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[CrossRef] [PubMed]

Sankaran, J.

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

Schwille, P.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
[CrossRef] [PubMed]

M. Burkhardt and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).
[CrossRef] [PubMed]

Serov, A.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Shi, X.

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

Sisan, D. R.

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[CrossRef] [PubMed]

Solimena, M.

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

Stelzer, E. H. K.

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Stephan, J.

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

Sudhaharan, T.

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

Sugiura, T.

M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
[CrossRef]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Tokunaga, M.

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[CrossRef] [PubMed]

Tokunga, M.

M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
[CrossRef]

Urbach, J. S.

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[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]

Wittbrodt, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Wohland, T.

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[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]

Xu, Y.

D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
[CrossRef] [PubMed]

Zerubia, J.

B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[CrossRef] [PubMed]

Anal. Chem.

M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).
[CrossRef] [PubMed]

B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).
[CrossRef] [PubMed]

B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,” Anal. Chem. 79(12), 4463–4470 (2007).
[CrossRef] [PubMed]

Appl. Opt.

B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[CrossRef] [PubMed]

Biophys. J.

J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).
[CrossRef] [PubMed]

J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639 (2009).
[CrossRef] [PubMed]

D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).
[CrossRef] [PubMed]

D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).
[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]

ChemPhysChem

L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).
[CrossRef] [PubMed]

J. Biomed. Opt.

M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler, “Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed. Opt. 9(5), 913–921 (2004).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys.

M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J. Appl. Phys. 49(6), 060208 (2010).
[CrossRef]

Nat. Methods

M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).
[CrossRef] [PubMed]

M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).
[CrossRef]

Opt. Express

J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).
[CrossRef] [PubMed]

M. Burkhardt and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).
[CrossRef] [PubMed]

T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10), 10627–10641 (2010).
[CrossRef] [PubMed]

Plant J.

C. A. Konopka and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).
[CrossRef]

Probab. Theory Relat. Fields

D. Freedman and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields 57, 453–476 (1981).

Science

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Other

R. Rigler, H. Vogel, Z. Petrášek, and P. Schwille, “Scanning Fluorescence Correlation Spectroscopy,” in Single Molecules and Nanotechnology (Springer Berlin Heidelberg, 2008), pp. 83–105.

“Tiff 6.0 specification,” http://partners.adobe.com/public/developer/en/tiff/TIFF6.pdf .

W. S. Rasband, “ImageJ,” (U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/ , 1997–2009).

K. Schaetzel, and R. Peters, “Noise on multiple-tau photon correlation data,” S. S. Kenneth, ed., (SPIE, 1991), pp. 109–115.

X. Shi, and T. Wohland, “Fluorescence Correlation Spectroscopy,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy A. Diaspro, ed. (CRC Press, 2010).

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).

M. Matsumoto, T. Sugiura, and K. Minato, “Spatially resolved fluorescence correlation spectroscopy based on electron multiplying CCD - art. no. 663017,” in Confocal, Multiphoton, and Nonlinear Microscopic Imaging III, T. Wilson, and A. Periasamy, eds. (2007), pp. 63017–63017.

B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “A study of Gaussian approximations of fluorescence microscopy PSF models - art. no. 60900K,” in Conference on Three-Dimensional and Multidimensional Microscopy - Image Acquisition and Processing XIII, J. A. Conchello, C. J. Cogswell, and T. Wilson, eds., (SPIE, San Jose, CA, 2006), pp. K900–K900.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Illumination schemes in camera based FCS are shown here. ITIR-FCS schematic is shown in A in which super-critical illumination is performed and the volume isolation is provided by an exponentially decaying evanescent wave exciting the fluorophores near the cover slide. IVA-FCS is performed just by decreasing the angle of incidence to values less than the critical angle leading to selective excitation in the bulk sample as seen in B. C is a schematic of SPIM illumination where the fluorophores are excited by a diffraction limited light sheet. A is restricted to surfaces like 2D lipid bilayers and cell membranes while B and C are capable of exciting fluorophores in a physiologically relevant 3D environment inside biological samples.

Fig. 2
Fig. 2

Diffusion in a fluorescently labeled lipid bilayer was studied using ITIR-FCS. The entire set of 441 curves and 2 representative correlations are shown in A. The raw data is shown in grey and the fitted curves are shown in black, the fitted parameters of D and N are displayed as images in B and C. Diffusion of a fluorescently labeled protein (EGFR-EGFP) on a living cell membrane was probed by ITIR-FCS. Unlike the previous set, all the curves are not fitted. These are seen by regions of white pixels in the D and N plots shown in E and F. 2 illustrative curves out of the ensemble are displayed in D. Unlike the previous case, there is more variability in the shape of the curves and the molecules exhibit a wide range of D values as seen by the inset in D. G, H and I are measurements of diffusion of beads in solution by IVA-FCS. The curves were fitted and parameters (D and N) were extracted and displayed as H and I. 2 typical correlation curves along with the complete group is seen in G.

Fig. 3
Fig. 3

Forward and backward cross-correlations of an isotropic process (diffusion) and an anisotropic diffusion (flow) are shown in A and B. 2 distinct populations are seen only in B and not in A since the forward cross-correlation along the direction of flow exhibit a peak while the cross-correlation against the direction of flow does not. The forward and backward cross-correlations in diffusion do not exhibit any differences since diffusion is a random process. Characteristic forward and backward cross-correlations from the above two processes are shown in C. The ΔCCF distributions of flow and diffusion are shown in D. Diffusion exhibits a Gaussian distribution centered at zero while the distribution for flow is centered at a non-zero number. Hence the ΔCCF distribution can be used as a discriminant to differentiate isotropic and anisotropic transport. The ΔCCF images of diffusion and flow are shown in A and B as insets drawn to the same scale.

Fig. 4
Fig. 4

ITIR-FCCS and SPIM-FCCS provide vectorial information. A fluorescently labeled lipid bilayer was moved using a microscope stage to simulate processes exhibiting both diffusion and flow and was studied using ITIR-FCS (A-E). Beads were injected into the vein of living zebra fish embryo and studied by SPIM-FCS (F-J). The autocorrelations (raw data-grey, fitted curve–black) were fitted and D and N were obtained as seen in A(F), C(H), and D(I). To identify the direction of flow, 4 different cross-correlations were performed in B and G. The velocity in magnitude and direction is depicted as arrow plots in E and J.

Equations (7)

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

G A B ( τ ) = F A ( 0 ) F B ( τ ) F A ( t ) F B ( t )
G A B B A ( τ ) = G A B ( τ ) G B A ( τ ) G A B C B ( τ ) = G A B ( τ ) G C B ( τ )
τ linear ( m ) = m Δ τ { m | 0 m < t e n d Δ τ + 1 }
F r min = p 1 + p 2 i = 1 q 1 2 i
G ( k Δ τ ) = ( n k ) i = 0 n k 1 F A ( i Δ τ ) F B ( ( i + k ) Δ τ ) i = 0 n k 1 F A ( i Δ τ ) i = k n 1 F B ( i Δ τ ) { k | 0 k < x } { linear : x = t e n d Δ τ + 1 Semi-logarithmic :  x  =  p }
G ( ( 2 l ( k + p 2 + 1 ) 1 ) Δ τ ) = ( n 2 l k p 2 ) i = 0 ( n 2 l k p 2 1 ) j = 2 l × i ( 2 l × ( i + 1 ) 1 ) F A ( j Δ τ ) j = 2 l × ( i + k + p 2 ) ( 2 l × ( i + k + p 2 + 1 ) 1 ) F B ( j Δ τ ) i = 0 ( n 2 l k p 2 1 ) j = 2 l × i ( 2 l × ( i + 1 ) 1 ) F A ( j Δ τ ) i = 0 ( n 2 l k p 2 1 ) j = 2 l × ( i + k + p 2 ) ( 2 l × ( i + k + p 2 + 1 ) 1 ) F B ( j Δ τ ) { k , l | 0 k < p 2 1 l < q }
N u m b e r o f h i s t o g r a m b i n s = ( max min ) s 3 2 ( Q 3 Q 1 )

Metrics