Extending the Clapper–Yule model to rough printing supports

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The Clapper-Yule model is the only classical spectral reflection model for halftone prints that takes explicitly into account both the multiple internal reflections between the print-air interface and the paper substrate and the lateral propagation of light within the paper bulk. However, the Clapper-Yule model assumes a planar interface and does not take into account the roughness of the print surface. In order to extend the Clapper-Yule model to rough printing supports (e.g., matte coated papers or calendered papers), we model the print surface as a set of randomly oriented microfacets. The influence of the shadowing effect is evaluated and incorporated into the model. By integrating over all incident angles and facet orientations, we are able to express the internal reflectance of the rough interface as a function of the rms facet slope. By considering also the rough interface transmittances both for the incident light and for the emerging light, we obtain a generalization of the Clapper-Yule model for rough interfaces. The comparison between the classical Clapper-Yule model and the model extended to rough surfaces shows that the influence of the surface roughness on the predicted reflectance factor is small. For high-quality papers such as coated and calendered papers, as well as for low-quality papers such as newsprint or copy papers, the influence of surface roughness is negligible, and the classical Clapper-Yule model can be used to predict the halftone-print reflectance factors. The influence of roughness becomes significant only for very rough and thick nondiffusing coatings.