Abstract

Photon correlation spectroscopy (PCS) is routinely used to investigate the dynamics of colloidal particles undergoing Brownian motion. This technique is applicable to low-density colloidal suspensions in which the effects of multiple light scattering are minimal. We introduce a new low-coherence heterodyne PCS technique that allows direct investigation of colloidal suspensions of higher concentration than previously accessible with standard PCS. In this technique, low-coherence optical heterodyne interferometry is used to suppress multiple light scattering, allowing preferential detection of single-scattering events.

© 1998 Optical Society of America

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References

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  1. R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. 40, 1604–1614 (1964).
    [CrossRef]
  2. H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
    [CrossRef]
  3. H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light-Beating Spectroscopy (Plenum, New York, 1974).
  4. R. Pecora, ed., Dynamic Light Scattering, Applications of Photon Correlation Spectroscopy (Plenum, New York, 1985), pp. 277–406.
  5. D. Yu Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spectrosc. (USSR) 55, 950–953 (1983).
  6. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  7. 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]
  8. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  9. M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
    [CrossRef]
  10. A. Schmidt, R. Corey, P. Saulnier, “Imaging through random media by use of low-coherence optical heterodyning,” Opt. Lett. 20, 404–406 (1995).
    [CrossRef] [PubMed]
  11. E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
    [CrossRef]

1995

1991

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

1988

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

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

1987

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]

1983

D. Yu Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spectrosc. (USSR) 55, 950–953 (1983).

1970

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

1964

R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. 40, 1604–1614 (1964).
[CrossRef]

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[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]

Corey, R.

Cummins, H. Z.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Herbolzheimer, E.

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

Ichimura, T.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Inaba, H.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Ivanov, D. Yu

D. Yu Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spectrosc. (USSR) 55, 950–953 (1983).

Jakeman, E.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Knable, N.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Kondo, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Kostko, A. F.

D. Yu Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spectrosc. (USSR) 55, 950–953 (1983).

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]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Pecora, R.

R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. 40, 1604–1614 (1964).
[CrossRef]

Pike, E. R.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Pine, D. J.

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

Saulnier, P.

Schmidt, A.

Stephen, M. J.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Toida, M.

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

Weitz, D. A.

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]

Yeh, Y.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Appl. Phys. B

M. Toida, M. Kondo, T. Ichimura, H. Inaba, “Two-dimensional coherent detection imaging in multiple scattering media based on the directional resolution capability of the optical heterodyne method,” Appl. Phys. B 52, 391–394 (1991).
[CrossRef]

J. Chem. Phys.

R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. 40, 1604–1614 (1964).
[CrossRef]

J. Phys. A

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Opt. Lett.

Opt. Spectrosc. (USSR)

D. Yu Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spectrosc. (USSR) 55, 950–953 (1983).

Phys. Rev. B

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Phys. Rev. Lett.

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

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Z. Phys. B

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

H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light-Beating Spectroscopy (Plenum, New York, 1974).

R. Pecora, ed., Dynamic Light Scattering, Applications of Photon Correlation Spectroscopy (Plenum, New York, 1985), pp. 277–406.

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Figures (4)

Fig. 1
Fig. 1

Modified Mach–Zehnder interferometer used to conduct a heterodyne photon-correlation spectroscopic experiment. A diode laser (800 nm) and a He–Ne laser (633 nm) were used along with other major components; SF, spatial filter; BS1, BS2, beam splitters; AOM1, AOM2, acousto-optic modulators; BE, beam expander; TS, translation stage; PH1 (1 mm), PH2 (200 μm), PH3 (1 mm), pinholes; and PD, photodiode detector. The lock-in reference was obtained by electronically mixing the 80.1-MHz and the 80-MHz AOM signals.

Fig. 2
Fig. 2

Diode laser (800-nm) interferogram. The zero interferometer optical path-length difference is indicated as the location of maximum fringe visibility. Regions of enhanced visibility, coherent side modes, are also clearly indicated outside the central coherent peak.

Fig. 3
Fig. 3

Scatterer diameter (d exp), determined experimentally, expressed as a fraction of the manufacturer’s reported diameter (d manf) versus the optical thickness L/ℓ, where L = 1 cm is the sample cell thickness and ℓ is the photon-scattering mean-free-path length. Data were obtained with 0.997-μm polystyrene spheres in water with a He–Ne laser source possessing a coherence length of 0.4 m. The inset shows a typical normalized correlation function and corresponding fit for L/ℓ ≈ 0.75.

Fig. 4
Fig. 4

Scatterer diameter (d exp), determined experimentally, expressed as a fraction of the manufacturer’s reported diameter (d manf) versus the optical thickness L/ℓ, where L = 1 cm is the sample cell thickness and ℓ is the photon-scattering mean-free-path length. Data were obtained with 0.997-μm polystyrene spheres in water with a diode laser source possessing a coherence length of 400 μm. The inset shows a typical normalized correlation function and corresponding fit for L/ℓ ≈ 0.75. The difference in time scale probed for the two laser sources is a result of the differing wavelength and a small change in the scattering angle.

Equations (2)

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G τ = 1 + A   exp - 2 Dq 2 τ ,
D = k B T 6 π η r ,

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