Revised Kubelka-Munk theory. I. Theory and application

Using a statistical analysis of light propagation in media, we propose a revision to Kubelka-Munk (K-M) theory by taking into account the effect of scattering on the path length of light propagation (path variation). This leads to new relationships between the K-M scattering S and absorbing K coefficients and the intrinsic scattering s and absorbing a coefficients of a material that indicate that the S and K coefficients depend non-linearly on both a and s. The additivity law that bridges K-M S and K coefficients of a composite medium, such as dye-dispersed paper (dyed paper) and those of its material components (dye and paper), is also revised. It is further shown that experimental findings on dyed paper that the original K-M theory failed to explain can be clearly understood and accommodated by the new K-M theoretical framework (two-flux approach). Numerical simulations with the revised theory on model ink, paper, and dyed paper have been carried out.