Generalized Kubelka-Munk theory - A derivation and extension from radiative transfer
- Author(s): Sandoval, Christopher Thomas
- Advisor(s): Kim, Arnold D
- et al.
Kubelka-Munk (KM) theory is a broadly used simplification to the radiative transfer equation (RTE) that is solvable analytically for a restricted set of very simple problems. Despite this simplicity and popularity, KM theory has never had its theoretical basis formally established. In this work, we derive KM theory systematically from the radiative transfer equation (RTE) by application of the spectrally convergent double spherical harmonics method, of order one, and analysis of the resulting, transformed, system of equations in the positive- and negative-going fluxes. We call these the generalized Kubelka-Munk (gKM) equations, and they are able to account for general boundary sources and nonhomogeneous terms. Having established theoretical footing for KM theory, we extend gKM's four-flux method to higher dimensions, applying it to a Gaussian boundary source and demonstrating the method's range of validity. Finally, we examine the application of the gKM method to the vector radiative transport equation (vRTE), allowing for the modeling of sources with polarized light. These methods offer a low cost approximation to the solutions of the scalar and vector RTE's, which we validate through comparison with benchmark solutions of the transport equation.