OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 7 — Jul. 1, 2008
  • pp: 1521–1534

Ray scattering model for spherical transparent particles

Lionel Simonot, Mathieu Hébert, Roger D. Hersch, and Hélène Garay  »View Author Affiliations

JOSA A, Vol. 25, Issue 7, pp. 1521-1534 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (284 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a model for the reflectance of a particle medium made of identical, large, spherical, and absorbing particles in a clear binder. A 3D geometrical description of light scattering is developed by relying on the laws of geometrical optics. The amount of light backscattered by a single particle is determined as a function of its absorbance and refractive index. Then, we consider a set of coplanar particles, called a particle sublayer, whose reflectance and transmittance are functions of the particle backscattering ratio and the particle concentration. The reflectance of an infinite particle medium is derived from a description of multiple reflections and transmissions between many superposed particle sublayers. When the binder has a refractive index different from that of air, the medium’s reflectance factor accounts for the multiple reflections occurring beneath the air–binder interface as well as for the measuring geometry. The influences of various parameters, such as the refractive indices and the particle absorption coefficient, are examined.

© 2008 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(160.2710) Materials : Inhomogeneous optical media

ToC Category:
Geometric optics

Original Manuscript: October 29, 2007
Revised Manuscript: April 2, 2008
Manuscript Accepted: April 13, 2008
Published: June 4, 2008

Lionel Simonot, Mathieu Hébert, Roger D. Hersch, and Hélène Garay, "Ray scattering model for spherical transparent particles," J. Opt. Soc. Am. A 25, 1521-1534 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
  3. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 200-227.
  4. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  5. K. Stamnes, S. Chee Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layer media,” Appl. Opt. 27, 2502-2510 (1988). [CrossRef] [PubMed]
  6. L. Simonot, M. Elias, and E. Charron, “Special visual effect of art glazes explained by the radiative transfer equation,” Appl. Opt. 43, 2580-2587 (2004). [CrossRef] [PubMed]
  7. P. S. Mudgett and L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485-1502 (1971). [CrossRef] [PubMed]
  8. W. E. Vargas and G. A. Niklasson, “Applicability conditions of the Kubelka-Munk theory,” Appl. Opt. 36, 5580-5586 (1997). [CrossRef] [PubMed]
  9. P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931) (in German).
  10. P. Kubelka, “New contributions to the optics of intensely light-scattering material, part I,” J. Opt. Soc. Am. 38, 448-457 (1948). [CrossRef] [PubMed]
  11. M. Hébert and R. D. Hersch, “Reflectance and transmittance model for recto-verso halftone prints,” J. Opt. Soc. Am. A 23, 2415-2432 (2006). [CrossRef]
  12. G. Stokes, “On the intensity of light reflected from or transmitted through a pile of plates,” Mathematical and Physical Papers of Sir George Stokes, IV (Cambridge U. Press, 1904), pp. 145-156.
  13. P. Kubelka, “New contributions to the optics of intensely light-scattering materials, part II: Non homogeneous layers,” J. Opt. Soc. Am. 44, 330-335 (1954). [CrossRef]
  14. G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, 1969).
  15. M. Vöge and K. Simon, “The Kubelka-Munk and Dyck paths,” J. Stat. Mech.: Theory Exp. 2007, P02018 (2007). [CrossRef]
  16. K. Simon and B. Trachsler, “A random walk approach for light scattering in material,” Discrete Math. Theor. Comp. Sci. AC, 289-300 (2003).
  17. M. Hébert, R. Hersch, and J.-M. Becker, “Compositional reflectance and transmittance model for multilayer specimens,” J. Opt. Soc. Am. A 24, 2628-2644 (2007). [CrossRef]
  18. Z. Bodo, “Some optical properties of luminescent powders,” Acta Phys. Acad. Sci. Hung. 1, 135-150 (1951). [CrossRef]
  19. N. T. Melamed, “Optical properties of powders: Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance,” J. Appl. Phys. 34, 560-570 (1963). [CrossRef]
  20. A. Mandelis, F. Boroumand, and H. van den Bergh, “Quantitative diffuse reflectance spectroscopy of large powders: The Melamed model revisited,” Appl. Opt. 29, 2853-2860 (1990). [CrossRef] [PubMed]
  21. H. Garay, O. Eterradossi, and A. Benhassaine, “Should Melamed's spherical model of size-colour dependence in powders be adapted to non spheric particles?” Powder Technol. 156, 8-18 (2005). [CrossRef]
  22. Y. G. Shkuratov, L. Starukhina, H. Hoffmann, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implication to optical properties of the Moon,” Icarus 137, 235-246 (1999). [CrossRef]
  23. Y. G. Shkuratov and Y. S. Grynko, “Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry, and polarimetry of planetary regoliths,” Icarus 173, 16-28 (2005). [CrossRef]
  24. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).
  25. M. Hébert and R. D. Hersch, “Classical print reflection models: A radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).
  26. CRC Concise Encyclopedia of Mathematics (CRC Press, 1998), p. 1580.
  27. W. R. McCluney, Introduction to Radiometry and Photometry (Artech House, 1994).
  28. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983), p. 172.
  29. B. Mayer and S. Madronich, “Photolysis frequencies in water droplets: Mie calculations and geometrical optics limits,” Atmos. Chem. Phys. Discuss. 4, 4105-4130 (2004). [CrossRef]
  30. W. J. Glantschnig and S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499-2509 (1981). [CrossRef] [PubMed]
  31. L. Simonot, M. Hébert, and R. Hersch, “Extension of the Williams-Clapper model to stacked nondiffusing colored coatings with different refractive indices,” J. Opt. Soc. Am. A 23, 1432-1441 (2006). [CrossRef]
  32. J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-736 (1942). [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