Abstract

For describing the fluctuating signal scattered from a multiple-scattering system, diffusive-wave spectroscopy makes use of a diffusion model that provides the path-length distribution of scattered waves for a specific geometry. Using the recently introduced optical path-length spectroscopy, we show that the diffusion model fails to describe wave propagation in the low-order multiple-scattering regime. We propose a new methodology with which to obtain information about the dynamic properties of nondiffusive scattering systems. We use optical path-length spectroscopy to obtain experimentally the path-length distribution of optical waves scattered from dynamic colloids, which are multiply scattering but not in the diffusion limit. The experimental results show that, with this new technique, the accuracy of dynamic measurements is significantly improved in subdiffusive scattering regimes.

© 2001 Optical Society of America

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References

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  1. B. J. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics, (Wiley, New York, 1976).
  2. G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
    [Crossref]
  3. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [Crossref] [PubMed]
  4. D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
    [Crossref]
  5. T. G. Mason, H. Guang, D. A. Weitz, “Diffusing-wave spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. A 14, 139–149 (1997).
    [Crossref]
  6. E. M. Furst, A. P. Gast, “Particle dynamics in magnetorheological suspensions using diffusing-wave spectroscopy,” Phys. Rev. E 58, 3372–3376 (1998).
    [Crossref]
  7. P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
    [Crossref]
  8. T. Gisler, D. A. Weitz, “Scaling of the microrheology of semidilute F-actin solutions,” Phys. Rev. Lett. 82, 1606–1609 (1999).
    [Crossref]
  9. G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
    [Crossref]
  10. M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
    [Crossref]
  11. P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
    [Crossref]
  12. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  13. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
    [Crossref]
  14. K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [Crossref] [PubMed]
  15. G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
    [Crossref]
  16. G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
    [Crossref]
  17. J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  18. J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
    [Crossref] [PubMed]

2000 (3)

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
[Crossref]

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[Crossref]

1999 (3)

T. Gisler, D. A. Weitz, “Scaling of the microrheology of semidilute F-actin solutions,” Phys. Rev. Lett. 82, 1606–1609 (1999).
[Crossref]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[Crossref]

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

1998 (1)

E. M. Furst, A. P. Gast, “Particle dynamics in magnetorheological suspensions using diffusing-wave spectroscopy,” Phys. Rev. E 58, 3372–3376 (1998).
[Crossref]

1997 (2)

P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
[Crossref]

T. G. Mason, H. Guang, D. A. Weitz, “Diffusing-wave spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. A 14, 139–149 (1997).
[Crossref]

1994 (1)

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[Crossref]

1991 (1)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[Crossref] [PubMed]

1990 (2)

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

1987 (1)

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[Crossref]

Alfano, R. R.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics, (Wiley, New York, 1976).

Candau, S. J.

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

Clapper, M. F.

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

Collura, J. S.

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

Dogariu, A.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[Crossref]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[Crossref]

Duderstadt, J. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Durian, D. J.

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
[Crossref]

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[Crossref]

Fisch, M. R.

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

Furst, E. M.

E. M. Furst, A. P. Gast, “Particle dynamics in magnetorheological suspensions using diffusing-wave spectroscopy,” Phys. Rev. E 58, 3372–3376 (1998).
[Crossref]

Gast, A. P.

E. M. Furst, A. P. Gast, “Particle dynamics in magnetorheological suspensions using diffusing-wave spectroscopy,” Phys. Rev. E 58, 3372–3376 (1998).
[Crossref]

Gisler, T.

T. Gisler, D. A. Weitz, “Scaling of the microrheology of semidilute F-actin solutions,” Phys. Rev. Lett. 82, 1606–1609 (1999).
[Crossref]

Guang, H.

Hamilton, L. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Harrison, D.

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

Hebraud, P.

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
[Crossref]

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Lemieux, P.-A.

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
[Crossref]

Lequeux, F.

P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
[Crossref]

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Maret, G.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[Crossref]

Mason, T. G.

Mujat, C.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[Crossref]

Munch, J.-P.

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
[Crossref]

Nissato, G.

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

Pecora, R.

B. J. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics, (Wiley, New York, 1976).

Pine, D. J.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

Popescu, G.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[Crossref]

G. Popescu, A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24, 442–444 (1999).
[Crossref]

Vera, M. U.

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
[Crossref]

Weitz, D. A.

T. Gisler, D. A. Weitz, “Scaling of the microrheology of semidilute F-actin solutions,” Phys. Rev. Lett. 82, 1606–1609 (1999).
[Crossref]

T. G. Mason, H. Guang, D. A. Weitz, “Diffusing-wave spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. A 14, 139–149 (1997).
[Crossref]

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

Wolf, P. E.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[Crossref]

Yoo, K. M.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Zhu, J. X.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[Crossref] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

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

J. Phys. (Paris) (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[Crossref] [PubMed]

Phys. Rev. E (6)

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[Crossref]

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[Crossref]

G. Nissato, P. Hebraud, J.-P. Munch, S. J. Candau, “Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels,” Phys. Rev. E 61, 2879–2887 (2000).
[Crossref]

M. F. Clapper, J. S. Collura, D. Harrison, M. R. Fisch, “Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres,” Phys. Rev. E 59, 3631–3636 (1999).
[Crossref]

P.-A. Lemieux, M. U. Vera, D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (2000).
[Crossref]

E. M. Furst, A. P. Gast, “Particle dynamics in magnetorheological suspensions using diffusing-wave spectroscopy,” Phys. Rev. E 58, 3372–3376 (1998).
[Crossref]

Phys. Rev. Lett. (4)

P. Hebraud, F. Lequeux, J.-P. Munch, “Yielding and rearrangements in disordered emulsions,” Phys. Rev. Lett. 78, 4657–4660 (1997).
[Crossref]

T. Gisler, D. A. Weitz, “Scaling of the microrheology of semidilute F-actin solutions,” Phys. Rev. Lett. 82, 1606–1609 (1999).
[Crossref]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[Crossref] [PubMed]

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Z. Phys. B (1)

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[Crossref]

Other (3)

B. J. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics, (Wiley, New York, 1976).

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

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Figures (6)

Fig. 1
Fig. 1

Michelson geometry for OPS measurements: LCS, low-coherence source; BS, beam splitter; M, mirror; D, detector; S, sample under investigation.

Fig. 2
Fig. 2

(a) OPS signals for 0.356-µm polystyrene microspheres suspended in water at different volume fractions, as indicated. (b) OPS data for 0.51-µm polystyrene particles with a volume fraction of 10%; also shown is the fit with the diffusion model.

Fig. 3
Fig. 3

Experimental setup for dynamic scattering measurements: FC, fiber coupler; PM, photomultiplier; BI9000, digital correlator; PC, computer.

Fig. 4
Fig. 4

P(s) measured for suspensions with four values of l t , as indicated. The thin continuous curves were obtained from the diffusion model of Eq. (2).

Fig. 5
Fig. 5

Normalized field autocorrelation functions for colloidal suspensions of various values of l t , as indicated. The continuous curves are the best fits to the data obtained by numerical evaluation of the Laplace transform of Eq. (3) with the measured P(s) distributions. The dashed curves correspond to DWS, as described in the text.

Fig. 6
Fig. 6

Relative error of the experimental value τ0 exp with respect to the theoretical value τ0 for a series of colloidal suspensions characterized by different parameters s m /l t .

Equations (6)

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

IdΔs=IsΔs+Iref+2IsΔsIref1/2|γΔs|cos2πΔs/λ,
Ids=alt-3/2zes-5/2 exp- 3ze2lt4s,
g1τ=0 Psexp-2ττ0slt.
It=Ist+IFt+2 ReEstEF*texpiΦt,
G2τ=ItIt+τ*=IF2+2IFIs+IstIst+τ*+IFG1τ+G1τ*.
g2τ=1+2β Reg1τ,

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