In this talk we first assess the use of the Williams-Clapper [1] model for first-principles calculation of CIELAB color coordinates of hard copy xerographic monocolor images. This model produces color coordinates a* and b* which are in good agreement with the observed colors for xerographic monocolor images. Typical chroma errors produced by this model are on the order of ΔC*=5, with an equal spread both above and below the observed values. However, the Williams-Clapper model does not make accurate predictions for the image lightness L*. Typical lightness errors are on the order of ΔL* = 15, and the predicted lightness is always too low; too little light is predicted to be reflected. We attribute this failure to the lack of backscattered light from embedded pigment particles.We modify the Williams-Clapper model by including the scattering of light from dispersed pigment particles in the fused toner layer. Renormalization group techniques are used to include all orders of light scattering between the front surface, the pigment particles in the image, and the rough paper surface. The model presented here reduces to the Williams-Clapper model in the limit that scattering from the pigment particles vanishes.
Robert J. Meyer, "Theory of the effect of light scattering from dispersed pigment particles on hard copy monochrome color" in Proc. IS&T 7th Color and Imaging Conf., 1999, pp 273 - 277, https://doi.org/10.2352/CIC.1999.7.1.art00052