OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 6 — Feb. 20, 2002
  • pp: 1022–1028

One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater

Vladimir I. Haltrin  »View Author Affiliations

Applied Optics, Vol. 41, Issue 6, pp. 1022-1028 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (132 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A one-parameter two-term Henyey-Greenstein (TTHG) phase function of light scattering in seawater is proposed. The original three-parameter TTHG phase function was reduced to the one-parameter TTHG phase function by use of experimentally derived regression dependencies between integral parameters of the marine phase functions. An approach to calculate a diffuse attenuation coefficient in the depth of seawater is presented.

© 2002 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.7340) Atmospheric and oceanic optics : Water
(290.0290) Scattering : Scattering
(290.7050) Scattering : Turbid media

Original Manuscript: April 24, 2001
Revised Manuscript: August 31, 2001
Published: February 20, 2002

Vladimir I. Haltrin, "One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater," Appl. Opt. 41, 1022-1028 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  2. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980) Vol. 1.
  3. C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).
  4. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  5. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975). [CrossRef]
  6. V. I. Haltrin, “Theoretical and empirical phase functions for Monte Carlo calculations of light scattering in seawater,” in Proceedings of the Fourth International Conference on Remote Sensing for Marine and Coastal Environments (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1997), pp. 509–518.
  7. T. J. Petzold, “Volume scattering functions for selected ocean waters,” Final Tech. Rep. SIO Ref. 72–78 (Scripps Institution of Oceanography Visibility Laboratory, San Diego, Calif., 1972), p. 79.
  8. V. A. Timofeyeva, “Relation between light-field parameters and between scattering phase function characteristics of turbid media, including seawater,” Izv. Acad. Sci. USSR Atmos. Ocean Phys. 14, 843–848 (1978).
  9. The regressions in Eqs. (11) and (12) are custom-made regressions. They were derived manually and nonformally by the trial and error method. The original regressions given in Ref. 8 are valid in the range of experimental measurements 0.05 ≤ B ≤ 0.25. The full range of variability of backscattering probability B = bb/b is between 0 (highly anisotropic delta-shaped in forward-direction scattering) and 0.5 (isotropic scattering). The original experimental data by Timofeyeva, who is regarded as one of the top experimentalists in hydrological optics of the 1960s and 1970s, were recovered from the scan of the figure published in Ref. 8 and checked with the original nonphysical regressions. I obtained the new regressions manually by forcing them to obey both the experimental points and the physical requirements listed above.
  10. V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Appl. Opt. 38, 6826–6832 (1999). [CrossRef]
  11. V. I. Haltrin, “An algorithm to restore spectral signatures of all inherent optical properties of seawater using a value of one property at one wavelength,” in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition/21st Canadian Symposium on Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999), pp. I-680–I-687.
  12. V. A. Timofeyeva, “Optical characteristics of turbid media of the sea-water type,” Izv. Acad. Sci. USSR Atmos. Ocean Phys. 7, 1326–1329 (1971).
  13. V. I. Haltrin, “Empirical algorithms to restore a complete set of inherent optical properties of seawater using any two of these properties,” Can. J. Remote Sens. 26, 440–445 (2000).
  14. B. Bulgarelli, V. B. Kisselev, L. Roberti, “Radiative transfer in the atmosphere-ocean system: the finite-element method,” Appl. Opt. 38, 1530–1542 (1999). [CrossRef]
  15. V. I. Haltrin, “An analytic Fournier-Forand scattering phase function as an alternative to the Henyey-Greenstein phase function in hydrologic optics,” in IGARSS ’98: 1998 IEEE International Geoscience and Remote Sensing Symposium ProceedingsT. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), Vol. 2, pp. 910–912.
  16. V. I. Haltrin, “Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth, and surface illumination,” Appl. Opt. 37, 3773–3784 (1998). [CrossRef]
  17. V. I. Haltrin, “Apparent optical properties of the sea illuminated by Sun and sky,” Appl. Opt. 37, 8336–8340 (1998). [CrossRef]
  18. V. I. Haltrin, “Diffuse reflection coefficient of a stratified sea,” Appl. Opt. 38, 932–936 (1999). [CrossRef]
  19. V. I. Khalturin (a.k.a. V. I. Haltrin), “Propagation of light in the sea depth,” in Optical Remote Sensing of the Sea and the Influence of the Atmosphere, V. A. Urdenko, G. Zimmermann, eds. (German Democratic Republic Academy of Sciences Institute for Space Research, Berlin, 1985), Chap. 21, pp. 20–62 (in Russian).
  20. V. I. Haltrin, “Exact solution of the characteristic equation for transfer in the anisotropically scattering and absorbing medium,” Appl. Opt. 27, 599–602 (1988). This paper proposes a one-parameter analytic phase function that, if used with the scalar radiative transfer equation, produces in the asymptotic regime an analytical solution that has the form of the Henyey-Greenstein function.
  21. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  22. V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in IGARSS ’99: Proceeding of the International Geoscience and Remote Sensing SymposiumT. I. Stein, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1423–1425.
  23. V. M. Loskutov, “Light regime in deep layers of turbid medium with strongly elongated phase function,” Vestn. Leningr. Univ. 13, 143–149 (1969); in Russian.

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 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited