Theory for Off-Specular Reflection From Roughened Surfaces*

1967/09/01 by K. E. Torrance, E. M. Sparrow · 30 citations
Engineering · Mathematics · Physics and Astronomy · #Calibration and Measurement Techniques #Color Science and Applications #Diffuse reflection #Flux (metallurgy) #Geometry #Masking (illustration) #Materials science #Mathematics #Optical Polarization and Ellipsometry #Optics #Physics #Reflection (computer programming) #Scattering #Specular highlight #Specular reflection #Surface (topology)

paper · doi:10.1364/josa.57.001105

published in Journal of the Optical Society of America 57(9), 1105 (Optica Publishing Group)

openalex publication_date 1967/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

The directional distribution of radiant flux reflected from roughened surfaces is analyzed on the basis of geometrical optics. The analytical model assumes that the surface consists of small, randomly disposed, mirror-like facets. Specular reflection from these facets plus a diffuse component due to multiple reflections and/or internal scattering are postulated as the basic mechanisms of the reflection process. The effects of shadowing and masking of facets by adjacent facets are included in the analysis. The angular distributions of reflected flux predicted by the analysis are in very good agreement with experiment for both metallic and nonmetallic surfaces. Moreover, the analysis successfully predicts the off-specular maxima in the reflection distribution which are observed experimentally and which emerge as the incidence angle increases. The model thus affords a rational explanation for the off-specular peak phenomenon in terms of mutual masking and shadowing of mirror-like, specularly reflecting surface facets.

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