Classical Print Reflection Models: A Radiometric Approach

©2004, IS&T—The Society for Imaging Science and Technology Spoonhower3 have extended the Williams–Clapper model to any refractive index of the coating and for any angular measurement geometry including the integrating sphere geometry. Most printed colors are produced by halftoning, where the ink is distributed on the paper as little ink dots according to given nominal coverage values. Simple models like the Murray–Davies model4 assume that between the dots the surface properties are those of the coated paper. In practice however, the light interacts both with printed and unprinted areas during its propagation within the paper. This phenomenon is called optical dot gain. In 1952, Clapper and Yule presented a model to predict the spectrum of a halftone print on paper, including the modeling of optical dot gain, taking into account multiple internal reflections and lateral scattering of light within the paper bulk.5 The Williams–Clapper2 as well as the Clapper–Yule model5 are the starting points for a wide range of color prediction models.6,7 In the present contribution, we study the interaction of light with a coated Lambertian substrate by relying on the laws of optics and by following the conventions of radiometry. We make the following assumptions: • the substrate is a perfectly diffuse reflector, • the refractive index of the substrate is the same as the refractive index of the coating, thereby avoiding any Fresnel reflection or refraction at the interface between the substrate (paper bulk) and the paper coating, • the air-coating interface is a perfectly planar interface, • the incident light is perfectly collimated and unpolarized.