Abstract

Interpretation of spatially resolved optical spectroscopies requires knowledge of the optical excitation and collection profiles of the experimental apparatus. This paper describes measurement of the relative norms of the spatial profile of a microscope- and laser-based optical system. The profile is given by the product of the spatial intensity of a focused laser beam and the point collection efficiency of the microscope. Experimental determination of the values of the norms is essential to the use of high order autocorrelation in fluorescence correlation spectroscopy to measure the concentrations and relative fluorescence yields of different fluorescent components (e.g., monomers and oligomers) in a multicomponent solution and also permits evaluation of theoretical models of the optical spatial intensity profile. In addition, the results may have applicability to high order autocorrelation in other optical spectroscopies, to confocal microscopy and to nonlinear optics in general.

© 1989 Optical Society of America

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  1. J. B. Suck, D. Quitman, B. Maier, Eds., Workshop on Investigation of Higher Order Correlation Functions, J. Phys.46(C9) (1985).
  2. B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), pp. 25–40.
  3. A. W. Lohman, B. Wirnitzer, “Triple Correlations,” Proc. IEEE 72, 889 (1984).
  4. L. Basano, P. Ottonello, “Third Order Correlator for Point Processes,” Rev. Sci. Instrum. 58, 579 (1987).
    [CrossRef]
  5. A. G. Palmer, N. L. Thompson, “Molecular Aggregation Characterized by High Order Autocorrelation in Fluorescence Correlation Spectroscopy,” Biophys. J. 52, 257 (1987).
    [CrossRef] [PubMed]
  6. A. G. Palmer, N. L. Thompson, “Intensity Dependence of High Order Autocorrelation Functions in Fluorescence Correlation Spectroscopy,” Rev. Sci. Instr. (1989), in press.
    [CrossRef]
  7. A. G. Palmer, N. L. Thompson, “High Order Fluorescence Fluctuation Analysis of Model Protein Clusters,” submitted.
  8. P. N. Pusey, “Statistical Properties of Scattered Radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins, E. R. Pike, Eds. (Plenum, New York, 1977), p. 45.
  9. C. J. Oliver, “Recent Techniques in Photon Correlation and Spectrum Analysis Techniques,” in Scattering Techniques Applied to Supramolecular and Nonequilibrium Systems, S. Chen, B. Chu, R. Nossal, Eds. (Plenum, 1981), pp. 87–120.
    [CrossRef]
  10. P. N. Pusey, J. G. Rarity, “Measurement of Higher-Order Correlation Functions by Intensity Cross Correlation Light Scattering,” in Workshop on Investigation of Higher Order Correlation Functions, J. B. Suck, D. Quitman, B. Maier, Eds., J. Phys.46(C9), 43 (1985).
  11. B. Blumich, “Two Dimensional Interferometry,” Rev. Sci. Instrum. 58, 911 (1987).
    [CrossRef]
  12. L. S. Leibovitch, J. Fischbarg, “Determining the Kinetics of Membrane Pores from Patch Clamp Data Without Measuring the Open and Closed Times,” Biochim. Biophys. Acta 813, 132 (1985).
    [CrossRef]
  13. L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).
  14. L. S. Leibovitch, J. Fischbarg, “Membrane Pores: A Computer Simulation of Interacting Pores Analyzed by g1(τ) and g2(τ) Correlation Functions,” J. Theor. Biol. 119, 287 (1986).
    [CrossRef]
  15. B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
    [CrossRef] [PubMed]
  16. A. G. Palmer, N. L. Thompson, “Fluorescence Correlation Spectroscopy for Detecting Submicroscopic Clusters of Fluorescent Molecules in Membranes,” Chem. Phys. Lipids, in press.
    [PubMed]
  17. I. Steinberg, “On the Time Reversal of Noise Signals,” Biophys.J. 50, 171 (1986).
    [CrossRef] [PubMed]
  18. H. L. Royden, Real Analysis (Macmillan, New York, 1963), p.93.
  19. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, 1984), pp. 70–76
  20. S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.
  21. D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
    [CrossRef] [PubMed]
  22. N. L. Thompson, “Fluorescence Correlation Spectroscopy,” in Fluorescence Spectroscopy 2, J. Lakowicz, Ed. (Plenum, New York), in press.
  23. The point collection efficiency function T(r) is obtained by integrating the impulse response function of the optical system over the transverse image space coordinates at the location of the aperture along the optical axis.24
  24. D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
    [CrossRef] [PubMed]
  25. A. Yoshida, T. Asakura, “Electromagnetic Field Near the Focus of Gaussian Beams,” Optik 41, 281 (1974).
  26. P. Wahl, “Optimization of Laser Beams in FRAP Experiments of Microscopical Objects,” Biophys. Chem. 22, 317 (1985).
    [CrossRef] [PubMed]
  27. D. A. Agard, “Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191 (1984).
    [CrossRef]
  28. M. B. Schneider, W. W. Webb, “Measurement of Submicron Laser Beam Radii,” Appl. Opt. 20, 1382 (1981).
    [CrossRef] [PubMed]
  29. A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).
  30. R. D. Icenogle, E. L. Elson, “Fluorescence Correlation Spectroscopy and Photobleaching Recovery of Multiple Binding Reactions. I. Theory and FCS Measurements,” Biopolymers 22, 1919 (1983).
    [CrossRef] [PubMed]
  31. S. M. Sorscher, M. P. Klein, “Profile of a Focussed Collimated Laser Beam Near the Focal Minimum Characterized by Fluorescence Correlation Spectroscopy,” Rev. Sci. Instrum. 51, 98 (1980).
    [CrossRef]
  32. N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).
  33. N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
    [CrossRef] [PubMed]
  34. H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
    [CrossRef] [PubMed]
  35. N. L. Thompson, A. G. Palmer, “Model Membranes on Planar Substrates,” Commun. Mol. Cell. Biophys. 5, 39 (1988).

1988 (2)

A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).

N. L. Thompson, A. G. Palmer, “Model Membranes on Planar Substrates,” Commun. Mol. Cell. Biophys. 5, 39 (1988).

1987 (3)

L. Basano, P. Ottonello, “Third Order Correlator for Point Processes,” Rev. Sci. Instrum. 58, 579 (1987).
[CrossRef]

A. G. Palmer, N. L. Thompson, “Molecular Aggregation Characterized by High Order Autocorrelation in Fluorescence Correlation Spectroscopy,” Biophys. J. 52, 257 (1987).
[CrossRef] [PubMed]

B. Blumich, “Two Dimensional Interferometry,” Rev. Sci. Instrum. 58, 911 (1987).
[CrossRef]

1986 (3)

L. S. Leibovitch, J. Fischbarg, “Membrane Pores: A Computer Simulation of Interacting Pores Analyzed by g1(τ) and g2(τ) Correlation Functions,” J. Theor. Biol. 119, 287 (1986).
[CrossRef]

I. Steinberg, “On the Time Reversal of Noise Signals,” Biophys.J. 50, 171 (1986).
[CrossRef] [PubMed]

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

1985 (4)

B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
[CrossRef] [PubMed]

L. S. Leibovitch, J. Fischbarg, “Determining the Kinetics of Membrane Pores from Patch Clamp Data Without Measuring the Open and Closed Times,” Biochim. Biophys. Acta 813, 132 (1985).
[CrossRef]

L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).

P. Wahl, “Optimization of Laser Beams in FRAP Experiments of Microscopical Objects,” Biophys. Chem. 22, 317 (1985).
[CrossRef] [PubMed]

1984 (4)

D. A. Agard, “Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191 (1984).
[CrossRef]

N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).

N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
[CrossRef] [PubMed]

A. W. Lohman, B. Wirnitzer, “Triple Correlations,” Proc. IEEE 72, 889 (1984).

1983 (1)

R. D. Icenogle, E. L. Elson, “Fluorescence Correlation Spectroscopy and Photobleaching Recovery of Multiple Binding Reactions. I. Theory and FCS Measurements,” Biopolymers 22, 1919 (1983).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

S. M. Sorscher, M. P. Klein, “Profile of a Focussed Collimated Laser Beam Near the Focal Minimum Characterized by Fluorescence Correlation Spectroscopy,” Rev. Sci. Instrum. 51, 98 (1980).
[CrossRef]

1976 (1)

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

1974 (2)

A. Yoshida, T. Asakura, “Electromagnetic Field Near the Focus of Gaussian Beams,” Optik 41, 281 (1974).

D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
[CrossRef] [PubMed]

Ackerson, B. J.

B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
[CrossRef] [PubMed]

Agard, D. A.

D. A. Agard, “Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191 (1984).
[CrossRef]

Asakura, T.

A. Yoshida, T. Asakura, “Electromagnetic Field Near the Focus of Gaussian Beams,” Optik 41, 281 (1974).

Axelrod, D.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

Basano, L.

L. Basano, P. Ottonello, “Third Order Correlator for Point Processes,” Rev. Sci. Instrum. 58, 579 (1987).
[CrossRef]

Blumich, B.

B. Blumich, “Two Dimensional Interferometry,” Rev. Sci. Instrum. 58, 911 (1987).
[CrossRef]

Brian, A. A.

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).

Brown, C. S.

A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).

Burghardt, T. P.

N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
[CrossRef] [PubMed]

Clark, N. A.

B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
[CrossRef] [PubMed]

Elson, E. L.

R. D. Icenogle, E. L. Elson, “Fluorescence Correlation Spectroscopy and Photobleaching Recovery of Multiple Binding Reactions. I. Theory and FCS Measurements,” Biopolymers 22, 1919 (1983).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
[CrossRef] [PubMed]

Fischbarg, J.

L. S. Leibovitch, J. Fischbarg, “Membrane Pores: A Computer Simulation of Interacting Pores Analyzed by g1(τ) and g2(τ) Correlation Functions,” J. Theor. Biol. 119, 287 (1986).
[CrossRef]

L. S. Leibovitch, J. Fischbarg, “Determining the Kinetics of Membrane Pores from Patch Clamp Data Without Measuring the Open and Closed Times,” Biochim. Biophys. Acta 813, 132 (1985).
[CrossRef]

L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).

Fujimura, Y.

S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.

Golan, D. E.

A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).

Icenogle, R. D.

R. D. Icenogle, E. L. Elson, “Fluorescence Correlation Spectroscopy and Photobleaching Recovery of Multiple Binding Reactions. I. Theory and FCS Measurements,” Biopolymers 22, 1919 (1983).
[CrossRef] [PubMed]

Klein, M. P.

S. M. Sorscher, M. P. Klein, “Profile of a Focussed Collimated Laser Beam Near the Focal Minimum Characterized by Fluorescence Correlation Spectroscopy,” Rev. Sci. Instrum. 51, 98 (1980).
[CrossRef]

Koniarek, J. P.

L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).

Koppel, D. E.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

Leibovitch, L. S.

L. S. Leibovitch, J. Fischbarg, “Membrane Pores: A Computer Simulation of Interacting Pores Analyzed by g1(τ) and g2(τ) Correlation Functions,” J. Theor. Biol. 119, 287 (1986).
[CrossRef]

L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).

L. S. Leibovitch, J. Fischbarg, “Determining the Kinetics of Membrane Pores from Patch Clamp Data Without Measuring the Open and Closed Times,” Biochim. Biophys. Acta 813, 132 (1985).
[CrossRef]

Lin, S. H.

S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.

Lohman, A. W.

A. W. Lohman, B. Wirnitzer, “Triple Correlations,” Proc. IEEE 72, 889 (1984).

Magde, D.

D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
[CrossRef] [PubMed]

McConnell, H. M.

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).

N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
[CrossRef] [PubMed]

Neusser, H. J.

S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.

Oliver, C. J.

C. J. Oliver, “Recent Techniques in Photon Correlation and Spectrum Analysis Techniques,” in Scattering Techniques Applied to Supramolecular and Nonequilibrium Systems, S. Chen, B. Chu, R. Nossal, Eds. (Plenum, 1981), pp. 87–120.
[CrossRef]

Ottonello, P.

L. Basano, P. Ottonello, “Third Order Correlator for Point Processes,” Rev. Sci. Instrum. 58, 579 (1987).
[CrossRef]

Palmer, A. G.

N. L. Thompson, A. G. Palmer, “Model Membranes on Planar Substrates,” Commun. Mol. Cell. Biophys. 5, 39 (1988).

A. G. Palmer, N. L. Thompson, “Molecular Aggregation Characterized by High Order Autocorrelation in Fluorescence Correlation Spectroscopy,” Biophys. J. 52, 257 (1987).
[CrossRef] [PubMed]

A. G. Palmer, N. L. Thompson, “Intensity Dependence of High Order Autocorrelation Functions in Fluorescence Correlation Spectroscopy,” Rev. Sci. Instr. (1989), in press.
[CrossRef]

A. G. Palmer, N. L. Thompson, “High Order Fluorescence Fluctuation Analysis of Model Protein Clusters,” submitted.

A. G. Palmer, N. L. Thompson, “Fluorescence Correlation Spectroscopy for Detecting Submicroscopic Clusters of Fluorescent Molecules in Membranes,” Chem. Phys. Lipids, in press.
[PubMed]

Pusey, P. N.

P. N. Pusey, “Statistical Properties of Scattered Radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins, E. R. Pike, Eds. (Plenum, New York, 1977), p. 45.

P. N. Pusey, J. G. Rarity, “Measurement of Higher-Order Correlation Functions by Intensity Cross Correlation Light Scattering,” in Workshop on Investigation of Higher Order Correlation Functions, J. B. Suck, D. Quitman, B. Maier, Eds., J. Phys.46(C9), 43 (1985).

Rarity, J. G.

P. N. Pusey, J. G. Rarity, “Measurement of Higher-Order Correlation Functions by Intensity Cross Correlation Light Scattering,” in Workshop on Investigation of Higher Order Correlation Functions, J. B. Suck, D. Quitman, B. Maier, Eds., J. Phys.46(C9), 43 (1985).

Royden, H. L.

H. L. Royden, Real Analysis (Macmillan, New York, 1963), p.93.

Saleh, B.

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), pp. 25–40.

Schlag, E. W.

S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.

Schlessinger, J.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

Schneider, M. B.

Sheppard, C.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, 1984), pp. 70–76

Sorscher, S. M.

S. M. Sorscher, M. P. Klein, “Profile of a Focussed Collimated Laser Beam Near the Focal Minimum Characterized by Fluorescence Correlation Spectroscopy,” Rev. Sci. Instrum. 51, 98 (1980).
[CrossRef]

Steinberg, I.

I. Steinberg, “On the Time Reversal of Noise Signals,” Biophys.J. 50, 171 (1986).
[CrossRef] [PubMed]

Stolpen, A. H.

A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).

Taylor, T. W.

B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
[CrossRef] [PubMed]

Thompson, N. L.

N. L. Thompson, A. G. Palmer, “Model Membranes on Planar Substrates,” Commun. Mol. Cell. Biophys. 5, 39 (1988).

A. G. Palmer, N. L. Thompson, “Molecular Aggregation Characterized by High Order Autocorrelation in Fluorescence Correlation Spectroscopy,” Biophys. J. 52, 257 (1987).
[CrossRef] [PubMed]

N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
[CrossRef] [PubMed]

N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).

N. L. Thompson, “Fluorescence Correlation Spectroscopy,” in Fluorescence Spectroscopy 2, J. Lakowicz, Ed. (Plenum, New York), in press.

A. G. Palmer, N. L. Thompson, “Intensity Dependence of High Order Autocorrelation Functions in Fluorescence Correlation Spectroscopy,” Rev. Sci. Instr. (1989), in press.
[CrossRef]

A. G. Palmer, N. L. Thompson, “High Order Fluorescence Fluctuation Analysis of Model Protein Clusters,” submitted.

A. G. Palmer, N. L. Thompson, “Fluorescence Correlation Spectroscopy for Detecting Submicroscopic Clusters of Fluorescent Molecules in Membranes,” Chem. Phys. Lipids, in press.
[PubMed]

Wahl, P.

P. Wahl, “Optimization of Laser Beams in FRAP Experiments of Microscopical Objects,” Biophys. Chem. 22, 317 (1985).
[CrossRef] [PubMed]

Watts, T. H.

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

Webb, W. W.

M. B. Schneider, W. W. Webb, “Measurement of Submicron Laser Beam Radii,” Appl. Opt. 20, 1382 (1981).
[CrossRef] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
[CrossRef] [PubMed]

Weis, R. M.

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, 1984), pp. 70–76

Wirnitzer, B.

A. W. Lohman, B. Wirnitzer, “Triple Correlations,” Proc. IEEE 72, 889 (1984).

Yoshida, A.

A. Yoshida, T. Asakura, “Electromagnetic Field Near the Focus of Gaussian Beams,” Optik 41, 281 (1974).

Ann. Rev. Biophys. Bioeng. (1)

D. A. Agard, “Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191 (1984).
[CrossRef]

Appl. Opt. (1)

Biochim. Biophys. Acta (3)

N. L. Thompson, A. A. Brian, H. M. McConnell, “Covalent Linkage of a Synthetic Peptide to a Fluorescent Phospholipid and Its Incorporation into Supported Phospholipid Monolayers,” Biochim. Biophys. Acta 722, 10 (1984).

H. M. McConnell, T. H. Watts, R. M. Weis, A. A. Brian, “Supported Planar Membranes in Studies of Cell-Cell Recognition in the Immune System,” Biochim. Biophys. Acta 864, 95 (1986).
[CrossRef] [PubMed]

L. S. Leibovitch, J. Fischbarg, “Determining the Kinetics of Membrane Pores from Patch Clamp Data Without Measuring the Open and Closed Times,” Biochim. Biophys. Acta 813, 132 (1985).
[CrossRef]

Biophys. Chem. (1)

P. Wahl, “Optimization of Laser Beams in FRAP Experiments of Microscopical Objects,” Biophys. Chem. 22, 317 (1985).
[CrossRef] [PubMed]

Biophys. J. (4)

N. L. Thompson, H. M. McConnell, T. P. Burghardt, “Order in Supported Phospholipid Monolayers Detected by the Dichroism of Fluorescence Excited with Polarized Evanescent Illumination,” Biophys. J. 46, 729 (1984).
[CrossRef] [PubMed]

A. H. Stolpen, C. S. Brown, D. E. Golan, “Characterization of Microscopic Laser Beams by Two-Dimensional Scanning of Fluorescence Emission,” Biophys. J. 53, 477a (1988).

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, “Dynamics of Fluorescence Marker Concentration as a Probe of Mobility,” Biophys. J. 16, 1315 (1976).
[CrossRef] [PubMed]

A. G. Palmer, N. L. Thompson, “Molecular Aggregation Characterized by High Order Autocorrelation in Fluorescence Correlation Spectroscopy,” Biophys. J. 52, 257 (1987).
[CrossRef] [PubMed]

Biophys.J. (1)

I. Steinberg, “On the Time Reversal of Noise Signals,” Biophys.J. 50, 171 (1986).
[CrossRef] [PubMed]

Biopolymers (2)

D. Magde, W. W. Webb, E. L. Elson, “Fluorescence Correlation Spectroscopy. II. An Experimental Realization,” Biopolymers 13, 29 (1974).
[CrossRef] [PubMed]

R. D. Icenogle, E. L. Elson, “Fluorescence Correlation Spectroscopy and Photobleaching Recovery of Multiple Binding Reactions. I. Theory and FCS Measurements,” Biopolymers 22, 1919 (1983).
[CrossRef] [PubMed]

Commun. Mol. Cell. Biophys. (1)

N. L. Thompson, A. G. Palmer, “Model Membranes on Planar Substrates,” Commun. Mol. Cell. Biophys. 5, 39 (1988).

J. Theor. Biol. (1)

L. S. Leibovitch, J. Fischbarg, “Membrane Pores: A Computer Simulation of Interacting Pores Analyzed by g1(τ) and g2(τ) Correlation Functions,” J. Theor. Biol. 119, 287 (1986).
[CrossRef]

Math. Biosci. (1)

L. S. Leibovitch, J. Fischbarg, J. P. Koniarek, “Optical Correlation Functions Applied to the Random Telegraph Signal: How to Analyze Patch Clamp Data Without Measuring the Open and Closed Times,” Math. Biosci. 76, 1 (1985).

Optik (1)

A. Yoshida, T. Asakura, “Electromagnetic Field Near the Focus of Gaussian Beams,” Optik 41, 281 (1974).

Phys. Rev. A (1)

B. J. Ackerson, T. W. Taylor, N. A. Clark, “Characterization of the Local Structure of Fluids by Apertured Cross-Correlation Functions,” Phys. Rev. A 31, 3183 (1985).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. W. Lohman, B. Wirnitzer, “Triple Correlations,” Proc. IEEE 72, 889 (1984).

Rev. Sci. Instrum. (3)

L. Basano, P. Ottonello, “Third Order Correlator for Point Processes,” Rev. Sci. Instrum. 58, 579 (1987).
[CrossRef]

S. M. Sorscher, M. P. Klein, “Profile of a Focussed Collimated Laser Beam Near the Focal Minimum Characterized by Fluorescence Correlation Spectroscopy,” Rev. Sci. Instrum. 51, 98 (1980).
[CrossRef]

B. Blumich, “Two Dimensional Interferometry,” Rev. Sci. Instrum. 58, 911 (1987).
[CrossRef]

Other (13)

N. L. Thompson, “Fluorescence Correlation Spectroscopy,” in Fluorescence Spectroscopy 2, J. Lakowicz, Ed. (Plenum, New York), in press.

The point collection efficiency function T(r) is obtained by integrating the impulse response function of the optical system over the transverse image space coordinates at the location of the aperture along the optical axis.24

J. B. Suck, D. Quitman, B. Maier, Eds., Workshop on Investigation of Higher Order Correlation Functions, J. Phys.46(C9) (1985).

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), pp. 25–40.

A. G. Palmer, N. L. Thompson, “Intensity Dependence of High Order Autocorrelation Functions in Fluorescence Correlation Spectroscopy,” Rev. Sci. Instr. (1989), in press.
[CrossRef]

A. G. Palmer, N. L. Thompson, “High Order Fluorescence Fluctuation Analysis of Model Protein Clusters,” submitted.

P. N. Pusey, “Statistical Properties of Scattered Radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins, E. R. Pike, Eds. (Plenum, New York, 1977), p. 45.

C. J. Oliver, “Recent Techniques in Photon Correlation and Spectrum Analysis Techniques,” in Scattering Techniques Applied to Supramolecular and Nonequilibrium Systems, S. Chen, B. Chu, R. Nossal, Eds. (Plenum, 1981), pp. 87–120.
[CrossRef]

P. N. Pusey, J. G. Rarity, “Measurement of Higher-Order Correlation Functions by Intensity Cross Correlation Light Scattering,” in Workshop on Investigation of Higher Order Correlation Functions, J. B. Suck, D. Quitman, B. Maier, Eds., J. Phys.46(C9), 43 (1985).

A. G. Palmer, N. L. Thompson, “Fluorescence Correlation Spectroscopy for Detecting Submicroscopic Clusters of Fluorescent Molecules in Membranes,” Chem. Phys. Lipids, in press.
[PubMed]

H. L. Royden, Real Analysis (Macmillan, New York, 1963), p.93.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, Orlando, 1984), pp. 70–76

S. H. Lin, Y. Fujimura, H. J. Neusser, E. W. Schlag, Multiphoton Spectroscopy of Molecules (Academic, Orlando, 1984), pp. 89–99.

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Figures (5)

Fig. 1
Fig. 1

Dependence of theoretical relative norms on optical parameters. Shown is the theoretical dependence of n 1 γ n on the following experimentally relevant parameters, as calculated by numerically integrating Eq. (21): (a) radius of focused laser beam w0; (b) radius of image plane aperture in object space s0; (c) displacement of aperture along the optical axis in object space z0; (d) transverse displacement of the aperture in object space x0; (e) depth of fluorescence collection q; and (f) sample thickness L. The upper curve is for n = 4, the middle curve is for n = 3, and the lower curve is for n = 2. For each curve the fixed parameters are w0 = 0.5 μm, s0 = 1 μm, z0 = 0, x0 = 0, q = 1 μm, and L = 100 μm.

Fig. 2
Fig. 2

Measured fluorescence for B-phycoerythrin. Shown is the measured background-corrected fluorescence (arbitrary units) as a function of the concentration of BPE. The solid line is the linear least-squares fit. The standard errors in the mean of 4–5 independent measurements are smaller than the size of the plotted points.

Fig. 3
Fig. 3

High order FCS autocorrelation functions for 6 × 10−10-M B-phycoerythrin in phosphate-buffered saline. Shown are the experimentally obtained functions G1,1(τ), G1,2(τ), G1,3(τ), G2,2(τ) after correction for background intensity and the statistics of photon detection.6 Functions G2,1(τ) and G3,1(τ) (data not shown) are identical to G1,2(τ) and G1,3(τ), respectively, within experimental error.Solid lines are best fits to the theoretical functions for a single diffusing species given previously.5

Fig. 4
Fig. 4

Dependence of Xn(0) on the concentration of fluorescence molecules. Shown are the experimentally determined values of (a) X2(0) as a function of [BPE]−1, (b) X3(0) as a function of [BPE]−2, and (c) X4(0) as a function of [BPE]−3. The values of γn are determined as the slopes of the linear least-squares fits; in all cases, the values of intercepts were not significantly different from zero. Error bars indicate standard errors in the means of 4–5 separate measurements. Results from the least-squares analysis are shown in Table I.

Fig. 5
Fig. 5

Measurement of the depth of fluorescence collection. (a) Reciprocal of the normalized fluorescence of a Langmuir-Blodgett film as a function of the square of the distance between the film and the focal plane of the microscope objective. The focal plane was assumed to be at the location of maximum fluorescence. Solid lines are the linear least-squares fit to the data. The upper curve is for a 50-μm radius image plane aperture and gives a slope of 0.429 ± 0.015 μm−2; the lower curve is for a 100-μm radius aperture and gives a slope of 0.111 ± 0.009 μm−2. The depth of fluorescence collection was determined from the slope of the lines using Eqs. (19) and (24). The linear correlation coefficients were >0.9 and the intercepts were not significantly different from 1.0. The error bars are the standard errors in the mean of three measurements. (b) Normalized fluorescence as a function of the distance between the Langmuir-Blodgett film and the focal plane. The inner curve is for the 50-μm radius aperture, and the outer curve is for the 100-μm radius aperture. The solid lines are given by Eqs. (19) and (24) using the measured values of the beam radius and depth of collection. The error bars are the standard errors in the mean of three measurements.

Tables (1)

Tables Icon

Table I Measured and Calculated Values of the Relative Norms γn

Equations (25)

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G i , j ( τ ) = δ F i ( t + τ ) δ F j ( t ) δ F i ( t ) δ F j ( t ) F ( t ) i + j ,
G 1 , 1 ( 0 ) = γ 2 β 2 G 1 , 2 ( 0 ) = γ 3 β 3  , G 2 , 2 ( 0 ) = γ 4 β 4 + 2 γ 2 2 β 2 2  , G 1 , 3 ( 0 ) = γ 4 β 4 + 3 γ 2 2 β 2 2  ,
β n = k = 1 R α k n C k [ k = 1 R α k C k ] n  ,
α k = Q k / Q 1  ,
γ n = [ V n / V 1 ] n ,
V n = [ Ω 0 W n ( r ) d Ω ] 1 / n ,
W ( r ) = I ( r ) T ( r )  ,
G 1 , 1 ( 0 ) = γ 2 / C  , G 1 , 2 ( 0 ) = γ 3 / C 2 , G 2 , 2 ( 0 ) = γ 4 / C 3 + 2 ( γ 2 / C ) 2 , G 1 , 3 ( 0 ) = γ 4 / C 3 + 3 ( γ 2 / C ) 2 ,
X n ( 0 ) = γ n / C n 1 ,
X 2 ( 0 ) = G 1 , 1 ( 0 ) , X 3 ( 0 ) = [ G 1 , 2 ( 0 ) + G 1 , 2 ( 0 ) ] / 2  , X 4 ( 0 ) = [ G 1 , 3 ( 0 ) + G 3 , 1 ( 0 ) + G 2 , 2 ( 0 ) 8 G 1 , 1 2 ( 0 ) ] / 3.
I ( r ) = [ w 0 w ( z ) ] 2 exp [ 2 ( x 2 + y 2 ) w 2 ( z ) ] ,
w 2 ( z ) = w 0 2 + ρ w 2 z 2 ,
ρ w = λ 0 / ( η π w 0 ) ,
V 1 = 1 2 π w 0 2  , γ n = 1 / ( n V 1 n 1 ) .
V 1 = ½ π w 0 2 L , γ 2 = 1 2 Γ V 1 tan 1 Γ , γ n + 1 = 1 2 ( n 2 1 ) V 1 [ 1 ( 1 + Γ 2 ) n 1 V 1 n 1 + n ( 2 n 3 ) γ n ] ,
Γ = ρ w L / ( 2 w 0 ) .
T ( r ) = [ s 0 s ( z ) ] 2 exp { [ ( x x 0 ) 2 + y 2 ] s 2 ( z ) } ,
s 2 ( z ) = s 0 2 + ρ s 2 ( z z 0 ) 2 ,
ρ s = s 0 / ( 2 q ) ,
V 1 = π w 0 2 s 0 2 / ( w 0 2 + 2 s 0 2 )  , γ n = 1 / ( n V 1 n 1 ) .
V n n = π [ s 0 2 w 0 2 ] n n L / 2 L / 2 exp { 2 n x 0 2 / [ w 2 ( z ) + 2 s 2 ( z ) ] } d z [ s 2 ( z ) w 2 ( z ) ] n 1 [ w 2 ( z ) + 2 s 2 ( z ) ] .
ρ s = tan θ / 2 ,
θ = sin 1 ( N a / η ) ,
F ( z s ) I ( x , y , z s ) T ( x , y , z s ) d x d y ,
F ( z s ) F ( 0 ) = [ 1 + [ ρ w 2 + 2 ρ s 2 w 0 2 + 2 s 0 2 ] z s 2 ] 1

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