A Physically-based BRDF Model for Multilayer Systems with Uncorrelated Rough Boundaries

  • Isabelle Icart
  • Didier Arquès
Part of the Eurographics book series (EUROGRAPH)


This paper presents a new BRDF model allowing the simulation of the optical behaviour of multilayer systems formed of homogeneous and isotropic thin films with random rough boundaries. The boundaries are supposed to be locally smooth and generated by a stationary and isotropic Gaussian process. Moreover, it is assumed that they are mutually independent from the statistical point of view. The BRDF is composed of three terms: specular, directional diffuse and uniform diffuse terms, and accounts for interference, diffraction and polarization effects. The expressions for the specular and directional diffuse components are derived analytically, by means of the Abeles formalism, within the framework of the Kirchhoff theory of diffraction. We present pictures of composite multilayer materials obtained by incorporating this model in a spectral ray-tracing algorithm.


Complex Refractive Index Multilayer System Bidirectional Reflectance Distribution Function Rough Boundary Multilayer Material 
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  1. 1.
    F. Abelès, “Sur la Propagation des Ondes Electromagnétiques dans les Milieux stratifiés”, Ann. De Phys., 12ème série, vol. 10, pp. 505–581, 1948.Google Scholar
  2. 2.
    P. Beckmann and A. Spizzichino, “The Scattering of Electromagnetic Waves from Rough Surfaces”, Pergamon Press, 1963.MATHGoogle Scholar
  3. 3.
    M. Born and E. Wolf, Principles of Optics-Electromagnetic Theory of Propagation, Interference and Diffraction of Light, sixth (corrected) edition, Pergamon Press, Oxford, 1980.Google Scholar
  4. 4.
    P. Callet, “Physically Based Rendering of Metallic Paints and Coated Pigments”, Visualization and Modelling, R. Earnshaw, John Vince and Huw Jones, Academic Press, pp. 287–302, 1997.Google Scholar
  5. 5.
    Commission Internationale de l’Eclairage, International Lighting Vocabulary, CIE 17 (E-1.1), Paris, Troisième édition, 1970.Google Scholar
  6. 6.
    J. Dorsey, A. Edelman, J. Legakis, H. W. Jensen, H. K. Pedersen, “Modeling and Rendering of Weathered Stone”, ACM SIGGRAPH’99 Conference Proceedings, 1999.Google Scholar
  7. 7.
    J. S. Gondek, G. W. Meyer and J. G. Newman, “Wavelength Dependant Reflectance Functions”, Proceedings of Siggraph’94, p. 213–220, Orlando, Florida, 1994.Google Scholar
  8. 8.
    P. Hanrahan and W. Krueger, “Reflection from Layered Surfaces due to Subsurface Scattering”, Proceedings of SIGGRAPH ’93, pp. 165–174, 1993.Google Scholar
  9. 9.
    H. W. Jensen, J. Legakis and J. Dorsey, “Rendering of wet materials”, Rendering Techniques ’99, Proceedings of The Eurographics Workshop, Grenada, 1999, pp.273–280.Google Scholar
  10. 10.
    X. D. He, K. E. Torrance, F. X. Sillion et D. P. Greenberg, “A Comprehensive Physical Model for Light Reflection”, Computer Graphics Vol. 25(4), ACM SIGGRAPH’91 Conference Proceedings, 1991.Google Scholar
  11. 11.
    E. Hecht, Optics, Addison-Wesley Publishing Company, 1987.Google Scholar
  12. 12.
    I. Icart and D. Arquès, “An Illumination Model for a system of Isotropic Substrate-Isotropic Thin Film with Identical Rough Boundaries”, Rendering Techniques ’99, Proceedings of The Eurographics Workshop, Grenada, 1999, pp.261–272.Google Scholar
  13. 13.
    G. W. Meyer, “Wavelength Selection for Synthetic Image Generation”, Computer Vision, Graphics and Image Processing, vol. 41, 57–69, 1988.CrossRefGoogle Scholar
  14. 14.
    J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces, Institute of Physics Publishing, Bristol and Philadelphia 1991.MATHGoogle Scholar
  15. 15.
    I. Ohlídal and K. Navrátil, “Scattering of Light from Multilayer Systems with Rough Boundaries”, Progress in Optics, 34, Elsevier Science, 1995.Google Scholar
  16. 16.
    E. D. Palik, Handbook of Optical Constants of Solids, Academic Press, 1997.Google Scholar
  17. 17.
    G. Rougeron and B. Péroche, “Color Fidelity in Computer Graphics:a survey”, Computer Graphics Forum, 17, pp. 1–13, 1998.CrossRefGoogle Scholar
  18. 18.
    J. Stam, “Diffraction Shaders”, Proceedings of SIGGRAPH ’99, pp. 101–110, 1999.Google Scholar

Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Isabelle Icart
    • 1
  • Didier Arquès
    • 1
  1. 1.Université de Marne-La-ValléeMarne-La-Vallee CEDEX 2France

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