Spectral colour prediction model for a transparent fluorescent ink on paper

A new spectral colour prediction model for a fluorescent ink printed on paper is presented. It is based on our previous work on transparent support 4 and on a new mathematical formalism which generalizes the Kubelka-Munk theory. The printed paper is modelized by means of three matrices: an interface correction matrix, a matrix exponential modelizing the layer which contains the fluorescent ink, and a reflection matrix caracterising the substrate. The interface correction matrix allows to take multiple reflections into account by operating the Saunderson correction. These matrices are related to physical properties of ink and paper which must be measured: the transmittance spectra, the quantum yields, the absorption bands and the emission spectra of the fluorescent inks, and the reflection properties of the paper. Our new model can predict the reflection spectra of uniform samples for different ink concentrations and under different illuminants. It is applied successfully to predict the spectra of real samples with an average prediction improvement of about ΔE = 17 in comparison with Beer's law.