KubelkaMunkanalys

KubelkaMunkanalys, or Kubelka–Munk analysis, is a mathematical model used to describe light scattering and absorption in diffuse, multiply scattering media such as paints, coatings, and powdered pigments. Developed by P. Kubelka and F. Munk in the 1930s, the theory provides a simple relationship between the reflectance, transmittance, and the absorption (K) and scattering (S) coefficients of a material. The key assumption is that the material is optically dense, homogeneous, and that light transport can be approximated by two coupled first‑order differential equations for upward and downward fluxes.

The Kubelka–Munk function is defined as F(R) = (1−R)^2 / (2R), where R is the measured reflectance of a thick, diffusely reflecting sample. For a sample of thickness d, the relative absorption to scattering ratio is approximated by K/S = (1/d)·ln[(1−R)/R] for transmittance T or by F(R) for reflectance‑only measurements. By measuring R (and possibly T) across wavelengths, one can determine K(λ) and S(λ), revealing how pigments absorb and scatter light. This is particularly valuable for color matching, pigment formulation, and quality control in the paint and printing industries.

Kubelka–Munk theory is frequently combined with spectral reflectance measurements using diffuse reflectance spectrophotometers. Despite its simplifications, the model predicts color accurately for many layered paint systems and is still widely taught in color science courses. The method’s practicality lies in requiring only a single reflectance measurement to retrieve optical constants, making it a standard tool for evaluating pigmentation in thin films and coatings.