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 nonlinearly 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.
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