Abstract

A dual-beam dynamic light-scattering arrangement is devised to measure the time-dependent mean squared relative displacement of a pair of tracer particles with a small separation of micrometers. The technique is tested by the measurement of the relative diffusion of polymer latex spheres suspended in a simple viscous fluid. The experiment verifies the theory and demonstrates its applications. The dual-beam dynamic light-scattering technique, when combined with an optical microscope, provides a powerful tool for the study of two-particle microrheology of soft materials. The advantages of the new technique are its high statistical accuracy, faster temporal response, and ease of use.

© 2004 Optical Society of America

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References

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  1. B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  2. T. G. Mason, D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
    [CrossRef] [PubMed]
  3. T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
    [CrossRef]
  4. A. J. Levine, T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
    [CrossRef] [PubMed]
  5. A. J. Levine, T. C. Lubensky, “Two-point microrheology and the electrostatic analogy,” Phys. Rev. E 65, 011501 (2001).
    [CrossRef]
  6. T. Gisler, D. A. Weitz, “Tracer microrheology in complex fluids,” Curr. Opin. Colloid Interface Sci. 3, 586–592 (1998).
    [CrossRef]
  7. F. C. MacKintosh, C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300–307 (1999).
    [CrossRef]
  8. M. L. Gardel, M. T. Valentine, D. A. Weitz, “Microrheology,” in Microscale Diagnostic Techniques, K. Breuer, ed. (Springer-Verlag, New York, to be published).
  9. Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
    [CrossRef]
  10. J.-C. Meiners, S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
    [CrossRef]
  11. Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
    [CrossRef] [PubMed]
  12. X. Ye, P. Tong, L. J. Fetters, “Transport of probe particles in semidilute polymer solutions,” Macromolecules 31, 5785–5793 (1998).
    [CrossRef]
  13. J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
    [CrossRef] [PubMed]
  14. J. C. Crocker, D. G. Grier, “Methods of digital video microscopy,” J. Colloid Interface Sci. 179, 298–310 (1996).
    [CrossRef]
  15. H. Z. Cummins, H. L. Swinney, “Light beating spectroscopy,” in Progress in Optics, Vol. VIII, E. Wolf, ed. (Elsevier North-Holland, Amsterdam, 1970).
    [CrossRef]
  16. E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
    [CrossRef] [PubMed]
  17. D. L. Ermak, J. A. Mecammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
    [CrossRef]
  18. G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74, 1–29 (1976).
    [CrossRef]
  19. J. C. Crocker, “Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal particles,” J. Chem. Phys. 106, 2837–2840 (1997).
    [CrossRef]
  20. T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).
    [CrossRef]
  21. Y.-X. Du, B. J. Ackerson, P. Tong, “Velocity difference measurement with a fiber-optic coupler,” J. Opt. Soc. Am. A 15, 2433–2439 (1998).
    [CrossRef]
  22. P. D. Kaplan, V. Trappe, D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).
    [CrossRef]
  23. E. J. Hinch, L. C. Nitsche, “Non-linear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions,” J. Fluid Mech. 256, 343–401 (1993).
    [CrossRef]
  24. M. T. Valentine, A. K. Popp, D. A. Weitz, P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. 26, 890–892 (2001).
    [CrossRef]

2002 (2)

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
[CrossRef] [PubMed]

2001 (2)

A. J. Levine, T. C. Lubensky, “Two-point microrheology and the electrostatic analogy,” Phys. Rev. E 65, 011501 (2001).
[CrossRef]

M. T. Valentine, A. K. Popp, D. A. Weitz, P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. 26, 890–892 (2001).
[CrossRef]

2000 (3)

A. J. Levine, T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef] [PubMed]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

1999 (3)

F. C. MacKintosh, C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300–307 (1999).
[CrossRef]

J.-C. Meiners, S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

P. D. Kaplan, V. Trappe, D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).
[CrossRef]

1998 (3)

Y.-X. Du, B. J. Ackerson, P. Tong, “Velocity difference measurement with a fiber-optic coupler,” J. Opt. Soc. Am. A 15, 2433–2439 (1998).
[CrossRef]

T. Gisler, D. A. Weitz, “Tracer microrheology in complex fluids,” Curr. Opin. Colloid Interface Sci. 3, 586–592 (1998).
[CrossRef]

X. Ye, P. Tong, L. J. Fetters, “Transport of probe particles in semidilute polymer solutions,” Macromolecules 31, 5785–5793 (1998).
[CrossRef]

1997 (3)

J. C. Crocker, “Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal particles,” J. Chem. Phys. 106, 2837–2840 (1997).
[CrossRef]

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).
[CrossRef]

1996 (1)

J. C. Crocker, D. G. Grier, “Methods of digital video microscopy,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

1995 (1)

T. G. Mason, D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
[CrossRef] [PubMed]

1993 (1)

E. J. Hinch, L. C. Nitsche, “Non-linear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions,” J. Fluid Mech. 256, 343–401 (1993).
[CrossRef]

1978 (1)

D. L. Ermak, J. A. Mecammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[CrossRef]

1976 (1)

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74, 1–29 (1976).
[CrossRef]

Ackerson, B. J.

Batchelor, G. K.

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74, 1–29 (1976).
[CrossRef]

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Brenner, M. P.

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Cheung, C.

Crocker, J. C.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

J. C. Crocker, “Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal particles,” J. Chem. Phys. 106, 2837–2840 (1997).
[CrossRef]

J. C. Crocker, D. G. Grier, “Methods of digital video microscopy,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, H. L. Swinney, “Light beating spectroscopy,” in Progress in Optics, Vol. VIII, E. Wolf, ed. (Elsevier North-Holland, Amsterdam, 1970).
[CrossRef]

Du, Y.-X.

Dufresne, E. R.

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Ermak, D. L.

D. L. Ermak, J. A. Mecammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[CrossRef]

Fetters, L. J.

X. Ye, P. Tong, L. J. Fetters, “Transport of probe particles in semidilute polymer solutions,” Macromolecules 31, 5785–5793 (1998).
[CrossRef]

Ganesan, K.

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

Gardel, M. L.

M. L. Gardel, M. T. Valentine, D. A. Weitz, “Microrheology,” in Microscale Diagnostic Techniques, K. Breuer, ed. (Springer-Verlag, New York, to be published).

Gisler, T.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

T. Gisler, D. A. Weitz, “Tracer microrheology in complex fluids,” Curr. Opin. Colloid Interface Sci. 3, 586–592 (1998).
[CrossRef]

Goldburg, W. I.

Grier, D. G.

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

J. C. Crocker, D. G. Grier, “Methods of digital video microscopy,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Hinch, E. J.

E. J. Hinch, L. C. Nitsche, “Non-linear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions,” J. Fluid Mech. 256, 343–401 (1993).
[CrossRef]

Kaplan, P. D.

M. T. Valentine, A. K. Popp, D. A. Weitz, P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. 26, 890–892 (2001).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

P. D. Kaplan, V. Trappe, D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).
[CrossRef]

Kole, T. P.

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
[CrossRef] [PubMed]

Kuo, S. C.

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

Lee, S.-H. J.

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

Levine, A. J.

A. J. Levine, T. C. Lubensky, “Two-point microrheology and the electrostatic analogy,” Phys. Rev. E 65, 011501 (2001).
[CrossRef]

A. J. Levine, T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef] [PubMed]

Lubensky, T. C.

A. J. Levine, T. C. Lubensky, “Two-point microrheology and the electrostatic analogy,” Phys. Rev. E 65, 011501 (2001).
[CrossRef]

A. J. Levine, T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef] [PubMed]

MacKintosh, F. C.

F. C. MacKintosh, C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300–307 (1999).
[CrossRef]

Mason, T. G.

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

T. G. Mason, D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
[CrossRef] [PubMed]

Mecammon, J. A.

D. L. Ermak, J. A. Mecammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[CrossRef]

Meiners, J.-C.

J.-C. Meiners, S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

Narayanan, T.

Nitsche, L. C.

E. J. Hinch, L. C. Nitsche, “Non-linear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions,” J. Fluid Mech. 256, 343–401 (1993).
[CrossRef]

Pecora, R.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Popp, A. K.

Quake, S. R.

J.-C. Meiners, S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

Schmidt, C. F.

F. C. MacKintosh, C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300–307 (1999).
[CrossRef]

Squires, T. M.

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Swinney, H. L.

H. Z. Cummins, H. L. Swinney, “Light beating spectroscopy,” in Progress in Optics, Vol. VIII, E. Wolf, ed. (Elsevier North-Holland, Amsterdam, 1970).
[CrossRef]

Tong, P.

Trappe, V.

Tseng, Y.

Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
[CrossRef] [PubMed]

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

Valentine, M. T.

M. T. Valentine, A. K. Popp, D. A. Weitz, P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. 26, 890–892 (2001).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

M. L. Gardel, M. T. Valentine, D. A. Weitz, “Microrheology,” in Microscale Diagnostic Techniques, K. Breuer, ed. (Springer-Verlag, New York, to be published).

van Zanten, J. H.

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

Weeks, E. R.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

Weitz, D. A.

M. T. Valentine, A. K. Popp, D. A. Weitz, P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. 26, 890–892 (2001).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

P. D. Kaplan, V. Trappe, D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).
[CrossRef]

T. Gisler, D. A. Weitz, “Tracer microrheology in complex fluids,” Curr. Opin. Colloid Interface Sci. 3, 586–592 (1998).
[CrossRef]

T. G. Mason, D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
[CrossRef] [PubMed]

M. L. Gardel, M. T. Valentine, D. A. Weitz, “Microrheology,” in Microscale Diagnostic Techniques, K. Breuer, ed. (Springer-Verlag, New York, to be published).

Wirtz, D.

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
[CrossRef] [PubMed]

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

Wu, X.-L.

Ye, X.

X. Ye, P. Tong, L. J. Fetters, “Transport of probe particles in semidilute polymer solutions,” Macromolecules 31, 5785–5793 (1998).
[CrossRef]

Yodh, A. G.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

Appl. Opt. (2)

Biophys. J. (1)

Y. Tseng, T. P. Kole, D. Wirtz, “Micromechanical mapping of live cells by multiple-particle-tracking microrheology,” Biophys. J. 83, 3162–3176 (2002).
[CrossRef] [PubMed]

Curr. Opin. Colloid Interface Sci. (3)

T. Gisler, D. A. Weitz, “Tracer microrheology in complex fluids,” Curr. Opin. Colloid Interface Sci. 3, 586–592 (1998).
[CrossRef]

F. C. MacKintosh, C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300–307 (1999).
[CrossRef]

Y. Tseng, T. P. Kole, S.-H. J. Lee, D. Wirtz, “Local dynamics and viscoelastic properties of cell biological systems,” Curr. Opin. Colloid Interface Sci. 7, 210–217 (2002).
[CrossRef]

J. Chem. Phys. (2)

D. L. Ermak, J. A. Mecammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[CrossRef]

J. C. Crocker, “Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal particles,” J. Chem. Phys. 106, 2837–2840 (1997).
[CrossRef]

J. Colloid Interface Sci. (1)

J. C. Crocker, D. G. Grier, “Methods of digital video microscopy,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

J. Fluid Mech. (2)

E. J. Hinch, L. C. Nitsche, “Non-linear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions,” J. Fluid Mech. 256, 343–401 (1993).
[CrossRef]

G. K. Batchelor, “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74, 1–29 (1976).
[CrossRef]

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

Macromolecules (1)

X. Ye, P. Tong, L. J. Fetters, “Transport of probe particles in semidilute polymer solutions,” Macromolecules 31, 5785–5793 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

A. J. Levine, T. C. Lubensky, “Two-point microrheology and the electrostatic analogy,” Phys. Rev. E 65, 011501 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

T. G. Mason, D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
[CrossRef] [PubMed]

T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[CrossRef]

A. J. Levine, T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef] [PubMed]

J.-C. Meiners, S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef] [PubMed]

E. R. Dufresne, T. M. Squires, M. P. Brenner, D. G. Grier, “Hydrodynamic coupling of two Brownian spheres to a planar surface,” Phys. Rev. Lett. 85, 3317–3320 (2000).
[CrossRef] [PubMed]

Other (3)

H. Z. Cummins, H. L. Swinney, “Light beating spectroscopy,” in Progress in Optics, Vol. VIII, E. Wolf, ed. (Elsevier North-Holland, Amsterdam, 1970).
[CrossRef]

M. L. Gardel, M. T. Valentine, D. A. Weitz, “Microrheology,” in Microscale Diagnostic Techniques, K. Breuer, ed. (Springer-Verlag, New York, to be published).

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic diagram of the scattering geometry (z axis is perpendicular to the paper): k i , incident wave vector; k s , scattered wave vector; θ, scattering angle; q = k s - k i . (b) Schematic diagram of the experimental setup: LB, incident laser beam; BC, Bragg cell; L1, microscope objective; SC, sample cell; L2, collimating lens; FC, fiber-optic coupler; LS, He–Ne laser; PMT, photomultiplier tube; FS, frequency shifter; DSA, dynamical signal analyzer.

Fig. 2
Fig. 2

Typical trace of the scattered light intensity across two scattering volumes separated by l = 10.5 μm. The particle size is 0.14 μm, and the electronic carrier frequency Ω0 is 5 kHz.

Fig. 3
Fig. 3

Measured intensity autocorrelation function, g(τ) - 1, as a function of delay time τ for particles of size 1.6 μm. The circles are obtained when two incident beams are used, and the squares are obtained when only one incident beam is present. The solid curves are the simple exponential fits to the corresponding data points.

Fig. 4
Fig. 4

(a) Measured frequency power spectrum P(f) of the scattered light intensity when two incident beams are used (open circles). The solid curve is a fit to a Lorentzian function. In the measurement, Ω0 is set to zero and the particle size is 1.6 μm. The inset shows a linear plot of 103/P(f) versus (f - Ω0)2 for the same data set. (b) Corresponding log-log plot of 103/P(f) versus (f - Ω0)2.

Fig. 5
Fig. 5

Measured decay time τ0 as a function of particle size 2a. The solid circles are obtained when two incident beams are used. The open circles are obtained when only one incident beam is present. The solid curve is a fit to τ0 = t 0/(1 - γa/ l), with γ = 4 ± 1. The dashed line shows the one-beam decay time t 0 = (2q 2 D 0)-1.

Fig. 6
Fig. 6

Optical design of the dual-beam DLS microscope: IF, incident fiber; BC, Bragg cell; CP, collimating prism; L1, lens; DM, dichroic mirror; CO, condenser; SA, sample; OB, objective; BFP, back focal plane; TO, tube optics; SP, scattering plane; CF, collecting fiber; PMT, photomultiplier tube; FS, frequency shifter; DSA, dynamical signal analyzer.

Equations (12)

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Δr˜2s=3kBTπasG˜s,
gτ=E1t+τ+E2t+τE1t+τ+E2t+τ*E1t+E2tE1t+E2t*E1t+E2tE1t+E2t*2,
gτ=1+I12I1+I22 G1τ+I22I1+I22 G2τ+2I1I2I1+I22 G12τ 1+bG12τ,
G12τ=1N2i,jNexpiq·r2,it+τ-r1,jt+τ-r2,it-r1,jt-i2πΩτ+c.c.=expiq·Δr21τcos2πΩτ,
expiq·Δr21τ=exp-12q·Δr21τ2exp-12k2Δr2l, τ×1-cos θ2+Δr2l, τsin2 θ.
G12τ=exp-12k2Δr2l, τ1-cos θ2+Δr2l, τsin2 θcos2πΩτ.
Δr2l, τ=2Dτ, D=2D01-3a2l+Oa3l3,
Δr2l, τ=2Dτ, D=2D01-3a4l+Oa3l3,
G12τ=exp-k2D1-cos θ2+Dsin2 θτcos2πΩτ=exp-τ/τ0cos2πΩτ,
τ0=1k2D1-cos θ2+Dsin2 θ=t01-3a4l1+sin2 θ/2.
Pf=12π-expi2πfτG12τdτ11+2πτ02f-Ω2.
1/Pf=α+βf-Ω2.

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