Elementary Differential Equations With Mathematica
Elementary Differential Equations With Mathematica
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Future printer calibration systems will be based, at least partially, on color prediction models able to compute the reflection spectrum of a given printed sample knowing the physical properties of the ink and paper. Until now, the physical phenomena involved in light reflection were described separately by several classical models (Beer's absorption law, the Fresnel reflection, the Saunderson correction for multiple internal reflections, and the Kubelka-Munk model for scattering media). In this article we present a unified model based on a single formula describing the reflection of light on one or several uniform ink layers, both for transparent and partially opaque inks. We consider the phenomena of surface reflection, light absorption in the ink layers, diffuse light source, diffuse reflector (paper), internal reflections at the ink-air interface, scattering media (partially opaque inks), and the combination of several ink layers. Our approach unifies the classical models by using a new mathematical framework based on matrices. The model presented is currently limited to uniformly printed samples. To be usable for automatic printer calibration, it must be extended to halftoned patches.