Deriving Kubelka–Munk theory from radiative transport

We derive Kubelka–Munk (KM) theory systematically from the radiative transport equation (RTE) by analyzing the system of equations resulting from applying the double spherical harmonics method of order one and transforming that system into one governing the positive- and negative-going fluxes. Through this derivation, we establish the theoretical basis of KM theory, identify all parameters, and determine its range of validity. Moreover, we are able to generalize KM theory to take into account general boundary sources and nonhomogeneous terms, for example. The generalized Kubelka–Munk (gKM) equations are also much more accurate at approximating the solution of the RTE. We validate this theory through comparison with numerical solutions of the RTE.