Deducing ink-transmittance spectra from reflectance and transmittance measurements of prints

The color of prints is mainly determined by the light absorption of the inks deposited on top of paper. In order to predict the reflectance spectrum of prints, we use a spectral prediction model in which each ink is characterized by its spectral transmittance. In the present paper, we consider two classical reflectance prediction models: the Clapper-Yule model and the Williams-Clapper model. They rely on a same description of multiple reflection-transmission of light, but use a different description of the attenuation of light by the inks. In the Clapper-Yule model (non-orientational ink attenuation), the orientation of light traversing the ink is not taken into account. In the Williams-Clapper model, it is taken into account (orientational ink attenuation). In order to determine experimentally which of these two models is the more suitable for a given type of print, we propose a method using the reflectance and the transmittance of prints. We introduce a bimodal model, enabling spectral reflectance and transmittance predictions. Depending whether the direction of light into the ink is taken into account, we obtain a non-orientational bimodal model or an orientational bimodal model. Using these two models, we deduce the ink transmittance spectrum from various reflectance and transmittance measurements performed on a same print, and compare the different deduced spectra. The model which is the most adapted to the considered print is the one where the deduced spectra best match each other.