Bidirectional reflectance distribution function of specular surfaces with hemispherical pits

Sylvia C. Pont*, Jan J. Koenderink

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

23 Citations (Scopus)


We derive the bidirectional reflectance distribution function for a class of opaque surfaces that are rough on a macroscale and smooth on a microscale. We model this type of surface as a distribution of spherical mirrors. Since our study concerns geometrical optics, it is only the aperture of the concavities that is relevant, not the dimension. The three-dimensional problem is effectively transformed into a much simpler two-dimensional one involving the possibly infinitely many reflections in a spherical mirror. We find that these types of surface show very strong backscattering when the pits are deep but forward scattering when the pits are shallow. Such surfaces also show spectral effects as a result of multiple reflections and polarization effects that are due to the orientation of the effective surface. Both this model and the locally diffuse thoroughly pitted surface model [Int. J. Comput. Vision 31, 129 (1999)] are superior to other models in that they allow for an exact treatment for physically realizable surface geometries.

Original languageEnglish
Pages (from-to)2456-2466
Number of pages11
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number12
Publication statusPublished - 2002
Externally publishedYes

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