OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2840–2845

Transport equation for the time correlation function of scattered field in dynamic turbid media

Romain Pierrat  »View Author Affiliations


JOSA A, Vol. 25, Issue 11, pp. 2840-2845 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002840


View Full Text Article

Enhanced HTML    Acrobat PDF (116 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

I derive a transport equation for the time correlation function in transmission and reflexion and inside a turbid medium. This equation goes beyond the diffusion approximation that is at the root of the well-established diffusing-wave spectroscopy technique. It takes into account all the transport regimes from ballistic to diffusive and the relaxation in direction at each scattering event. The derivation is based on a generalized form of the Bethe–Salpeter equation coupled to a generalized form of the scattering operator. The method presented can be easily adapted to compute the correlation function in systems with several time scales encountered, for example, in biology and polymer physics. The obtained equation is easily solvable numerically using a Monte Carlo scheme.

© 2008 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.5620) Coherence and statistical optics : Radiative transfer
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media

ToC Category:
Scattering

History
Original Manuscript: July 9, 2008
Revised Manuscript: September 3, 2008
Manuscript Accepted: September 4, 2008
Published: October 24, 2008

Virtual Issues
Vol. 4, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Romain Pierrat, "Transport equation for the time correlation function of scattered field in dynamic turbid media," J. Opt. Soc. Am. A 25, 2840-2845 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-11-2840


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, 2001).
  2. B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, 1976).
  3. V. A. Bloomfield and T. K. Lim, “Quasi-elastic light scattering,” Methods Enzymol. 48, 415-494 (1978). [CrossRef] [PubMed]
  4. G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B: Condens. Matter 65, 409-413 (1987). [CrossRef]
  5. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134-1137 (1988). [CrossRef] [PubMed]
  6. F. Scheffold, W. Hartk, G. Maret, and E. Matijevic, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942-10952 (1998). [CrossRef]
  7. D. J. Durian, D. A. Weitz, and D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686-688 (1991). [CrossRef] [PubMed]
  8. P. D. Kaplan, A. G. Yodh, and D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393-396 (1992). [CrossRef] [PubMed]
  9. 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). [CrossRef] [PubMed]
  10. F. Scheffold and P. Schurtenberger, “Light scatteringprobes of viscoelastic fluids and solids,” Soft Mater. 1, 139-165 (2003). [CrossRef]
  11. B. Weber, C. Burger, M. T. Wyss, V. G. K. Schulthess, F. Scheffold, and A. Buck, “Optical imaging of the spatiotemporal dynamics of cerebral blood flow and oxidative metabolism in the rat barrel cortex,” Eur. J. Neurosci. 20, 2664-2670 (2004). [CrossRef] [PubMed]
  12. F. C. MacKintosh and S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2383-2406 (1989). [CrossRef]
  13. L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A 21, 1799-1804 (2004). [CrossRef]
  14. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948-3959 (1991). [CrossRef] [PubMed]
  15. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532-2538 (1995). [CrossRef]
  16. P.-A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E 57, 4498-4514 (1998). [CrossRef]
  17. R. Carminati, R. Elaloufi, and J.-J. Greffet, “Beyond the diffusion-wave spectroscopy model for the temporal fluctuations of scattered light,” Phys. Rev. Lett. 92, 213903 (2004). [CrossRef] [PubMed]
  18. R. Pierrat, N. Ben Braham, L. F. Rojas-Ochoa, F. Scheffold, and R. Carminati, “The influence of the scattering anisotropy parameter on diffuse reflection of light,” Opt. Commun. 281, 18-22 (2008). [CrossRef]
  19. G. Popescu and A. Dogariu, “Dynamic light scattering in subdiffusive regime,” Appl. Opt. 40, 4215-4221 (2001). [CrossRef]
  20. R. Pierrat, J.-J. Greffet, R. Elaloufi, and R. Carminati, “Spatial coherence in strongly scattering media,” J. Opt. Soc. Am. A 22, 2329-2337 (2005). [CrossRef]
  21. Y. N. Barabanenkov and V. M. Finkel'berg, “Radiation transport equation for correlated scatterers,” Sov. Phys. JETP 26, 587-591 (1968).
  22. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1989), Vol. 4.
  23. L. Tsang, K.-H. Ding, and B. Wen, “Dense media radiative transfer theory for dense discrete random media with particles of multiple sizes and permitivites,” Prog. Electromagn. Res. 6, 181-230 (1992).
  24. L. Ryzhik, G. Papanicolaou, and J. B. Keller, “Transport equations for elastic and other waves in random media,” Wave Motion 24, 327-370 (1996). [CrossRef]
  25. Y. N. Barabanenkov, L. M. Zurk, and M. Y. Barabanenkov, “Single scattering and diffusion approximations for modified radiative transfer theory of wave multiple scattering in dense media near resonance,” Prog. Electromagn. Res. 15, 27-61 (1997). [CrossRef]
  26. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000), Vol. 2, Chap. 7. [CrossRef]
  27. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000), Vol. 3, Chap. 7. [CrossRef]
  28. F. Jaillon, S. E. Skipetrov, J. Li, G. Dietsche, G. Maret, and T. Gisler, “Diffusing-wave spectroscopy from head-like tissue phantoms: influence of a non-scattering layer,” Opt. Express 14, 10181-10194 (2001). [CrossRef]
  29. L. Le Goff, C. Amblard, F. Furst, and E. M. Furst, “Motor-driven dynamics in actin-myosin networks,” Phys. Rev. Lett. 88, 018101 (2001). [CrossRef]
  30. L. A. Apresyan and Y. A. Kravtsov, Radiation Transfer--Statistical and Wave Aspects (Gordon & Breach, 1996).
  31. U. Frish, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A.T.Bharuch-Reid, ed. (Academic, 1968), Vol. 1, pp. 75-198.
  32. F. Dyson, “The radiation theories of Tomonaga, Schwinger and Feynmann,” Phys. Rev. 75, 486-502 (1949). [CrossRef]
  33. F. Dyson, “The s matrix in quantum electrodynamics,” Phys. Rev. 75, 1736-1755 (1949). [CrossRef]
  34. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256-1259 (1968). [CrossRef]
  35. S. Chandrasekhar, Radiative Transfer (Dover, 1950).
  36. A. F. Molisch and B. P. Oehry, Radiation Trapping in Atomic Vapours (Clarendon, 1998).
  37. J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods (Chapman & Hall, 1964). [CrossRef]
  38. G. S. Fishman, Monte Carlo Concepts, Algorithms and Applications (Springer Verlag, 1996).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited