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: Franco Gori
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 2169–2174

Single-scattering solutions to radiative transfer in infinite turbid media

Margarita L. Shendeleva  »View Author Affiliations


JOSA A, Vol. 30, Issue 11, pp. 2169-2174 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002169


View Full Text Article

Enhanced HTML    Acrobat PDF (301 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An instantaneous point source generating a light field in an infinite turbid medium with anisotropic individual scatterers is considered. Single-scattering solutions are sought as the first term of a series expansion of the solution of the radiative transfer equation in successive scattering orders. A simple formula for a single-scattering solution in media with an arbitrary axially symmetric phase function is derived. Applications of this formula are shown for the Henyey–Greenstein phase function, an ellipsoidal phase function, and a linear phase function. In addition, the single-scattering term of the RTE solution derived by Kholin [Zh. Vych. Mat. i Mat. Fys. 4, 1126 (1964)] for media with a phase function represented by a finite series in Legendre polynomials is considered in more detail.

© 2013 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(290.4210) Scattering : Multiple scattering

ToC Category:
Scattering

History
Original Manuscript: July 17, 2013
Revised Manuscript: September 9, 2013
Manuscript Accepted: September 10, 2013
Published: October 2, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Margarita L. Shendeleva, "Single-scattering solutions to radiative transfer in infinite turbid media," J. Opt. Soc. Am. A 30, 2169-2174 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-11-2169


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Florescu, J. C. Schotland, and V. A. Markel, “Single-scattering optical tomography,” Phys. Rev. E 79, 036607 (2009). [CrossRef]
  2. D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. Am. 69, 464–470 (1979). [CrossRef]
  3. V. Pegoraro and S. G. Parker, “An analytical solution to single scattering in homogeneous participating media,” Comput. Graph. Forum 28, 329–335 (2009). [CrossRef]
  4. A. S. Monin, “A statistical interpretation of the scattering of microscopic particles,” Theory Probab. Appl. 1, 298–311 (1956). [CrossRef]
  5. J. C. J. Paasschens, “Solution of time-dependent Boltzmann equation,” Phys. Rev. E 56, 1135–1141 (1997). [CrossRef]
  6. S. A. Kholin, “Certain exact solutions of the nonstationary kinetic equation without taking retardation into account,” Zh. Vych. Mat. i Mat. Fys. 4, 1126–1131 (1964).
  7. S. A. Kholin, I. M. Anisina, and A. Yu. Madyanov, “Green’s functions for non-stationary kinetic equation with constant speed,” Transp. Theory Stat. Phys. 37, 361–376 (2008). [CrossRef]
  8. V. N. Fomenko and F. M. Shvarts, “Exact description of photon migration in isotropically scattering media,” Proc. SPIE 3194, 334–342 (1998). [CrossRef]
  9. V. N. Fomenko, F. M. Shvarts, and M. A. Shvarts, “Exact description of photon migration in anisotropically scattering media,” Phys. Rev. E 61, 1990–1995 (2000). [CrossRef]
  10. B. D. Ganapol, “Solution of the one-group time-dependent neutron transport equation in an infinite medium by polynomial reconstruction,” Nucl. Sci. Eng. 92, 272–279 (1986).
  11. H. Sato, “Energy propagation including scattering effects. Single isotropic scattering approximation,” J. Phys. Earth 25, 27–41 (1977). [CrossRef]
  12. H. Sato, “Formulation of the multiple non-isotropic scattering process in 3-D space on the basis of energy transport theory,” Geophys. J. Int. 121, 523–531 (1995). [CrossRef]
  13. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  14. L. O. Reynolds and N. J. McCormick, “Approximate two-parameter phase function for light scattering,” J. Opt. Soc. Am. 70, 1206–1212 (1980). [CrossRef]
  15. G. D. Pedersen, N. J. McCormick, and L. O. Reynolds, “Transport calculations for light scattering in blood,” Biophys. J. 16, 199–207 (1976). [CrossRef]
  16. Z. X. Wang and D. R. Guo, Special Functions (World Scientific, 1989).
  17. K. Rinzema, B. J. Hoenderst, H. A. Ferwerda, and J. J. Ten Bosch, “Low-degree polynomial phase-functions with high g-value,” Phys. Med. Biol. 38, 1343–1350 (1993). [CrossRef]

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