Abstract

We introduce a charge-coupled device (CCD) camera-based detection scheme in dynamic light scattering that provides information on the single-scattered autocorrelation function even for fairly turbid samples. It is based on the single focused laser beam geometry combined with the selective cross-correlation analysis of the scattered light intensity. Using a CCD camera as a multispeckle detector, we show how spatial correlations in the intensity pattern can be linked to single- and multiple-scattering processes. Multiple-scattering suppression is then achieved by an efficient cross-correlation algorithm working in real time with a temporal resolution down to 0.02 s. Our approach allows access to the extensive range of systems that show low-order scattering by selective detection of the singly scattered light. Model experiments on slowly relaxing suspensions of titanium dioxide in glycerol were carried out to establish the validity range of our approach. Successful application of the method is demonstrated up to a scattering coefficient of more than μs=5cm1 for the sample size of L=1  cm.

© 2006 Optical Society of America

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References

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  1. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).
  2. W. van Megen and P. Pusey, "Dynamic light scattering study of the glass transition in colloidal suspension," Phys. Rev. A 43, 5429-5441 (1991).
    [CrossRef]
  3. C. Urban and P. Schurtenberger, "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods," J. Colloid Interface Sci. 207, 150-158 (1998).
    [CrossRef]
  4. D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
    [CrossRef]
  5. J. Thomas and S. Tjin, "Fiber optic dynamic light scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989).
    [CrossRef]
  6. D. Lilge and D. Horn, "Diffusion in concentrated dispersions a study with fiber-optic quasi-elastic light scattering (FOQELS)," Colloid Polym. Sci. 269, 704-712 (1991).
    [CrossRef]
  7. H. Wiese and D. Horn, "Single-mode fibers in fiber-optic quasielastic light scattering: A study of the dynamics of concentrated latex dispersions," J. Chem. Phys. 94, 6429-6443 (1991).
    [CrossRef]
  8. F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
    [CrossRef]
  9. G. Phillies, "Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques," J. Chem. Phys. 74, 260-262 (1981).
    [CrossRef]
  10. G. Phillies, "Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques," Phys. Rev. A 24, 1939-1943 (1981).
    [CrossRef]
  11. K. Schätzel, "Suppression of multiple scattering by photon cross-correlation techniques," J. Mod. Opt. 38, 1849-1865 (1991).
  12. P. Pusey, "Suppression of multiple scattering by photon cross-correlation techniques," Curr. Opin. Colloid Interface Sci. 4, 177-185 (1999).
    [CrossRef]
  13. LS Instruments, http://www.lsinstruments.ch.
  14. W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, and P. Tin, "Multiple-scattering suppression by cross correlation," Appl. Opt. 36, 7551-7558 (1997).
  15. J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
    [CrossRef]
  16. J. Goodman, Statistical Optics (Wiley, 1985).
  17. J. A. Lock, "Role of multiple scattering in cross-correlated light scattering with a single laser beam," Appl. Opt. 36, 7559-7570 (1997).
  18. R.C.Weast, M.J.Astle, and W.H.Beyer, eds., CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, 1984).
  19. K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).
  20. D. Magatti and F. Ferri, "Fast multi-tau real-time software correlator for dynamic light scattering," Appl. Opt. 40, 4011-4021 (2001).
  21. L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev: Sci. Instrum. 70, 3214-3221 (1999).
    [CrossRef]
  22. S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing (California Technical Publishing, 1997).
  23. S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
    [CrossRef]
  24. A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
    [CrossRef]

2003 (1)

J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
[CrossRef]

2001 (1)

2000 (2)

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

1999 (2)

P. Pusey, "Suppression of multiple scattering by photon cross-correlation techniques," Curr. Opin. Colloid Interface Sci. 4, 177-185 (1999).
[CrossRef]

L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev: Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

1998 (2)

C. Urban and P. Schurtenberger, "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods," J. Colloid Interface Sci. 207, 150-158 (1998).
[CrossRef]

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

1997 (2)

1996 (1)

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

1991 (4)

D. Lilge and D. Horn, "Diffusion in concentrated dispersions a study with fiber-optic quasi-elastic light scattering (FOQELS)," Colloid Polym. Sci. 269, 704-712 (1991).
[CrossRef]

H. Wiese and D. Horn, "Single-mode fibers in fiber-optic quasielastic light scattering: A study of the dynamics of concentrated latex dispersions," J. Chem. Phys. 94, 6429-6443 (1991).
[CrossRef]

W. van Megen and P. Pusey, "Dynamic light scattering study of the glass transition in colloidal suspension," Phys. Rev. A 43, 5429-5441 (1991).
[CrossRef]

K. Schätzel, "Suppression of multiple scattering by photon cross-correlation techniques," J. Mod. Opt. 38, 1849-1865 (1991).

1989 (1)

J. Thomas and S. Tjin, "Fiber optic dynamic light scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989).
[CrossRef]

1988 (1)

K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).

1981 (2)

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

Bartsch, E.

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

Becker, A.

J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
[CrossRef]

Bellour, M.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Bergenholtz, J.

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

Cannell, D. S.

Cipelletti, L.

L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev: Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

Drewel, M.

K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).

Ferri, F.

Frenz, V.

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

Glatter, O.

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

Goodman, J.

J. Goodman, Statistical Optics (Wiley, 1985).

Harden, J. L.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Horn, D.

D. Lilge and D. Horn, "Diffusion in concentrated dispersions a study with fiber-optic quasi-elastic light scattering (FOQELS)," Colloid Polym. Sci. 269, 704-712 (1991).
[CrossRef]

H. Wiese and D. Horn, "Single-mode fibers in fiber-optic quasielastic light scattering: A study of the dynamics of concentrated latex dispersions," J. Chem. Phys. 94, 6429-6443 (1991).
[CrossRef]

Horn, F.

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

Kellner, G.

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

Kirsch, S.

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

Knaebel, A.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Lehner, D.

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

Lequeux, F.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Lilge, D.

D. Lilge and D. Horn, "Diffusion in concentrated dispersions a study with fiber-optic quasi-elastic light scattering (FOQELS)," Colloid Polym. Sci. 269, 704-712 (1991).
[CrossRef]

Lock, J. A.

Magatti, D.

Meyer, W. V.

Munch, J.-P.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

Phillies, G.

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

Pusey, P.

P. Pusey, "Suppression of multiple scattering by photon cross-correlation techniques," Curr. Opin. Colloid Interface Sci. 4, 177-185 (1999).
[CrossRef]

W. van Megen and P. Pusey, "Dynamic light scattering study of the glass transition in colloidal suspension," Phys. Rev. A 43, 5429-5441 (1991).
[CrossRef]

Richtering, W.

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

Schärtl, W.

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

Schätzel, K.

K. Schätzel, "Suppression of multiple scattering by photon cross-correlation techniques," J. Mod. Opt. 38, 1849-1865 (1991).

K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).

Schnablegger, H.

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

Schröder, J.-M.

J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
[CrossRef]

Schurtenberger, P.

C. Urban and P. Schurtenberger, "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods," J. Colloid Interface Sci. 207, 150-158 (1998).
[CrossRef]

Sillescu, H.

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

Smart, A. E.

Smith, S. W.

S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing (California Technical Publishing, 1997).

Stimac, S.

K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).

Taylor, T. W.

Thomas, J.

J. Thomas and S. Tjin, "Fiber optic dynamic light scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989).
[CrossRef]

Tin, P.

Tjin, S.

J. Thomas and S. Tjin, "Fiber optic dynamic light scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989).
[CrossRef]

Urban, C.

C. Urban and P. Schurtenberger, "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods," J. Colloid Interface Sci. 207, 150-158 (1998).
[CrossRef]

van Megen, W.

W. van Megen and P. Pusey, "Dynamic light scattering study of the glass transition in colloidal suspension," Phys. Rev. A 43, 5429-5441 (1991).
[CrossRef]

Viasnoff, V.

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

Wagner, N.

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

Weitz, D.

L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev: Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

Wiegand, S.

J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
[CrossRef]

Wiese, H.

H. Wiese and D. Horn, "Single-mode fibers in fiber-optic quasielastic light scattering: A study of the dynamics of concentrated latex dispersions," J. Chem. Phys. 94, 6429-6443 (1991).
[CrossRef]

Willenbacher, N.

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

Appl. Opt. (3)

Colloid Polym. Sci. (1)

D. Lilge and D. Horn, "Diffusion in concentrated dispersions a study with fiber-optic quasi-elastic light scattering (FOQELS)," Colloid Polym. Sci. 269, 704-712 (1991).
[CrossRef]

Curr. Opin. Colloid Interface Sci. (1)

P. Pusey, "Suppression of multiple scattering by photon cross-correlation techniques," Curr. Opin. Colloid Interface Sci. 4, 177-185 (1999).
[CrossRef]

Europhys. Lett. (1)

A. KnaebelM. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle suspensions," Europhys. Lett. 52, 73-79 (2000).
[CrossRef]

J. Chem. Phys. (4)

S. Kirsch, V. Frenz, W. Schärtl, E. Bartsch, and H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758-1761 (1996).
[CrossRef]

J.-M. Schröder, A. Becker, and S. Wiegand, "Suppression of multiple scattering for the critical mixture polystyrene/cyclohexane: Application of the one-beam cross correlation technique," J. Chem. Phys. 118, 11307-11314 (2003).
[CrossRef]

H. Wiese and D. Horn, "Single-mode fibers in fiber-optic quasielastic light scattering: A study of the dynamics of concentrated latex dispersions," J. Chem. Phys. 94, 6429-6443 (1991).
[CrossRef]

G. 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. Colloid Interface Sci. (4)

F. Horn, W. Richtering, J. Bergenholtz, N. Willenbacher, and N. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166-178 (2000).
[CrossRef]

C. Urban and P. Schurtenberger, "Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods," J. Colloid Interface Sci. 207, 150-158 (1998).
[CrossRef]

D. Lehner, G. Kellner, H. Schnablegger, and O. Glatter, "Static light scattering on dense colloidal systems: new instrumentation and experimental results," J. Colloid Interface Sci. 201, 34-47 (1998).
[CrossRef]

J. Thomas and S. Tjin, "Fiber optic dynamic light scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989).
[CrossRef]

J. Mod. Opt. (2)

K. Schätzel, "Suppression of multiple scattering by photon cross-correlation techniques," J. Mod. Opt. 38, 1849-1865 (1991).

K. Schätzel, M. Drewel, and S. Stimac, "Photon correlation at large lag times: Improving statistical accuracy," J. Mod. Opt. 35, 711-718 (1988).

Phys. Rev. A (2)

W. van Megen and P. Pusey, "Dynamic light scattering study of the glass transition in colloidal suspension," Phys. Rev. A 43, 5429-5441 (1991).
[CrossRef]

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

Rev: Sci. Instrum. (1)

L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev: Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

Other (5)

S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing (California Technical Publishing, 1997).

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

R.C.Weast, M.J.Astle, and W.H.Beyer, eds., CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, 1984).

J. Goodman, Statistical Optics (Wiley, 1985).

LS Instruments, http://www.lsinstruments.ch.

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Figures (8)

Fig. 1
Fig. 1

(a) Illustration of the van Cittert–Zernike theorem: Small coherently illuminated areas (such as a focused laser beam) produce large correlated areas (speckles) and vice versa: Large coherence areas (halo from multiple scattering) produce small speckles. (b) Suggested suppression scheme using cross-correlation processing: (I) intensity values measured within the same speckle are correlated, (II) two different speckles are uncorrelated, (III) for a superposition of small and large speckles, intensities detected at a certain distance will be correlated only for the larger speckles.

Fig. 2
Fig. 2

Experimental setup. Light scattered at an angle of 90° inside the sample cell of thickness L = 1 cm passes a diaphragm and is collected by a CCD digital camera. In the opposite direction, light is collected by a monomode fiber and a photon counting module to be processed by a hardware correlator. The transmitted collimated intensity is measured to determine the scattering parameters μ s.

Fig. 3
Fig. 3

(a) Principles of the multi-tau correlation scheme. Sequential intensity values I(t) are integrated for the computation of larger lag times. (b) Simplified object scheme to illustrate the cascading of linear correlators used for the realization of the multi-tau correlation scheme.

Fig. 4
Fig. 4

Left: Representative area taken from the recorded images for a weakly scattering (A) and a strongly scattering (B) sample. Right: Spatial intensity fluctuations along the vertical columns of the CCD matrix. Sample A: μ s = 0.101 cm−1, estimated speckle size δx = 28.02 pixels; sample B: μ s = 5.92 cm−1, δx = 0.76 pixels.

Fig. 5
Fig. 5

Spatial autocorrelation for different sample turbidities as a function of vertical pixel separation Δx: (○) μ s = 0.10 cm−1, (■) μ s = 0.39 cm−1, (▿) μ s = 0.88 cm−1, (♦) μ s = 1.43 cm−1; (▵) μ s = 2.54 cm−1, (★) μ s = 5.92 cm−1. The dashed curve (- - -) represents the spatial correlation function estimated in the horizontal dimension. The inset shows speckle sizes δx (○) and δy (■) as a function of μ s for both vertical and horizontal separations, respectively. The maximum amplitude of the correlation function is limited to about 0.5 since the speckle size in the y direction is comparable to the pixel size.

Fig. 6
Fig. 6

Autocorrelation functions obtained with different binning areas together with the cross-correlation function. As the vertical size of the binning area increases the ACF approaches the CCF indicating partial but not sufficient suppression of multiple scattering. The inset shows the estimated particle size (○) as a function of binning size. The actual size is indicated by a dashed line.

Fig. 7
Fig. 7

Correlation functions obtained by different means for an essentially multiple-scattering sample (μ s = 3.93 cm−1). The ACF obtained from the hardware correlator (- - -), the ACF from CCD detection with no binning (□) and the CCF with a separation Δx = 40 pixels (○) are shown together with the ACF obtained for singly scattering sample (●). The inset shows the intercepts for ACF (□) and CCF with separation Δx = 40 (●).

Fig. 8
Fig. 8

Particle size D determined by different methods as a function of sample turbidity. The CCF diameter (∗) remains unchanged up to the limit of strong multiple scattering. Estimated sizes from the hardware correlator (●) and from the CCD camera ACF without binning (□) show a rapid decrease as the scattering coefficient μ s increases. The shaded area indicates the experimental value expected for single scattering (including the uncertainty in particle size and solvent viscosity).

Equations (10)

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

g 2 ( q , τ ) = I ( q , t ) I ( q , t + τ ) t I ( q , t ) t     2 ,
g 2 ( q , τ ) = 1 + β | g 1 ( q , τ ) | 2 ,
g 1 ( q , τ ) = exp ( D 0 q 2 τ ) = exp ( τ / τ c ) ,
D 0 = k T 6 πηR ,
λ z S 1 Δ x λ z S 2 ,
g 2     Δ x ( q , τ ) = I ( q , t , 0 ) I ( q , t + τ , Δ x ) t I ( q , t , 0 ) t I ( q , t , Δ x ) t ,
g 2     a d ( τ ) = I ( x , t ) I ( x , t + τ ) t x I ( x , t ) t x     2 = I ( x , t ) I ( x , t + τ ) t x I ¯ 2 ,
lim τ g 2 ( τ ) = I ( x , t ) t     2 x I ¯ 2 = [ I ( x , t ) t I ¯ ] 2 x I ¯ 2 + 1 = K + 1 ,
g 2     d a ( τ ) = I ( x , t ) I ( x , t + τ ) t I ( x , t ) t     2 x .
g 2     s ( Δ x ) = I ( x ) I ( x + Δ x ) x , t I ( x ) x , t I ( x + Δ x ) x , t ,

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