Bidirectional reflectance of a diffuse background covered by a partly absorbing layer

The reflectance factor of a diffuse plane background covered by a non-diffuse but partly absorbing layer is computed as a function of the incident and observer angles, and of the background reflectance factor. The particular case of backscattering configuration is then studied. Numerical simulations are presented and discussed for a lambertian background and a transparent layer. Measurements with a gonio-spectrophotometer using optical fibers are implemented on paintings without and with varnish. The experimental results are found to be in good agreement with the predictions. The study is intended to provide a better knowledge of pictorial layers and help for restoration of works of art. (C) 2001 Published by Elsevier Science B.V.