Deriving Kubelka-Munk theory from radiative transport

Area of Science:

• Physics
• Optics
• Radiative Transfer Theory

Background:

• The Kubelka-Munk (KM) theory is a widely used model for describing light propagation in scattering and absorbing media.
• However, its theoretical underpinnings and range of validity have not been fully established from fundamental principles.
• Existing models often struggle with complex boundary conditions and non-uniform properties.

Purpose of the Study:

• To systematically derive the Kubelka-Munk (KM) theory from the radiative transport equation (RTE).
• To establish the theoretical basis, identify parameters, and determine the range of validity for KM theory.
• To generalize KM theory to handle more complex scenarios, including non-homogeneous media and general boundary sources.

Main Methods:

• Systematic derivation of KM theory from the radiative transport equation (RTE).
• Application of the double spherical harmonics method of order one.
• Transformation of the resulting system into equations governing positive- and negative-going fluxes.
• Generalization of KM theory to incorporate non-homogeneous terms and boundary sources.

Main Results:

• Successful derivation of KM theory from the RTE, providing a rigorous theoretical foundation.
• Identification of all parameters within the KM theory and definition of its range of validity.
• Development of generalized Kubelka-Munk (gKM) equations capable of handling complex boundary sources and non-homogeneous media.
• Demonstrated superior accuracy of gKM equations compared to numerical solutions of the RTE.

Conclusions:

• The study provides a rigorous theoretical derivation of Kubelka-Munk theory from the radiative transport equation.
• The generalized Kubelka-Munk equations offer a more accurate and versatile approach to solving radiative transfer problems.
• This work establishes a robust framework for understanding and applying light propagation models in diverse scientific and engineering fields.