Relationship between the Kubelka-Munk scattering and radiative transfer coefficients

Area of Science:

• Optics
• Materials Science
• Radiative Transfer Theory

Background:

• The Kubelka-Munk (K-M) model is widely used to describe the optical properties of scattering and absorbing materials.
• Existing models often struggle with accuracy across a wide range of optical properties, particularly for collimated light.
• The relationship between K-M theory and the fundamental transport scattering coefficient requires further clarification.

Purpose of the Study:

• To derive and validate a semi-empirical relationship between the Kubelka-Munk (K-M) model and the transport scattering coefficient.
• To assess the accuracy of the K-M model and related expressions under various incident light conditions (diffuse vs. collimated).
• To establish a unified approach for quantifying absorption and scattering effects regardless of incident light characteristics.

Main Methods:

• Developed a semi-empirical approach to relate the K-M coefficients to the transport scattering coefficient.
• Compared derived results with existing models (Gate, Star et al., Brinkworth) and exact solutions of the radiative transfer equation.
• Investigated the K-M model's applicability to collimated incident light by incorporating an anisotropy factor.

Main Results:

• The semi-empirical approach yields results consistent with Gate's model for diffuse incident light.
• Previous models incorporating absorption components showed inaccuracies over a broad range of optical properties.
• The K-M model accurately represents reflectance for collimated light on thick slabs when adjusted with an anisotropy-dependent function.
• The K-M transform effectively provides a measure of the absorption-to-scattering ratio for both diffuse and collimated beams.

Conclusions:

• The K-M model, when appropriately modified, is versatile and applicable to both diffuse and collimated incident light.
• The derived semi-empirical relationship enhances the predictive power of the K-M model for diverse optical scenarios.
• This work provides a robust method for analyzing the interplay of absorption and scattering in materials, crucial for optical design and characterization.