Interaction between Light, Paper and and Color Halftones: Challenges and Modelization Approaches

We review the phenomena having an impact on the interaction between light, paper and color halftones. They comprise surface reflections and refractions at the air-paper interface, propagation of light within the paper, internal reflections at the paper-air interface, as well as ink spreading and trapping. We introduce basic notions from radiometry and optics, such as the definitions of radiant flux, irradiance, radiance, Lambert reflector, as well as collimated and diffuse light reflection and refraction. We then present classical spectral reflection models, their extension to multi-ink color halftones and the impact of different measuring devices (radiant detector, integrated sphere). Finally we briefly review ink spreading models and highlight the topics deserving further research. Introduction Accurate models of the interaction between light, paper and halftones may offer new ways of performing automatically the calibration of printing devices, e.g. upon change of the paper or of the ink cartridges. They may also help in regulating printing devices by ensuring that print parameters, such as the amount of deposited ink, remain constant, independently of the fact that the printer has just started printing or has been printing for a few hours. Finally, for printers capable of printing with many custom inks, spectral prediction models may help in computing the optimal combination of inks yielding a desired color. Phenomena Let us briefly review the main phenomena occurring when light hits a halftone image printed on paper (Fig. 1). Light incident on the print is partly reflected and partly refracted at the air-print interface. The amount of specularly reflected light and its angular distribution depends on the surface properties of the print and on the angular distribution of the incident light. The part of the incident light transmitted (refracted) into the print is the part that is not reflected at the print surface. The transmitted light is then further attenuated by the ink halftone layer and penetrates the paper bulk where it is scattered in all directions. Light scattering within the paper bulk induces both a lateral propagation of the light and a reflection from the paper bulk towards the ink halftone layer located beneath the print-air interface. There, it is attenuated by the ink halftones. At the print-air interface, part of the light is reflected towards the paper bulk and part of the light is transmitted (refracted) into the air. The part reflected for the second time by the paper bulk is again attenuated by the ink halftone and again reflected by the paper bulk and reemitted towards the print-air interface. The successive reflections between the paper bulk and the print-air interface yield the so-called multiple internal reflections. At print time, there are further interactions between ink halftones and paper and between ink halftones and previously printed ink layers. Ink halftone Paper substrate Air (1) Specular reflection (4) Internal reflections at the printair interface (3) Lateral propagation of light and reflection within the substrate (2) Transmission of light through the ink layer Figure 1. Phenomena contributing to the interaction between light, ink halftones and paper A single ink halftone layer printed on paper generates an ink dot surface coverage which is generally larger than the corresponding nominal dot surface coverage value. The enlargement of the printed ink dot is called dot gain. The dot gain is the difference between effective dot surface coverage and nominal dot surface coverage. When an ink halftone is printed on top of another ink, e.g. a solid ink (100% surface coverage), the dot gain of the ink halftone is different than when it is printed alone on paper (Fig. 2). Dot gain therefore strongly depends on the superposition condition, i.e. on which other inks a given ink halftone is superposed. Note that the dot gain of an already printed ink halftone may be modified by a second ink printed on top of that ink halftone. 0 0.25 0.5 0.75 1 -0.02 0 0.05 0.1 0.15 0.2