Abstract

The autocorrelation function of the backscattered intensity in a diffusing-wave spectroscopy experiment that uses a point source is calculated by use of the diffusive-wave model. We show that in this approximation the calculated autocorrelation function decays faster than if the plane-source approximation were used. The design of a probe that implements this geometry is presented together with preliminary results that show the utility of the probe as a sizing tool in concentrated dispersions.

© 2001 Optical Society of America

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References

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  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]
  2. M. J. Stephen, G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
    [CrossRef] [PubMed]
  3. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  4. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  5. D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
    [CrossRef] [PubMed]
  6. D. S. Horne, “Particle size measurement in concentrated latex suspensions using fibre optic photon correlation spectroscopy,” J. Phys. D 22, 1257–4265 (1989).
    [CrossRef]
  7. D. G. Dalgleish, D. S. Horne, “Studies of gelation and acidified renneted milks using diffusing wave spectroscopy,” Milchwissenschaft 46, 417–420 (1991).
  8. H. Wiese, D. Horn, “Single mode fibers in fiberoptic quasi-elastic light scattering: a study of the dynamics of concentrated suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
    [CrossRef]
  9. H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated dispersions: the on-line process control of carotenoid micronization,” Ber. Bunsenges. Phys. Chem. 97, 1589–1597 (1993).
    [CrossRef]
  10. D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, the Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, 1993), pp. 652–720.
  11. E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
    [CrossRef]
  12. E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
    [CrossRef]
  13. C. J. Lloyd, E. A. Perkins, R. J. G. Carr, “Dynamic light scattering and its applications in concentrated suspensions,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Norwood, Mass., 1997), pp. 109–127.
  14. E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
    [CrossRef]
  15. B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
    [CrossRef]
  16. R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
    [CrossRef]
  17. D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
    [CrossRef] [PubMed]
  18. D. J. Durian, J. Rudnick, “Spatially resolved backscattering: implementation of extrapolation boundary conditions and exponential source,” J. Opt. Soc. Am. A 16, 837–844 (1999).
    [CrossRef]
  19. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959).

1999 (1)

1995 (1)

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
[CrossRef] [PubMed]

1994 (2)

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
[CrossRef]

1993 (3)

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated dispersions: the on-line process control of carotenoid micronization,” Ber. Bunsenges. Phys. Chem. 97, 1589–1597 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
[CrossRef]

1992 (1)

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

1991 (2)

D. G. Dalgleish, D. S. Horne, “Studies of gelation and acidified renneted milks using diffusing wave spectroscopy,” Milchwissenschaft 46, 417–420 (1991).

H. Wiese, D. Horn, “Single mode fibers in fiberoptic quasi-elastic light scattering: a study of the dynamics of concentrated suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

1989 (2)

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

D. S. Horne, “Particle size measurement in concentrated latex suspensions using fibre optic photon correlation spectroscopy,” J. Phys. D 22, 1257–4265 (1989).
[CrossRef]

1988 (2)

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 (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]

M. J. Stephen, G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[CrossRef] [PubMed]

Ackerson, B. J.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Boas, D. A.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
[CrossRef] [PubMed]

Campbell, L. E.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
[CrossRef] [PubMed]

Carr, R. J. G.

C. J. Lloyd, E. A. Perkins, R. J. G. Carr, “Dynamic light scattering and its applications in concentrated suspensions,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Norwood, Mass., 1997), pp. 109–127.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959).

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]

Cwilich, G.

M. J. Stephen, G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[CrossRef] [PubMed]

Dalgleish, D. G.

D. G. Dalgleish, D. S. Horne, “Studies of gelation and acidified renneted milks using diffusing wave spectroscopy,” Milchwissenschaft 46, 417–420 (1991).

Dorr-Nowkoorani, F.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Dougherty, R. L.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Durian, D. J.

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]

Horn, D.

E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated dispersions: the on-line process control of carotenoid micronization,” Ber. Bunsenges. Phys. Chem. 97, 1589–1597 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
[CrossRef]

H. Wiese, D. Horn, “Single mode fibers in fiberoptic quasi-elastic light scattering: a study of the dynamics of concentrated suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Horne, D. S.

D. G. Dalgleish, D. S. Horne, “Studies of gelation and acidified renneted milks using diffusing wave spectroscopy,” Milchwissenschaft 46, 417–420 (1991).

D. S. Horne, “Particle size measurement in concentrated latex suspensions using fibre optic photon correlation spectroscopy,” J. Phys. D 22, 1257–4265 (1989).
[CrossRef]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959).

Lloyd, C. J.

C. J. Lloyd, E. A. Perkins, R. J. G. Carr, “Dynamic light scattering and its applications in concentrated suspensions,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Norwood, Mass., 1997), pp. 109–127.

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]

Nobbmann, U.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Perkins, E. A.

C. J. Lloyd, E. A. Perkins, R. J. G. Carr, “Dynamic light scattering and its applications in concentrated suspensions,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Norwood, Mass., 1997), pp. 109–127.

Pine, D. J.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

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

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, the Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, 1993), pp. 652–720.

Pusey, P. N.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Reguigui, N. M.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Rudnick, J.

Stephen, M. J.

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

M. J. Stephen, G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[CrossRef] [PubMed]

Tough, R. J. A.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Van Keuren, E. R.

E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
[CrossRef]

Weitz, D. A.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

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

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, the Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, 1993), pp. 652–720.

Wiese, H.

E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
[CrossRef]

H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated dispersions: the on-line process control of carotenoid micronization,” Ber. Bunsenges. Phys. Chem. 97, 1589–1597 (1993).
[CrossRef]

H. Wiese, D. Horn, “Single mode fibers in fiberoptic quasi-elastic light scattering: a study of the dynamics of concentrated suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

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]

Yodh, A. G.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
[CrossRef] [PubMed]

Ber. Bunsenges. Phys. Chem. (2)

H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated dispersions: the on-line process control of carotenoid micronization,” Ber. Bunsenges. Phys. Chem. 97, 1589–1597 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Fiber-optic diffusing-wave spectroscopy of concentrated dispersions of large polymer latex spheres,” Ber. Bunsenges. Phys. Chem. 98, 269–271 (1994).
[CrossRef]

Colloids Surf. A (1)

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions—and investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

J. Chem. Phys. (1)

H. Wiese, D. Horn, “Single mode fibers in fiberoptic quasi-elastic light scattering: a study of the dynamics of concentrated suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

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

J. Phys. D (1)

D. S. Horne, “Particle size measurement in concentrated latex suspensions using fibre optic photon correlation spectroscopy,” J. Phys. D 22, 1257–4265 (1989).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

J. Thermophys. Heat Transfer (1)

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbmann, “Correlation transfer: applications of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Langmuir (1)

E. R. Van Keuren, H. Wiese, D. Horn, “Fiberoptic quasi-elastic light scattering in concentrated latex dispersions: angular dependent measurements of singly scattered light,” Langmuir 9, 2883–2887 (1993).
[CrossRef]

Milchwissenschaft (1)

D. G. Dalgleish, D. S. Horne, “Studies of gelation and acidified renneted milks using diffusing wave spectroscopy,” Milchwissenschaft 46, 417–420 (1991).

Phys. Rev. B (1)

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

Phys. Rev. Lett. (4)

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

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

M. J. Stephen, G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[CrossRef] [PubMed]

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation functions,” Phys. Rev. Lett. 75, 1855–1888 (1995).
[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)

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, the Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, 1993), pp. 652–720.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959).

C. J. Lloyd, E. A. Perkins, R. J. G. Carr, “Dynamic light scattering and its applications in concentrated suspensions,” in Optical Fibre Sensors, J. Dakin, B. Culshaw, eds. (Artech House, Norwood, Mass., 1997), pp. 109–127.

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of the experimental setup: (a) laser source, (b) input fiber, (c) output fiber, (d) armored cable, (e) probe head, (f) detector, (g) computer, (h) illumination fiber, (i) detector fiber, (j) optical glue, (k) steel tube. The fibers are glued to the steel tube by an optical adhesive that also fills the gaps. The fibers are polished flush to the face of the steel tube. The sizes of the elements are not to scale: The diameter of the probe is 1.5 cm, and the diameter of the fibers is 125 µm.

Fig. 2
Fig. 2

Because of the limited numerical aperture of the fibers, the photons propagating ballistically in the scattering medium will be propagated by the detector fiber only if they are scattered at a distance greater than d from the probe.

Fig. 3
Fig. 3

Geometry used for calculating the autocorrelation function. Light enters the medium at (0, 0, 0) and propagates diffusively from (0, 0, z 0).

Fig. 4
Fig. 4

Comparison of the intensity autocorrelation functions of multiply backscattered light from a plane (dashed curve) and from a point source (solid curve). The equation used for the plane source is the one given by Weitz and Pine10 (p. 675). For the point source Eq. (11) was used.

Fig. 5
Fig. 5

Experimental arrangement: (a) and (b), optical fibers; (c), probe body; (d), sample; (e), sample cell. The sizes of the elements are not to scale: The diameter of the probe is 1.5 cm, and the diameter of the fibers is 125 µm.

Fig. 6
Fig. 6

Backscattering measurements from suspensions of a volume fraction of ϕ = 0.10 of latex beads with diameters of 0.1 µm (+), 0.5 µm (×), and 1.0 µm (*). The solid curves were obtained from fits of the linear part of the plot to Eq. (13).

Tables (1)

Tables Icon

Table 1 Results of Fitting the Autocorrelation Functions from the Latex Samples to Eq. (13)a

Equations (19)

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

G1τ  0 Psexp-2τ/τ0s/l*ds,
g1τ=U¯r, τU¯r, 0,
Ut=D12U
Ur, t=0=U0δr-r0, t.
U+23l*nˆU=0,
U¯=14πD10ξη J0ξRexp-ηz0-z+A exp-ηzdξ,
A=2ηl*-32ηl*+3exp-ηz0,
g1τ=0ξ/ηJ0ξRexp-ηz0-z+2ηl*-3/2ηl*+3exp-ηz0+zdξ0 J0ξRexp-ξz0-z+2ξl*-3/2ξl*+3exp-ξz0+zdξ.
g1τ=0ξ/ηexp-ηz0dξ+0ξ/η2ηl*-3/2ηl*+3exp-ηz0dξ0exp-ξz0dξ+02ξl*-3/2ξl*+3exp-ξz0dξ,
g1τ=1+6γ26τ/τ01/2+321+2γ3exp-γ6τ/τ01/2.
g2τ=1+1+6γ26τ/τ01/2+321+2γ32exp-2γ6τ/τ01/2.
g2τ=1+exp-γ6τ/τ01/21+26τ/τ01/232.
g2τ=P1+P21+6γ26τ/τ01/2+321+2γ32×exp-2γ6τ/τ01/2,
0ξηexp-ηz0dξ=αexp-ηz0dη,
0ξη2ηl*-32ηl*+3exp-ηz0dξ=α2ηl*-32ηl*+3exp-ηz0dη,
αexp-ηz0dη=exp-αz0z0.
α2ηl*-32ηl*+3exp-ηz0dη=-2l* exp-ηz0+6z0 exp3z0/2l*Ei1, z02l*η+32l*2l*z0α,
Ei1, x=1exp-xtxdt.
α2ηl*-32ηl*+3exp-ηz0dη=exp-αz0z01+24l*z02l*α+32.

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