OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 27, Iss. 3 — Feb. 1, 1988
  • pp: 599–602

Exact solution of the characteristic equation for transfer in the anisotropically scattering and absorbing medium

Vladimir I. Haltrin  »View Author Affiliations

Applied Optics, Vol. 27, Issue 3, pp. 599-602 (1988)

View Full Text Article

Enhanced HTML    Acrobat PDF (405 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A special form of anisotropic scattering phase function is shown to provide an exact solution of the characteristic equation for radiation transfer at depth within a scattering and absorbing medium. The solution is the Henyey-Greenstein function, the degree of extension of which depends on the albedo for single scattering and on the parameter of the phase function. Good applicability of the formulas obtained for a description of integral parameters of light fields in the seawater depth has been demonstrated.

© 1988 Optical Society of America

Original Manuscript: June 8, 1987
Published: February 1, 1988

Vladimir I. Haltrin, "Exact solution of the characteristic equation for transfer in the anisotropically scattering and absorbing medium," Appl. Opt. 27, 599-602 (1988)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. This study was reported at the Ninth Plenary Session of Working Group on Oceanic Optics USSR Academy of Sciences, Batumi, 3–5 Oct. 1984: V. I. Khalturin (V. I. Haltrin), “One Accurate Solution of the Equation for Transport in the Depth of a Scattering Medium,” in Optics of Sea and Atmosphere: Theses of Reports, K. S. Shifrin, B. I. Utenkov, Eds. (S. I. Vavilov State Optical Institute, Leningrad, 1984), pp. 175–176.
  2. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer in Scattering Media (NaukaTekh., Minsk, 1985), 328 pp.
  3. B. Friedman, Principles and Techniques of Applied Mathematics (Wiley, New York, 1965), 315 pp.
  4. V. S. Vladimirov, Equations of Mathematical Physics (Dekker, New York, 1971), 418 pp.
  5. A. Morel, R. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5 (4), 335 (1982). [CrossRef]
  6. V. A. Timofeyeva, “Determination of Light-Field Parameters in the Depth Regime from Irradiance Measurements,” Izv. Akad. Nauk. SSSR Fiz. Atmos. Okeana 15, 774 (1979).
  7. H. R. Gordon, D. B. Brown, M. M. Jackobs, “Computed Relationships Between the Inherent and Apparent Optical Properties of a Flat Homogeneous Ocean,” Appl. Opt. 14, 417 (1975). [CrossRef] [PubMed]
  8. G. A. Gamburtsev, “The Question of Sea Color,” J. Russ. Phys. Chem. Soc. Phys. Sec.56, 226 (1924).
  9. M. Gurevich, “Über eine Rationelle Klassifikation der Lichtenstreuenden Medien,” Phys. Z. 31, 753 (1930).
  10. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593 (1931).
  11. A. Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. Oceanogr. 22, 709 (1977). [CrossRef]
  12. V. I. Khalturin (V. I. Haltrin), “The Self-Consistent Two-Flux Approximation to the Theory of Radiation Transfer,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 589 (1985).

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