Revised Kubelka-Munk theory. I. Theory and application

Area of Science:

• Optics and Photonics
• Materials Science
• Statistical Physics

Background:

• The Kubelka-Munk (K-M) theory is a widely used model for describing light propagation in scattering and absorbing media.
• However, the original K-M theory has limitations in explaining experimental observations, particularly for composite materials like dyed paper.

Purpose of the Study:

• To revise the Kubelka-Munk (K-M) theory by accounting for the effect of scattering on light path length (path variation).
• To establish new, non-linear relationships between K-M coefficients (S, K) and intrinsic material properties (a, s).
• To re-evaluate the additivity law for composite media and explain experimental anomalies in dyed paper.

Main Methods:

• Statistical analysis of light propagation in media.
• Development of a revised theoretical framework (two-flux approach) incorporating path variation.
• Numerical simulations on model systems (ink, paper, dyed paper).

Main Results:

• New relationships reveal non-linear dependencies of K-M scattering (S) and absorption (K) coefficients on intrinsic scattering (s) and absorption (a) coefficients.
• The revised additivity law accurately describes composite media.
• The new K-M theoretical framework successfully explains experimental findings on dyed paper that were inconsistent with the original theory.

Conclusions:

• The revised K-M theory, considering path variation, provides a more accurate and comprehensive model for light propagation in scattering and absorbing materials.
• This enhanced theoretical framework resolves discrepancies in previous models and offers better predictive capabilities for composite materials.
• The findings have implications for understanding and modeling optical properties of various materials, including paper and inks.