Abstract

Fluorescence correlation spectroscopy (FCS) is an important spectroscopic technique which can be used for measuring the diffusion and thus size of fluorescing molecules at pico- to nanomolar concentrations. Recently, we introduced an extension of conventional FCS, which is called dual-focus FCS (2fFCS) and allows absolute diffusion measurements with high precision and repeatability. It was shown experimentally that the method is robust against most optical and sample artefacts which are troubling conventional FCS measurements, and is furthermore able to yield absolute values of diffusion coefficients without referencing against known standards. However, a thorough theoretical treatment of the performance of 2fFCS is still missing. The present paper aims at filling this gap. Here, we have systematically studied the performance of 2fFCS with respect to the most important optical and photophysical factors such as cover slide thickness, refractive index of the sample, laser beam geometry, and optical saturation. We show that 2fFCS has indeed a superior performance when compared with conventional FCS, being mostly insensitive to most potential aberrations when working under optimized conditions.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]

2008 (5)

Z. Petrasek and P. Schwille, "Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy," Biophys. J. 94, 1437-1448 (2008).
[CrossRef]

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[CrossRef]

M. Leutenegger and T. Lasser, "Detection efficiency in total internal reflection fluorescence microscopy," Opt. Express 16, 8519-8531 (2008).
[CrossRef] [PubMed]

C. B. Müller, K. Wei??, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Express 16, 4322-9 (2008).
[CrossRef] [PubMed]

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

2007 (2)

G. Donnert, C. Eggeling, and S. W Hell, "Major signal increase in fluorescence microscopy through dark-state relaxation," Nature Meth. 4, 81-86 (2007).
[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, 433-443 (2007).
[CrossRef] [PubMed]

2006 (3)

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

J. Ries and P. Schwille, "Studying Slow Membrane Dynamics with Continuous Wave Scanning Fluorescence Correlation Spectroscopy," Biophys. J. 91, 1915-1924 (2006).
[CrossRef] [PubMed]

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, "Fast focus field calculations," Opt. Express 14, 11277-11291 (2006).
[CrossRef] [PubMed]

2005 (6)

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-70 (2005).
[CrossRef] [PubMed]

I. Gregor and J. Enderlein "Focusing astigmatic Gaussian beams through optical systems with a high numerical aperture," Opt. Lett. 30, 2527-9 (2005).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

P. R. T. Munro and P. Török, "Vectorial, high numerical aperture study of Nomarski's differential interference contrast microscope," Opt. Express 13, 6833-47 (2005).
[CrossRef] [PubMed]

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-170 (2005).
[CrossRef] [PubMed]

2004 (2)

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: confocal and multiphoton microscopy," Opt. Commun. 235, 1 (2004).
[CrossRef]

G. Nishimura and M. Kinjo "Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence," Anal. Chem. 76, 1963-1970 (2004).
[CrossRef] [PubMed]

2003 (4)

2001 (1)

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

2000 (1)

1999 (1)

P. D. Higdon, P. Török, and T. Wilson, "Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes," J. Microsc. 193, 127-141 (1999).
[CrossRef]

1998 (2)

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

1997 (1)

1995 (1)

1974 (2)

E. L. Elson and D. Magde "Fluorescence Corelation Spectroscopy I. Conceptual Basis and Theory," Bioploymers 13, 1-27 (1974).
[CrossRef]

D. Magde, E. Elson, and W. W. Webb "Fluorescence Corelation Spectroscopy II. An Experimental Realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

1972 (1)

D. Magde, E. Elson, and W. W. Webb "Thermodynamic fluctuations in a reacting system - measurement by fluorescence correlation spectroscopy," Phys. Rev. Lett. 29, 705-708, (1972).
[CrossRef]

1970 (1)

G. Nomarski, "Interference Microscopy - State of Art and Its Future," J. Opt. Soc. Am. 60, 1575-1575 (1970).

1959 (2)

E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Proc. Roy. Soc. London A 253, 349-357 (1959).
[CrossRef]

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Ameloot, M.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Ammar, M.

Benda, A.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Benes, M.

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Berland, K.

Böhmer, M.

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Booker, J.

Bräuchle, C.

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

Dertinger, T.

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[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, 433-443 (2007).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

Donnert, G.

G. Donnert, C. Eggeling, and S. W Hell, "Major signal increase in fluorescence microscopy through dark-state relaxation," Nature Meth. 4, 81-86 (2007).
[CrossRef]

Eggeling, C.

G. Donnert, C. Eggeling, and S. W Hell, "Major signal increase in fluorescence microscopy through dark-state relaxation," Nature Meth. 4, 81-86 (2007).
[CrossRef]

Egner, A.

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211 (1998).
[CrossRef]

Elson, E.

D. Magde, E. Elson, and W. W. Webb "Fluorescence Corelation Spectroscopy II. An Experimental Realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

D. Magde, E. Elson, and W. W. Webb "Thermodynamic fluctuations in a reacting system - measurement by fluorescence correlation spectroscopy," Phys. Rev. Lett. 29, 705-708, (1972).
[CrossRef]

Elson, E. L.

E. L. Elson and D. Magde "Fluorescence Corelation Spectroscopy I. Conceptual Basis and Theory," Bioploymers 13, 1-27 (1974).
[CrossRef]

Enderlein, J.

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[CrossRef]

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

C. B. Müller, K. Wei??, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Express 16, 4322-9 (2008).
[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, 433-443 (2007).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-70 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-170 (2005).
[CrossRef] [PubMed]

I. Gregor and J. Enderlein "Focusing astigmatic Gaussian beams through optical systems with a high numerical aperture," Opt. Lett. 30, 2527-9 (2005).
[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, 3583-91 (2003).
[CrossRef] [PubMed]

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Engelborghs, Y.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Erdmann, R.

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Fagulova, V.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Furukawa, H.

Gielen, E.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

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, 433-443 (2007).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-70 (2005).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

I. Gregor and J. Enderlein "Focusing astigmatic Gaussian beams through optical systems with a high numerical aperture," Opt. Lett. 30, 2527-9 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-170 (2005).
[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, 3583-91 (2003).
[CrossRef] [PubMed]

Haeberlé, O.

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: confocal and multiphoton microscopy," Opt. Commun. 235, 1 (2004).
[CrossRef]

O. Haeberlé, M. Ammar, H. Furukawa, K. Tenjimbayashi, and P. Török, "The point spread function of optical microscopes imaging through stratified media," Opt. Express 11, 2964 (2003).
[CrossRef] [PubMed]

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, 433-443 (2007).
[CrossRef] [PubMed]

Hell, S. W

G. Donnert, C. Eggeling, and S. W Hell, "Major signal increase in fluorescence microscopy through dark-state relaxation," Nature Meth. 4, 81-86 (2007).
[CrossRef]

Hell, S. W.

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211 (1998).
[CrossRef]

Hermens, W.T.

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, "Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes," J. Microsc. 193, 127-141 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

Hof, M.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Humpolicková, J.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Kaupp, U. B.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

Kinjo, M.

G. Nishimura and M. Kinjo "Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence," Anal. Chem. 76, 1963-1970 (2004).
[CrossRef] [PubMed]

Koberling, F.

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[CrossRef]

Laczik, G. R.

Lamb, D. C.

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

Lasser, T.

Leitgeb, R. A.

Leutenegger, M.

Lhotsky, A.

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Loman, A.

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[CrossRef]

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

C. B. Müller, K. Wei??, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Express 16, 4322-9 (2008).
[CrossRef] [PubMed]

Magde, D.

E. L. Elson and D. Magde "Fluorescence Corelation Spectroscopy I. Conceptual Basis and Theory," Bioploymers 13, 1-27 (1974).
[CrossRef]

D. Magde, E. Elson, and W. W. Webb "Fluorescence Corelation Spectroscopy II. An Experimental Realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

D. Magde, E. Elson, and W. W. Webb "Thermodynamic fluctuations in a reacting system - measurement by fluorescence correlation spectroscopy," Phys. Rev. Lett. 29, 705-708, (1972).
[CrossRef]

Marecek, V.

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Müller, B. K.

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

Müller, C. B.

C. B. Müller, K. Wei??, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Express 16, 4322-9 (2008).
[CrossRef] [PubMed]

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

Munro, P. R. T.

Nishimura, G.

G. Nishimura and M. Kinjo "Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence," Anal. Chem. 76, 1963-1970 (2004).
[CrossRef] [PubMed]

Nomarski, G.

G. Nomarski, "Interference Microscopy - State of Art and Its Future," J. Opt. Soc. Am. 60, 1575-1575 (1970).

Pacheco, V.

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[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, 433-443 (2007).
[CrossRef] [PubMed]

Pampaloni, F.

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Patra, D.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-70 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-170 (2005).
[CrossRef] [PubMed]

Patting, M.

Petrasek, Z.

Z. Petrasek and P. Schwille, "Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy," Biophys. J. 94, 1437-1448 (2008).
[CrossRef]

Rahn, H. J.

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Rao, R.

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Richtering, W.

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

C. B. Müller, K. Wei??, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Express 16, 4322-9 (2008).
[CrossRef] [PubMed]

Ries, J.

J. Ries and P. Schwille, "Studying Slow Membrane Dynamics with Continuous Wave Scanning Fluorescence Correlation Spectroscopy," Biophys. J. 91, 1915-1924 (2006).
[CrossRef] [PubMed]

Schrader, M.

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211 (1998).
[CrossRef]

Schwille, P.

Z. Petrasek and P. Schwille, "Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy," Biophys. J. 94, 1437-1448 (2008).
[CrossRef]

J. Ries and P. Schwille, "Studying Slow Membrane Dynamics with Continuous Wave Scanning Fluorescence Correlation Spectroscopy," Biophys. J. 91, 1915-1924 (2006).
[CrossRef] [PubMed]

Shen, G.

Tenjimbayashi, K.

Török, P.

VandeVen, M.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Varga, P.

Varga, Z.

Vercammen, J.

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

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, 433-443 (2007).
[CrossRef] [PubMed]

Wahl, M.

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, 3583-91 (2003).
[CrossRef] [PubMed]

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Webb, W. W.

D. Magde, E. Elson, and W. W. Webb "Fluorescence Corelation Spectroscopy II. An Experimental Realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

D. Magde, E. Elson, and W. W. Webb "Thermodynamic fluctuations in a reacting system - measurement by fluorescence correlation spectroscopy," Phys. Rev. Lett. 29, 705-708, (1972).
[CrossRef]

Wei??, K.

Willbold, D.

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

Wilson, T.

P. D. Higdon, P. Török, and T. Wilson, "Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes," J. Microsc. 193, 127-141 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

Wolf, E.

E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Proc. Roy. Soc. London A 253, 349-357 (1959).
[CrossRef]

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Zaychikov, E.

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

Anal. Chem. (1)

G. Nishimura and M. Kinjo "Systematic error in fluorescence correlation measurements identified by a simple saturation model of fluorescence," Anal. Chem. 76, 1963-1970 (2004).
[CrossRef] [PubMed]

Appl. Opt. (2)

Biophys. J. (3)

J. Ries and P. Schwille, "Studying Slow Membrane Dynamics with Continuous Wave Scanning Fluorescence Correlation Spectroscopy," Biophys. J. 91, 1915-1924 (2006).
[CrossRef] [PubMed]

Z. Petrasek and P. Schwille, "Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy," Biophys. J. 94, 1437-1448 (2008).
[CrossRef]

B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
[CrossRef] [PubMed]

Biophys. J. Biophys. Lett. (1)

J. Humpolicková, E. Gielen, A. Benda, V. Fagulova, J. Vercammen, M. VandeVen, M. Hof, M. Ameloot, and Y. Engelborghs, "Probing Diffusion Laws within Cellular Membranes by Z-Scan Fluorescence Correlation Spectroscopy," Biophys. J. Biophys. Lett. 91, L23-L25 (2006).

Bioploymers (1)

E. L. Elson and D. Magde "Fluorescence Corelation Spectroscopy I. Conceptual Basis and Theory," Bioploymers 13, 1-27 (1974).
[CrossRef]

Biopolymers (1)

D. Magde, E. Elson, and W. W. Webb "Fluorescence Corelation Spectroscopy II. An Experimental Realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

A. Loman, T. Dertinger, F. Koberling, and J. Enderlein, "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy," Chem. Phys. Lett. 459, 18-21 (2008).
[CrossRef]

ChemPhysChem (4)

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, 433-443 (2007).
[CrossRef] [PubMed]

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, "Performance of Fluorescence Correlation Spectroscopy for Measuring Diffusion and Concentration," ChemPhysChem 6, 2324-2336 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-70 (2005).
[CrossRef] [PubMed]

I. Gregor, D. Patra, and J. Enderlein, "Optical Saturation in Fluorescence Correlation Spectroscopy under Continuous-Wave and Pulsed Excitation," ChemPhysChem 6, 164-170 (2005).
[CrossRef] [PubMed]

Eur. Phys. Lett. (1)

C. B. Müller, A. Loman, V. Pacheco, F. Koberling, D. Willbold, W. Richtering, and J. Enderlein, "Precise Measurement of Diffusion by Multi-Color Dual-Focus Fluorescence Correlation Spectroscopy," Eur. Phys. Lett. 83, 46001 (2008).
[CrossRef]

J. Microsc. (1)

P. D. Higdon, P. Török, and T. Wilson, "Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes," J. Microsc. 193, 127-141 (1999).
[CrossRef]

J. Mod. Opt. (1)

P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

G. Nomarski, "Interference Microscopy - State of Art and Its Future," J. Opt. Soc. Am. 60, 1575-1575 (1970).

J. Opt. Soc. Am. A (1)

Langmuir (1)

A. Benda, M. Benes, V. Marecek, A. Lhotsky, W.T. Hermens, and M. Hof, "How To Determine Diffusion Coefficients in Planar Phospholipid Systems by Confocal Fluorescence Correlation Spectroscopy," Langmuir 19, 4120-4126 (2003).
[CrossRef]

Nature Meth. (1)

G. Donnert, C. Eggeling, and S. W Hell, "Major signal increase in fluorescence microscopy through dark-state relaxation," Nature Meth. 4, 81-86 (2007).
[CrossRef]

Opt. Commun. (2)

A. Egner, M. Schrader, and S. W. Hell, "Refractive index mismatch induced intensity and phase variations in fluorescence confocal, multiphoton and 4Pi-microscopy," Opt. Commun. 153, 211 (1998).
[CrossRef]

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: confocal and multiphoton microscopy," Opt. Commun. 235, 1 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

D. Magde, E. Elson, and W. W. Webb "Thermodynamic fluctuations in a reacting system - measurement by fluorescence correlation spectroscopy," Phys. Rev. Lett. 29, 705-708, (1972).
[CrossRef]

Proc. Roy. Soc. London A (2)

E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Proc. Roy. Soc. London A 253, 349-357 (1959).
[CrossRef]

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London A 253, 358-379 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Böhmer, F. Pampaloni, M. Wahl, H. J. Rahn, R. Erdmann, and J. Enderlein, "Time-resolved confocal scanning device for ultrasensitive fluorescence detection," Rev. Sci. Instrum. 72, 4145-4152 (2001).
[CrossRef]

Other (2)

J. Widengren and ??. Mets, Single-Molecule Detection in Solution - Methods and Applications, Eds. C. Zander, J. Enderlein, and R. A. Keller (Wiley-VCH, 2002) pp. 69-95.
[CrossRef]

R. Rigler and E. Elson, Eds. Fluorescence Correlation Spectroscopy (Springer, 2001).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of a 2fFCS set-up as theoretically studied in the present paper. For details see main text.

Fig. 2.
Fig. 2.

Visualization of the two overlapping MDFs for different laser beam diameters as indicate above each panel. For each MDF, three iso-surfaces are shown where the MDF has fallen off to 1/e, 1/e 2 and 1/e 3 of its maximum value. With increasing beam diameter, i.e. increasing laser beam focusing, the MDF becomes more structured, and for the largest beam diameter, one can clearly see the elongated shape (transverse to the optical axis) of each focus. This is typical for diffraction- limited focusing of a polarized beam by a lens with high numerical aperture.

Fig. 3.
Fig. 3.

(a) Left panel: Anatomy of the MDF of one of the two laser beams. Gaussian fits of the MDF distribution obtained by focusing a laser beam with radius R=1.25 mm. Shown are distributions in four different cross-sections at axial positions z=0.0, 0.9, 1.8, and 2.7 µm. As can be seen, a Gaussian is indeed a perfect fit to the actual distribution. Right panels: Fit (blue dashed line) of the z-dependence of radius w(z) and amplitude κ(z) of the wave-optically calculated MDF (red circles) by Eqs. (5) and (6). Shown also are curves (green solid line) obtained when using the parameters w 0 and R 0 from a global fit of the ACFs and CCF using Eq. (8). The expressions of Eqs.(5) and (6) are indeed a remarkably accurate description of the actual MDF, and the correlation function fit yields parameter values quite close to the best fit of Eqs. (5) and (6) to the actual MDF.

Fig. 3b.
Fig. 3b.

(b) Same as the previous figure but for a laser beam radius of R=4 mm. The chosen cross-sections are now at axial positions z=0.0, 0.4, 0.8, and 1.2 µm. The Gaussian approximation now shows significant deviations from the actual distributions for cross-sections farther away from the focal plane.

Fig. 4.
Fig. 4.

Dependence of the fitted absolute value of the diffusion coefficient on laser beam diameter. Over the full range of considered radius values, the fit error is less than 2 % of its actual value. For the intermediate laser beam radius close to 2 mm, the error is negligible.

Fig. 5.
Fig. 5.

Dependence of the fitted absolute value of the diffusion coefficient on cover slide thickness deviation. Shown are global fit results of a 2fFCS measurement with four different laser beam radii between 1.25 and 4 mm. For comparison, the fit results from a single-focus FCS measurement are also shown, for the two limiting laser beam radii of 1.25 and 4 mm. Because a single-focus FCS measurement cannot measure absolute diffusion coefficients, the two curves are normalized by their value at δ=0 µm. Remarkably, for a laser beam radius below 2 mm, a 2fFCS measurement is nearly independent on aberrations introduced by cover slide thickness deviations (and similarly, to aberrations due to refractive index mismatch).

Fig. 6.
Fig. 6.

Dependence of the fitted absolute value of the diffusion coefficient on excited state saturation with no intersystem crossing. Shown are the global fit results of a 2fFCS measurement with four different laser beam radii between 1.25 and 4 mm. Similar to cover-slide thickness deviation, the best results are achieved for an intermediate laser beam radius of 2 mm. In that case, the fitted value of the diffusion coefficient stays close to its actual value by better than 1 % even at high optical saturation values.

Fig. 7.
Fig. 7.

(a) Anatomy of the MDF for focusing a laser beam with radius R=2 mm and a S0→S1 optical saturation parameter of one. Clearly, the Gaussian approximation is no longer a valid approximation of the actual MDF. Remarkably, the empirical model of Eqs.(4) through (7) which lies behind the fitting of the 2fFCS measurements still yields satisfactorily accurate diffusion coefficients.

Fig. 7b.
Fig. 7b.

(b) Fit quality of the global fit of an 2fFCS experiment under ideal optical conditions (left couple of curves) and for a S0→S1 optical saturation of one (right couple of curves). Dots are the theoretically calculated auto- and cross-correlation curves (cross-correlation always having lower amplitude than autocorrelation); solid lines are the best global fit. As can be seen, even under high optical saturation, apparent fit quality is still excellent.

Fig. 8.
Fig. 8.

Dependence of the fitted absolute value of the diffusion coefficient on excited state saturation with different ratios κ of intersystem crossing rate constant to phosphorescence rate constant, i.e. k isc /k ph . Shown are the global fit results of a 2fFCS measurement assuming a laser beam radius of 2 mm. For comparison, fit results from a single-focus FCS measurement are also shown, for the two limiting κ-values of 0 (no triplet state dynamics, compare with Fig.7) and 8. Because a single-focus FCS measurement cannot measure absolute diffusion coefficients, the two curves are again normalized by their value at zero optical saturation, i.e. in the limit of zero excitation intensity.

Fig. 9.
Fig. 9.

Dependence of the detection volume as calculated from the empirical parameters w 0 and R 0 (as returned by the global 2fFCS fit) on cover slide thickness deviation for the four laser beam radii of 1.25, 1.5, 2, 3, and 4 mm (from bottom to top).

Equations (11)

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

U ( r ) = Σ m = U m ( ρ , z ) e i m ϕ
g ( τ ) = π c Σ m = 0 ( 1 + δ m , 0 ) d ρ ρ dz U m ( ρ , z ) F m ( ρ , z , τ ) + [ 2 π c d ρ ρ dz U 0 ( ρ , z ) + I bg ] 2
F m ( ρ , z , τ ) =
2 π i m exp ( ρ 2 4 D τ ) ( 4 π D τ ) 3 2 0 d ρ 0 ρ 0 dz 0 U m ( ρ 0 , z 0 ) J m ( i ρ ρ 0 2 D τ ) exp [ ρ 0 2 + ( z z 0 ) 2 4 D τ ]
U ( r ) = κ ( z ) w 2 ( z ) exp { 2 w 2 ( z ) [ ( x ± δ 2 ) 2 + y 2 ] }
w ( z ) = w 0 [ 1 + ( λ ex z π w 0 2 n ) 2 ] 1 2
κ ( z ) = 1 exp ( 2 a 2 R 2 ( z ) )
R ( z ) = R 0 [ 1 + ( λ em z π R 0 2 n ) 2 ] 1 2 .
g ( τ , δ ) = c 4 π D τ dz 1 dz 2 κ ( z 1 ) κ ( z 2 ) 8 D τ + w 2 ( z 1 ) + w 2 ( z 2 ) ·
exp [ ( z 2 z 1 ) 2 4 D τ 2 δ 2 8 D τ + w 2 ( z 1 ) + w 2 ( z 2 ) ]
V eff = [ d r U ( r ) ] 2 d r U 2 ( r ) .

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