Spectral transmittance model for stacks of transparencies printed with halftone colors

The present work investigates the transmission of light through stacks of halftone printed transparencies. We propose a spectral transmittance model describing the multiple reflections of light between the transparencies, whose individual reflectance and transmittance have themselves been obtained by a prediction model. The model for single printed transparency involves the multiple reflections of light between the interfaces as well as the orientation-dependent attenuations of light within the plastic and ink layers. A procedure enables converting the nominal ink surface coverages into effective ones by taking into account the spreading of the inks. Calibration of the model is based on printing a small number of color patches on one transparency and measuring their spectral transmittance. Regarding the stacks of transparencies, an experimental test carried out with inkjet printed samples shows good agreement between predictions and measurements for stacks of two, three and four transparencies. Stochastic halftones are used in order to avoid the apparition of moiré patterns when superposing the halftones. By inversion of the model, we are able to determine the halftone colors to print on each transparency in order to obtain by superposition one targeted color. An original application of this, called “color matching”, consists in producing one color of stack from various combinations of colors on the transparencies. The prediction accuracy of the proposed model guarantees the good visual uniformity of the resulting colored area.