Yule-Nielsen effect in printing: a physical analysis

The Yule-Nielsen curve-fitting parameter n is derived in terms of the point spread function describing the scattering of light in paper substrates upon which are printed halftone dot or line patterns. The value of n is shown not to depend strongly on either screen frequency or area coverage at low area coverages or highlight regions. However, when the shadow regions are considered, n becomes increasingly dependent on both of these parameters. This dependence is not explicitly allowed for by the Yule-Nielsen equation. It is analytically shown that the value of n approaches 1.0 as the substrate approaches a specular surface and approaches 2.0 as the substrate becomes a perfect diffuser. The value of this analysis is the following. First, it indicates that the Yule-Nielsen equation is physically adequate in highlight and medium shadow regions. Second, an accurate determination of n at any screen frequency can be made from a single measurement of n at any other frequency using an inferred scattering length. Third, this analysis shows that the empirical (Yule-Nielsen) determination of n from dot density and fractional area coverages is valid only in the regions below about 50% area coverage.