Abstract

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented.

© 1997 Optical Society of America

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  1. G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
    [CrossRef]
  2. G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
    [CrossRef]
  3. J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1563 (1983).
    [CrossRef]
  4. H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
    [CrossRef]
  5. K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
    [CrossRef]
  6. D. Y. Ivanov, A. F. Kostko, “Spectrum of multiply quasi-elastically scattered light,” Opt. Spektrosk. 55, 950–953 (1983).
  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. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).
    [CrossRef] [PubMed]
  9. W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).
  10. W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
    [CrossRef]
  11. J. A. Lock, “Role of multiple scattering in cross-correlated light scattering with a single laser beam,” Appl. Opt. 36, 7559–7570 (1997).
    [CrossRef]
  12. See, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 508–516.
  13. U. Nobbmann, S. W. Jones, B. J. Ackerson, “Multiple-scattering suppression: cross correlation with tilted single-mode fibers,” Appl. Opt. 36, 7571–7576 (1997).
    [CrossRef]
  14. See, for example, B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  15. Č. Koňák, J. Jakeš, P. Štěpánek, F. Petráš, M. Kárská, J. Křepelka, J. Peřina, “Effect of multiple scattering on transmitted and scattered light,” Appl. Opt. 30, 4865–4867 (1991).
    [CrossRef]

1997 (2)

1991 (2)

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (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]

1986 (1)

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

1983 (2)

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1563 (1983).
[CrossRef]

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

1981 (2)

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

Ackerson, B. J.

Berne, B. J.

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

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 508–516.

Cannell, D. S.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

Chaikin, P. M.

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

Cheung, H. M.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

de Kruif, C. G.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1563 (1983).
[CrossRef]

Dhont, J. K. G.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1563 (1983).
[CrossRef]

Herbolzheimer, E.

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

Ivanov, D. Y.

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

Jakeš, J.

Jones, S. W.

Kárská, M.

Konák, C.

Kostko, A. F.

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

Krepelka, J.

Lock, J. A.

J. A. Lock, “Role of multiple scattering in cross-correlated light scattering with a single laser beam,” Appl. Opt. 36, 7559–7570 (1997).
[CrossRef]

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

Mann, J. A.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

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]

Meyer, W. V.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

Mos, H. J.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

Nobbmann, U.

Pathmamanoharan, C.

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

Pecora, R.

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

Perina, J.

Petráš, F.

Phillies, G. D. J.

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

Pine, D. J.

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

Schätzel, K.

K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
[CrossRef]

Smart, A. E.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

Štepánek, P.

Taylor, T. W.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

Tin, P.

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

Weitz, D. A.

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

Wolf, E.

See, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 508–516.

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]

Zhu, J. X.

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

Appl. Opt. (3)

J. Chem. Phys. (3)

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1563 (1983).
[CrossRef]

H. J. Mos, C. Pathmamanoharan, J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. II. Experimental,” J. Chem. Phys. 84, 45–49 (1986).
[CrossRef]

J. Mod. Opt. (1)

K. Schätzel, “Suppression of multiple scattering by photon cross-correlation techniques,” J. Mod. Opt. 38, 1849–1865 (1991).
[CrossRef]

Opt. Spektrosk. (1)

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

Phys. Rev. A (1)

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60, 1134 (1988).
[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 (4)

W. V. Meyer, J. A. Lock, D. S. Cannell, T. W. Taylor, P. Tin, A. E. Smart, J. X. Zhu, H. M. Cheung, J. A. Mann, “A single wavelength cross-correlation technique which suppresses multiple scattering,” in Photon Correlation and Scattering, Vol. 14 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 104–107 (presented at the Optical Society of America’s Photon Correlation and Scattering Topical Meeting, Capri, Italy, 21–24 August 1996).

W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Suppression of multiple scattering using a single beam cross-correlation method,” in Light Scattering and Photon Correlation Spectroscopy, E. R. Pike, J. B. Abbiss, eds., NATO ASI Series, (Kluwer, Dordrecht, The Netherlands, 1997), pp. 39–50.
[CrossRef]

See, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), pp. 508–516.

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

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Figures (10)

Fig. 1
Fig. 1

Optical geometry used to verify the concept of multiple-scattering suppression by spatial cross correlation. APD’s, avalanche photodiodes.

Fig. 2
Fig. 2

Normalized autocorrelation functions for increasing concentrations of nominally 107-nm-diameter polystyrene latex spheres in aqueous suspension.

Fig. 3
Fig. 3

Normalized cross-correlation functions for increasing concentrations of nominally 107-nm-diameter polystyrene latex spheres in aqueous suspension.

Fig. 4
Fig. 4

Particle diameter inferred from autocorrelation and cross-correlation functions by a two-cumulant fit.

Fig. 5
Fig. 5

Zero-delay time of normalized autocorrelation and cross-correlation functions for increasing concentration.

Fig. 6
Fig. 6

Normalized deviation plots for cross-correlation functions for 0.2, 0.5, and 1.0 wt. % of nominally 107-nm particles.

Fig. 7
Fig. 7

Normalized deviation plots for autocorrelation functions for 0.2, 0.5, and 1.0 wt. % of nominally 107-nm particles.

Fig. 8
Fig. 8

Measured and calculated transmissions for 10.1-mm-diameter samples of nominally 107-nm particles.

Fig. 9
Fig. 9

Particle diameter inferred from autocorrelation and cross-correlation functions by use of a two-cumulant fit for measurements made at scattering angles of 60°, 90°, 120°, and 135°.

Fig. 10
Fig. 10

Measured first cumulant K1 (in inverse seconds) for nominally 204-nm particles by use of both autocorrelation and cross correlation.

Equations (6)

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

Gτ=nt+τnt
GABτ=nAt+τnBt=nBt+τnAt
GABτ=A exp-2K1τ-K22τ2+B,
K1=Dq2,
q=4πnλ0sinθ2.
D=kBT6πηa,

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