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Optical Engineering

Forward scattering of fiber-containing surfaces studied by 3-D reflectance distribution simulations and measurements
Author(s): Hjalmar Granberg; Jon Jensen; Lars H. Mattsson
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Paper Abstract

Recent studies have shown that the angular distribution of diffuse reflectance, obtained from bidirectional reflectance distribution function (BRDF) measurements, differs strongly between paper sheets with and without fibers present in the top surface layer. For fiber-containing surfaces, in contrast to pigment-coated paper surfaces, there is a distinct forward scattering at angles much larger than the specular reflection angle. In the search for an explanation of this phenomenon, we have made calculations of reflectance distributions of a simulated paper web, containing randomly distributed hollow fibers. We did this on the assumption that fibers present in paper are considerably larger than the wavelength of visible light, and that the surface microroughness of the fibers can be treated as a diffraction broadening superposed on the ray calculated reflectance distribution. We investigate whether the structural shape and distribution of wood fibers can explain some of the observed forward-scattering phenomenon. We also compare these Monte-Carlo ray tracing calculations qualitatively with experimental BRDF measurements of the diffuse reflectance from a fiber-containing surface. From the calculations we found that the reflection at the inner fiber wall of the hollow fibers constituting the topmost layer plays a major role in forming a forward-scattering reflectance distribution. We also found that the Monte-Carlo-calculated bulk scattering distribution, i.e., the distribution of reflected light after a large number of reflections within the web structure, tended to be elongated perpendicular to the sheet plane of the fiber web, rather than being uniform.

Paper Details

Date Published: 1 August 2003
PDF: 7 pages
Opt. Eng. 42(8) doi: 10.1117/1.1589024
Published in: Optical Engineering Volume 42, Issue 8
Show Author Affiliations
Hjalmar Granberg, Acreo AB (Sweden)
Jon Jensen, Stoneridge Electronics Gårdsfogdev (Sweden)
Lars H. Mattsson, Royal Institute of Technology (Sweden)

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