OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 957–960

Simple approximate formula for the reflection function of a homogeneous, semi-infinite turbid medium

Alexander A. Kokhanovsky  »View Author Affiliations

JOSA A, Vol. 19, Issue 5, pp. 957-960 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (122 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A simple, approximate analytical formula is proposed for the reflection function of a semi-infinite, homogeneous particulate layer. It is assumed that the zenith angle of the viewing direction is equal to zero (thus corresponding to the case of nadir observations), whereas the light incidence direction is arbitrary. The formula yields accurate results for incidence–zenith angles less than approximately 85° and can be useful in analyzing satellite nadir observations of optically thick clouds.

© 2002 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.7050) Scattering : Turbid media

Original Manuscript: August 24, 2001
Revised Manuscript: November 8, 2001
Manuscript Accepted: November 14, 2001
Published: May 1, 2002

Alexander A. Kokhanovsky, "Simple approximate formula for the reflection function of a homogeneous, semi-infinite turbid medium," J. Opt. Soc. Am. A 19, 957-960 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Nauka, Moscow, 1972).
  2. H. C. Van de Hulst, Multiple Light Scattering: Tables, Formulas and Applications (Academic, New York, 1980).
  3. I. N. Minin, Radiative Transfer Theory in Planetary Atmospheres (Nauka, Moscow, 1988).
  4. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991).
  5. A. Kokhanovsky, Light Scattering Media Optics: Problems and Solutions (Praxis, Chichester, UK, 2001).
  6. S. Chandrasekhar, Radiative Transfer (Oxford Press, Oxford, UK, 1950).
  7. M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, N. T. Zakharova, “Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces,” J. Quant. Spectrosc. Radiat. Transf. 63, 409–432 (1999). [CrossRef]
  8. M. D. King, “Determination of the scaled optical thickness of clouds from reflected solar radiation measurements,” J. Atmos. Sci. 44, 1734–1751 (1987). [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