The Clapper-Yule model of halftone reflectance includes the effects of light diffusion and multiple internal reflection between the ink-layer and the paper substrate. it models complete scatter-the case in which the distance a photon diffuses is much greater than the screen period. The current work generalizes this to any degree of scatter. The model is presented in terms of probability functions, and the probabilities are calculated from the paper's point spread function (PSF). photon diffusion within paper is due to two processes: scatter and multiple internal reflection. The usually defined PSF includes both processes. Ink on the paper surface, however alters the internal reflectance, and so the usually defined PSF depends on the percent ink coverage. The current model separates the effects of scatter from the effects of internal reflection. The PSF introduced here accounts for scatter only-it is independent of the percent ink coverage. It is shown that the generalized Clapper-Yule model corresponds to Yule-Nielsen n-values significantly greater than 2, unlike the case of no infernal reflection for which the maximum n-value is equal to 2.