Spectral prediction model for variable dot-size printers

By printing a variable number of droplets onto the same pixel location, ink jet printers produce pixels at variable dot-sizes yielding several darkness levels. Varying the number of printed droplets affects the ink volume deposited onto the substrate. In the present contribution, we explore the possibility of producing accurate spectral reflectance predictions at all pixel dot-sizes. For this purpose, we use a Clapper-Yule model, extended according to Beer’s law, which accounts for ink thickness variations. This model expresses each colorant transmittance as a function of its constituent ink transmittances and their respective relative thicknesses. These relative thicknesses are initially computed when calibrating the model, at a given pixel dot-size, and can then be dynamically scaled according to the printed pixel dot-size. We first study the effect of varying pixel dot-sizes on the halftone’s physical (mechanical) dot-gain. We then express the ink volume variations as a function of pixel dotsizes. Lastly, we show how, using the thickness extended ClapperYule model, we can effectively predict reflectances for different configurations of ink pixel dot-sizes. Introduction Among the many printing technologies, ink jet is widely used. In recent ink jet printers, multiple darkness levels per pixel are obtained by varying the number of ink droplets, i.e. varying the ink volume. The larger the deposited volume, the darker the printed pixel dot. The Canon i990 printer, used to produce all results presented in this paper, enables printing with 8 different dot-sizes. No classical reflectance or color prediction model supports variations in ink volumes. An accurate spectral reflectance prediction model accounting for variable dot-size would be very useful for designing new color separation strategies exploiting the high potential offered by variable dot-size printers. Note that Yang [7] modeled solid ink and colorant layers printed at variable dot sizes by using the Kubelka-Munk model and by assimilating ink volume variations to ink thickness variations. In this work we propose to model the effect of variable dotsizes. To do so, we use a modified Clapper-Yule model taking into account ink thicknesses. By considering a printed halftone dot as a perfect cylinder of a fixed diameter, we can effectively model volume variations by thickness variations. After calibration of the model, it is then possible to account for the ink volume variations induced by the pixel dot-size variations. We start by describing the classical Clapper-Yule model and its extensions. We then analyse the physical halftone dot gain at different ink dot-sizes. We also express effective ink volume variations as a function of printed ink dot-sizes. We then measure the accuracy of spectral predictions obtained using the thickness enhanced spectral reflectance prediction model when applying the same dot-size variation to every ink. Then, in order to validate our model, we deduce ink volume variations and evaluate reflectance predictions for the general case, where the pixel dot-size differs for each ink. Finally, we draw the conclusions. The Clapper-Yule based spectral prediction model The Clapper-Yule model [2] is the only classical halftone spectral reflectance prediction model incorporating the notion of colorant transmittance. It models the multiple internal reflections occurring at the interface between the print and the air. Since we modify the printed pixel dot-sizes, and therefore the colorant transmittances, this model is of particular interest. For 3 inks, i.e. 8 Neugebauer primaries (colorants), the Clapper-Yule formula is: R(λ ) = K · rs + (1− rs) · rg · (1− ri) · (