OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 6 — Jun. 1, 2004
  • pp: 1018–1025

Lateral photon transport in dense scattering and weakly absorbing media of finite thickness: asymptotic analysis of the space–time Green function

Igor N. Polonsky and Anthony B. Davis  »View Author Affiliations

JOSA A, Vol. 21, Issue 6, pp. 1018-1025 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (182 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The asymptotic law for the radial distribution of radiance density from an isotropic point source placed in a slab of homogeneous absorbing and scattering material is obtained within the framework of diffusion theory. The exponential shape of the tail of the resulting Green function has been observed but was not theoretically explained until now. We derive formulas for both the steady-state and the time-dependent problems. The theoretical results are verified by comparison with Monte Carlo simulations.

© 2004 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(170.3660) Medical optics and biotechnology : Light propagation in tissues

Original Manuscript: October 6, 2003
Revised Manuscript: January 20, 2004
Manuscript Accepted: January 20, 2004
Published: June 1, 2004

Igor N. Polonsky and Anthony B. Davis, "Lateral photon transport in dense scattering and weakly absorbing media of finite thickness: asymptotic analysis of the space–time Green function," J. Opt. Soc. Am. A 21, 1018-1025 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. N. Holben, T. I. Eck, I. Slutsker, D. Tar, J. P. Buis, A. Setxer, J. E. Vemte, J. A. Reagan, K. Y. J. T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET–A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998). [CrossRef]
  2. M. Patterson, J. Moulton, B. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989). [CrossRef] [PubMed]
  3. S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: Temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992). [CrossRef] [PubMed]
  4. A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997). [CrossRef]
  5. D. Contini, F. Martelli, G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997). [CrossRef] [PubMed]
  6. A. B. Davis, R. F. Cahalan, J. D. Spinhirne, M. J. McGill, S. P. Love, “Off-beam lidar: An emerging technique in cloud remote sensing based on radiative Green-function theory in the diffusion domain,” Phys. Chem. Earth 24, 757–765 (1999). [CrossRef]
  7. A. B. Davis, A. Marshak, “Space–time characteristics of light transmitted by dense clouds. A Green function analysis,” J. Atmos. Sci. 59, 2713–2727 (2002). [CrossRef]
  8. H. Gordon, “Interpretation of airborne oceanic lidar: Effects of multiple scattering,” Appl. Opt. 21, 2996–3001 (1982). [CrossRef] [PubMed]
  9. H. Gordon, A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery, Vol. 4 of Lecture Notes on Coastal and Estuarine Studies (Springer-Verlag, New York, 1983). [CrossRef]
  10. S. Chandrasekhar, Radiative Transfer (Oxford U. Press, London, 1950).
  11. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  12. B. Davison, Neutron Transport Theory (Clarendon, Oxford, UK, 1957).
  13. E. Zege, A. Ivanov, I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, Heidelberg, Germany, 1991).
  14. J. Li, J. Geldart, P. Chylek, “Perturbation solution for 3D radiative transfer in a horizontally periodic inhomogeneous cloud field,” J. Atmos. Sci. 51, 2110–2122 (1994). [CrossRef]
  15. A. Davis, A. Marshak, “Multiple scattering in clouds: Insights from three-dimensional diffusion/P1 theory,” Nucl. Sci. Eng. 137, 251–280 (2001).
  16. T. Farrel, M. Patterson, M. Essenpreis, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998). [CrossRef]
  17. J. Hampel, E. Schleicher, R. Freyer, “Volume image reconstruction for diffuse optical tomography,” Appl. Opt. 41, 3816–3826 (2002). [CrossRef] [PubMed]
  18. M. Ostermeyer, S. Jacques, “Perturbation theory for diffuse light transport in complex biological tissues,” J. Opt. Soc. Am. A 14, 255–261 (1997). [CrossRef]
  19. S. P. Love, A. B. Davis, C. Ho, C. A. Rohde, “Remote sensing of cloud thickness and liquid water content with Wide-Angle Imaging Lidar (WAIL),” Atmos. Res. 59–60, 295–312 (2001). [CrossRef]
  20. P. I. Richards, “Scattering from a point-source in plane clouds,” J. Opt. Soc. Am. 46, 927–934 (1956). [CrossRef]
  21. J.-M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J.-P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements in biological tissues,” Opt. Commun. 124, 216–221 (1996). [CrossRef]
  22. R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44, 967–981 (1999). [CrossRef] [PubMed]
  23. S. Stolik, J. A. Delgado, A. Perez, L. Anasagasti, “Measurement of the penetration depths of red and near infrared light in human “ex vivo” tissues,” J. Photochem. Photobiol. B 57, 90–93 (2000). [CrossRef]
  24. A. A. Kokhanovsky, E. P. Zege, “On remote sensing of water clouds from space,” Adv. Space Res. 21, 425–428 (1998). [CrossRef]
  25. R. F. Cahalan, W. Ridgway, W. J. Wiscombe, S. Gollmer, Harshvardhan, “Independent pixel and Monte Carlo estimates of stratocumulus albedo,” J. Atmos. Sci. 51, 3776–3790 (1994). [CrossRef]
  26. A. Davis, A. Marshak, R. F. Cahalan, W. J. Wiscombe, “The Landsat scale-break in stratocumulus as a three-dimensional radiative transfer effect: Implications for cloud remote sensing,” J. Atmos. Sci. 54, 241–260 (1997). [CrossRef]
  27. B. D. Ganapol, D. E. Kornreich, J. A. Dahl, D. W. Nigg, S. N. Jahshan, C. A. Temple, “The searchlight problem for neutrons in a semi-infinite medium,” Nucl. Sci. Eng. 118, 38–53 (1994).
  28. L. M. Romanova, “Narrow light beam propagation in a stratified cloud: Higher transverse moments,” Izv., Acad. Sci., USSR Atmos. Oceanic Phys. 37, 748–756 (2001).
  29. G. C. Pomraning, “Diffusion theory via asymptotics,” Transp. Theory Stat. Phys. 18, 383–428 (1989). [CrossRef]
  30. P. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1952).
  31. A. Erdelyi, ed., Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).
  32. G. Doetsch, Guide to the Application of the Laplace and Z-Transforms (Van Nostrand Reinhold, New York, 1971).
  33. K. F. Evans, R. P. Lawson, P. Zmarzly, D. O’Connor, W. J. Wiscombe, “In situ cloud sensing with multiple scattering lidar: Simulations and demonstration,” J. Atmos. Oceanic Technol. 20, 1505–1522 (2003). [CrossRef]
  34. L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  35. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).
  36. A. Marshak, A. Davis, W. J. Wiscombe, R. F. Cahalan, “Radiative smoothing in fractal clouds,” J. Geophys. Res. 100, 26247–26261 (1995). [CrossRef]
  37. C. von Savigny, A. B. Davis, O. Funk, K. Pfeilsticker, “Time-series of zenith radiance and surface flux under cloudy skies: radiative smoothing, optical thickness retrievals and large-scale stationarity,” Geophys. Res. Lett. 29, 1825–1828 (2002). [CrossRef]
  38. A. Marshak, A. Davis, R. F. Cahalan, W. J. Wiscombe, “Nonlocal independent pixel approximation: direct and inverse problems,” IEEE Trans. Geosci. Remote Sens. 36, 192–205 (1998). [CrossRef]
  39. I. N. Polonsky, M. A. Box, A. B. Davis, “Radiative transfer through inhomogeneous turbid media: implementation of the adjoint perturbation approach at the first order,” J. Quant. Spectrosc. Radiat. Transf. 78, 85–98 (2003). [CrossRef]
  40. M. A. Box, I. N. Polonsky, A. B. Davis, “Higher-order perturbation theory applied to radiative transfer in non-plane-parallel media,” J. Quant. Spectrosc. Radiat. Transf. 78, 105–118 (2003). [CrossRef]
  41. G. Marchuk, “Equation for the value of information from weather satellite and formulation of inverse problems,” Kosm. Issled. 2, 462–477 (1964).
  42. I. N. Polonsky, M. A. Box, “General perturbation technique for the calculation of radiative effects in scattering and absorbing media,” J. Opt. Soc. Am. A 19, 2281–2292 (2002). [CrossRef]
  43. S. P. Love, A. B. Davis, C. A. Rohde, L. Tellier, C. Ho, “Active probing of cloud multiple scattering, optical depth, vertical thickness, and liquid water content using Wide-Angle Imaging Lidar,” in Atmospheric Radiation Measurements and Applications in Climate, J. A. Show, ed., Proc. SPIE4815, 129–138 (2002). [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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited