Ray scattering model for spherical transparent particles

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 Clapper-Yule model, we can effectively predict reflectances for different configurations of ink pixel dot-sizes.