Abstract

We present a new technique, polarization-modulation dual-focus fluorescence correlation spectroscopy (pmFCS), based on the recently introduced dual-focus fluorescence correlation spectroscopy (2fFCS) to measure the absolute value of diffusion coefficients of fluorescent molecules at pico- to nanomolar concentrations. Analogous to 2fFCS, the new technique is robust against optical saturation in yielding correct values of the diffusion coefficient. This is in stark contrast to conventional FCS where optical saturation leads to an apparent decrease in the determined diffusion coefficient with increasing excitation power. However, compared to 2fFCS, the new technique is simpler to implement into a conventional confocal microscope setup and is compatible with cw-excitation, only needing as add-ons an electro-optical modulator and a differential interference contrast prism. With pmFCS, the measured diffusion coefficient (D) for Atto655 maleimide in water at 25oC is determined to be equal to (4.09±0.07)×10-6cm2/s, in good agreement with the value of 4.04×10-6cm2/s as measured by 2fFCS.

© 2008 Optical Society of America

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  1. A. Einstein, Investigations on the theory of the Brownian movement (Dover Publications, New York, 1956), p. 119 p.
  2. D. Magde, E. Elson, and W. W. Webb, "Thermodynamic Fluctuations in a Reacting Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
    [CrossRef]
  3. D. M. Elliot L. Elson, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13, 1-27 (1974).
    [CrossRef]
  4. D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation spectroscopy. II. An experimental realization," Biopolymers 13, 29-61 (1974).
    [CrossRef] [PubMed]
  5. J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
    [CrossRef] [PubMed]
  6. 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]
  7. K. Berland and G. Shen, "Excitation saturation in two-photon fluorescence correlation spectroscopy," Appl. Opt. 42, 5566-5576 (2003).
    [CrossRef] [PubMed]
  8. 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]
  9. 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]
  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, 433-443 (2007).
    [CrossRef] [PubMed]
  11. B. K. Müller, E. Zaychikov, C. Bräuchle, and D. C. Lamb, "Pulsed interleaved excitation," Biophys. J. 89, 3508-3522 (2005).
    [CrossRef] [PubMed]
  12. D. V. O'Connor and D. Phillips, Time-correlated single photon counting (Academic Press, London; Orlando, 1984), pp. viii, 288 p.
  13. C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
    [CrossRef]
  14. K. Schätzel, Single Photon Correlation Techniques. Dynamic Light Scattering: The method and some applications (Clarendon Press, Oxford, 1993).
    [PubMed]

2008 (1)

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[CrossRef]

2007 (1)

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

2005 (3)

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

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]

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[CrossRef] [PubMed]

2003 (1)

1974 (2)

D. M. Elliot L. Elson, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13, 1-27 (1974).
[CrossRef]

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation 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 Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Berland, K.

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.

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]

Elson, E.

D. Magde, E. Elson, and W. W. Webb, "Thermodynamic Fluctuations in a Reacting Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Elson, E. L.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation spectroscopy. II. An experimental realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

Enderlein, J.

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (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]

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]

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]

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[CrossRef] [PubMed]

Fitter, J.

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[CrossRef] [PubMed]

Gregor, I.

T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, "Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements," ChemPhysChem 8, 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, 164-170 (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]

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[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]

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]

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]

Loman, A.

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[CrossRef]

Magde, D.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation 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 Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
[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. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[CrossRef]

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]

Pacheco, V.

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

Patra, D.

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]

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]

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[CrossRef] [PubMed]

Richtering, W.

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[CrossRef]

Shen, G.

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]

Webb, W. W.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation 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 Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Weiß, K.

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[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. (1)

Biophys. J. (1)

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

Biopolymers (2)

D. M. Elliot L. Elson, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13, 1-27 (1974).
[CrossRef]

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence correlation spectroscopy. II. An experimental realization," Biopolymers 13, 29-61 (1974).
[CrossRef] [PubMed]

ChemPhysChem (3)

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, 164-170 (2005).
[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]

Curr. Pharm. Biotechnol. (1)

J. Enderlein, I. Gregor, D. Patra, and J. Fitter, "Art and artefacts of fluorescence correlation spectroscopy," Curr. Pharm. Biotechnol. 5, 155-161 (2004).
[CrossRef] [PubMed]

Opt. Expr. (1)

C. B. Müller, K. Weiβ, W. Richtering, A. Loman, and J. Enderlein, "Calibrating Differential Interference Contrast Microscopy with dual-focus Fluorescence Correlation Spectroscopy," Opt. Expr. 16, 4322-4329 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

D. Magde, E. Elson, and W. W. Webb, "Thermodynamic Fluctuations in a Reacting Systems - Measurement by Fluorescence Correlation Spectroscopy," Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Other (3)

A. Einstein, Investigations on the theory of the Brownian movement (Dover Publications, New York, 1956), p. 119 p.

K. Schätzel, Single Photon Correlation Techniques. Dynamic Light Scattering: The method and some applications (Clarendon Press, Oxford, 1993).
[PubMed]

D. V. O'Connor and D. Phillips, Time-correlated single photon counting (Academic Press, London; Orlando, 1984), pp. viii, 288 p.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of the setup. Excitation is done by a single cw-laser (pulsed in the current embodiment). The polarization of the laser is periodically rotated with an EOM with 10 µs rotation period. The laser light is reflected by a dichroic beam splitter through a DIC prism. The DIC-prism deflects the laser light depending on it polarization. Thus, after focusing the light through the microscope objective, one obtains an excitation pattern which periodically swings between two laterally shifted foci. Fluorescence is collected by the same objective. The tube lens focuses the detected fluorescence from both excitation foci on a single pinhole. Subsequently, the fluorescence light is split by a 50/50 beam splitter and detected by two single photon avalanche diodes. (b) Simulation of two overlapping foci at the sample plan by exact waveoptical calculation of the excitation intensity distribution. Shown are iso-intensity surfaces for e -1, e -2, and e -3 times the maximum intensity value on optical axes in focal plane. (c) Two anti-correlated time traces at 10µs modulation period representing the time dependent intensity of each focus.

Fig. 2.
Fig. 2.

pmFCS measurements on an Atto655 maleimide in aqueous solution. (Excitation power: 60µW; measurement time: 30 min). The autocorrelation function shows modulation in amplitude with 10 µs period, which matches the input modulation period of the excitation laser polarization. The solid line shows the fitted curve using Eq. (7). Inset shows the zoom-in of a small portion of the curve and fit. The bottom panel shows the residual of the fitting.

Fig. 3.
Fig. 3.

Measured diffusion coefficient of Atto655 maleimide in aqueous solution at 25°C as a function of excitation power. Diffusion coefficients measured using pmFCS (squares) and 2fFCS (diamonds) are virtually independent of the excitation power up to 200 µW. The solid line is the average of these values. The results of the single-focus FCS (circles) and the second order polynomial fits (dashed line) are shown in comparison.

Equations (9)

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U ( r ) = κ ( z ) w 2 ( z ) exp [ 2 w 2 ( z ) ( x 2 + y 2 ) ]
w ( z ) = w 0 [ 1 + ( λ ex z π w 0 2 n ) 2 ] 1 2
κ ( z ) = 2 0 a d ρ ρ R 2 ( z ) exp ( 2 ρ 2 R 2 ( 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 .
U mod ( r , t ) = ε 1 cos 2 ( ω t 2 ) U ( r x ̂ δ 2 ) + ε 2 sin 2 ( ω t 2 ) U ( r + x ̂ δ 2 )
g ( t ) = g + c T 0 T d t 0 d r 1 d r 2 U mod ( r 2 , t 0 + t ) 1 ( 4 π D t ) 3 2 exp [ ( r 1 r 2 ) 2 4 D t ] U mod ( r 1 , t 0 )
g ( t ) = g + c 4 [ ( ε 1 2 + ε 2 2 ) ( 1 + cos ω t 2 ) g ACF ( t ) + 2 ε 1 ε 2 ( 1 cos ω t 2 ) g CCF ( t ) ]
g ˜ ( t , δ ) = c 4 π D t d z 1 d z 2 κ ( z 1 ) κ ( z 2 ) 8 D t + w 2 ( z 1 ) + w 2 ( z 2 ) ·
exp [ ( z 2 z 1 ) 2 4 D t 2 δ 2 8 D t + w 2 ( z 1 ) + w 2 ( z 2 ) ]

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