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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1651–1664

Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions

P.-A. Lemieux and D. J. Durian  »View Author Affiliations

JOSA A, Vol. 16, Issue 7, pp. 1651-1664 (1999)

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Dynamic light-scattering techniques provide noninvasive probes of diverse media, such as colloidal suspensions, granular materials, or foams. In homodyne photon correlation spectroscopy, the dynamical properties of the medium are extracted from the intensity autocorrelation g<sup>(2)</sup>(τ) of the scattered light by means of the Siegert relation g<sup>(2)</sup>(τ)=1+|〈E(0)E<sup>*</sup>(τ)〉|<sup>2</sup>/〈EE<sup>*</sup>〉<sup>2</sup>. This approach is unfortunately limited to systems where the electric field is a Gaussian random variable and thus breaks down when the scattering sites are few or correlated. We propose to extend the traditional analysis by introducing intensity correlation functions g<sup>(n)</sup> of higher order, which allow us both to detect non-Gaussian scattering processes and to extract information not available in g<sup>(2)</sup> alone. The g<sup>(n)</sup> are experimentally measured by a combination of a commercial correlator and a custom digital delay line. Experimental results for g<sup>(3)</sup> and g<sup>(4)</sup> are presented for both Gaussian and non-Gaussian light-scattering processes and compared with theoretical predictions.

© 1999 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(120.2920) Instrumentation, measurement, and metrology : Homodyning
(290.5820) Scattering : Scattering measurements
(300.0300) Spectroscopy : Spectroscopy

P.-A. Lemieux and D. J. Durian, "Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions," J. Opt. Soc. Am. A 16, 1651-1664 (1999)

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  1. H. Z. Cummins and H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
  2. H. Cummins and E. Pike, eds., Photon Correlation and Light-Beating Spectroscopy, Vol. B3 of NATO Advanced Study Institutes Series (Plenum, New York, 1974).
  3. H. Cummins and E. Pike, eds., Photon Correlation Spectroscopy and Velocimetry, Vol. B23 of NATO Advanced Study Institutes Series (Plenum, New York, 1977).
  4. R. Pecora, Dynamic Light Scattering: Application of Photon Correlation Spectroscopy (Plenum, New York, 1985).
  5. B. Chu, Laser Light Scattering, Basic Principles and Practice (Academic, New York, 1991).
  6. W. Brown, ed., Dynamic Light Scattering: The Method and Some Applications (Clarendon, Oxford, UK, 1993).
  7. W. Lauterborn, T. Kurz, and M. Wiesenfeldt, Coherent Optics: Fundamentals and Applications (Springer, Berlin, 1995).
  8. S. Chopra and L. Mandel, “Higher-order correlation properties of a laser beam,” Phys. Rev. Lett. 30, 60–63 (1973).
  9. C. D. Cantrel, M. Lax, and W. A. Smith, “Third- and higher-order intensity correlation in laser light,” Phys. Rev. A 7, 175–181 (1973).
  10. M. Corti, A. D. Agostini, and V. Degiorgio, “Fast digital correlator for weak optical signals,” Rev. Sci. Instrum. 45, 888–893 (1974).
  11. M. Corti and V. Degiorgio, “Intrinsic third-order correlations in laser light near threshold,” Phys. Rev. A 14, 1475–1478 (1976).
  12. L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
  13. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  14. A. Lohmann, G. Weigelt, and B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983).
  15. P. N. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, Vol. B23 of NATO Advanced Study Institutes Series, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1977), pp. 45–141.
  16. A. V. Balakrishnan, Introduction to Random Processes in Engineering (Wiley, New York, 1995).
  17. P. N. Pusey, Department of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Bldg., Mayfield Road, Edinburgh EH9 3JZ, UK. E-mail, p.n.pusey@ed.ac.uk (personal communication, 1998).
  18. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).
  19. E. Jakeman, “Photon correlation,” in Photon Correlation and Light-Beating Spectroscopy, Vol. B3 of NATO Advanced Study Institutes Series, H. Cummins and E. Pike, eds. (Plenum, New York, 1974), pp. 75–149.
  20. P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1989).
  21. H. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  22. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  23. D. Weitz and D. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, UK, 1993), pp. 652–720.
  24. G. Maret, “Diffusing-wave spectroscopy,” Curr. Opin. Colloid Interface Sci. 2, 251–257 (1997).
  25. P.-A. Lemieux, M. Vera, and D. Durian, “Diffusing-light spectroscopies outside the diffusive limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498–4515 (1998).
  26. V. Bluemel, L. M. Narducci, and R. A. Tuft, “Photon-count distributions and irradiance fluctuations of a log-normally distributed light field,” J. Opt. Soc. Am. 62, 1309–1314 (1972).
  27. B. Crosignani, P. DiPorto, and M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York,, 1975).
  28. M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, “Higher moments of scattered light fields by heterodyne analysis,” Appl. Opt. 33, 7226–7230 (1994).
  29. T. Bellini, M. A. Glaser, N. A. Clark, and V. Degiorgio, “Effects of finite laser coherence in quasielastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
  30. S. Brauer, G. Stephenson, M. Sutton, R. Bruning, E. Dufresne, S. Mochrie, G. Grubel, J. Als-Nielsen, and D. Abernathy, “X-ray intensity fluctuation spectroscopy observation of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74, 2010–2013 (1995).
  31. S. Dierker, R. Pindak, R. Fleming, I. Robinson, and L. Berman, “X-ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75, 449–452 (1995).
  32. M. T. Bishop, K. H. Langley, and F. E. Karasz, “Diffusion of a flexible polymer in a random porous material,” Phys. Rev. Lett. 57, 1741–1744 (1986).
  33. B. Frisken, F. Ferri, and D. Cannell, “Critical behavior in the presence of a disordered environment,” Phys. Rev. E 51, 5922–5943 (1995).
  34. I. Flammer, G. Bucher, and J. Ricka, “Diffusive wave illumination: light-scattering study of colloidal dynamics in opaque media,” J. Opt. Soc. Am. A 15, 2066–2077 (1998).
  35. P. N. Pusey and W. van Megen, “Dynamic light scattering by non-ergodic media,” Physica A 157, 705–741 (1989).
  36. J.-Z. Xue, D. J. Pine, S. T. Milner, X.-l. Wu, and P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
  37. T. G. Mason and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74, 1250–1253 (1995).
  38. A. Krall and D. Weitz, “Internal dynamics and elasticity of fractal colloidal gels,” Phys. Rev. Lett. 80, 778–781 (1998).
  39. P. N. Pusey, “Number fluctuations of interacting particles,” J. Phys. A 12, 1805–1818 (1979).
  40. L. E. Estes, L. M. Narducci, and R. A. Tuft, “Scattering of light from a rotating ground glass,” J. Opt. Soc. Am. 61, 1301–1306 (1971).
  41. N. Menon and D. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275, 1920–1922 (1997).

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