The Effect of Multiple Internal Reflections on the Densities of Half-tone Prints on Paper*

The equation relating dot area to half-tone density, when sideways scattering of light takes place in the paper, has been modified to take into account multiple internal reflections. Curves showing the relationship between dot area and density for various ink densities and amounts of first-surface reflectance are given. Callahan’s conclusion that these effects are negligible is not in accordance with the authors’ experience, and the new equations indicate the possibility of densities much higher than the limiting values derived from Callahan’s equations and from our earlier equation which neglected multiple internal reflectance.