Unlike the Beer-Lambert law, which is based solely on the light-absorption process, and the Neugebauer equations, which are based solely on the light-reflection process, several models developed for halftone printing are more sophisticated because they take into consideration absorption, reflection, and transmission, as well as scattering. This chapter presents several halftone-printing models with various degrees of complexity and sophistication. Perhaps the simplest one is the Murray-Davies model, considering merely halftone dot absorptions and direct reflections. Yule and Nielsen developed a detailed model that takes the light penetration and scattering into consideration. Clapper and Yule developed a rather complete model to account for light reflection, absorption, scattering, and transmission of the halftone process. The most comprehensive model is a computer simulation model developed by Kruse and Wedin for the purpose of describing the dot gain phenomenon, which consists of the physical and optical dot gain models that consider nearly all possible light paths and interactions in order to give a thorough and accurate account of the halftone process.
18.1 Murray-Davies Equation
Unlike the Neugebauer equations, which take reflectance as is, the Murray-Davies equation derives the reflectance via the absorption of halftone dots and the reflection of the substrate. Figure 18.1 depicts the Murray-Davies model of halftone printing. In a unit area, if the solid-ink reflectance is Ps, then the absorption by halftone dots is (1 â Ps) weighted by the dot area coverage a. The reflectance P of a unit halftone area is the unit white reflectance subtracting the dot absorptance.
If we take the unit white reflectance as a total reflection with a value of 1, we obtain Eq. (18.1) for the Murray-Davies equation. P=1âa(1âP s ). If we use the reflectance of the substrate Pw as the unit white reflectance, we obtain Eq. (18.2). P=P w âa(P w âP s ).
© 2006 Society of Photo-Optical Instrumentation Engineers
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