KubelkaMunk

Kubelka–Munk theory, also known as the Kubelka-Munk model, is a foundational framework in color science for describing the diffuse reflectance and transmittance of pigmented, dyed, or scattering media. Developed by Paul Kubelka and Franz Munk in 1931, it provides a simple two-flux approximation to the transport of light in a turbid medium. The model characterizes the optical properties with two coefficients: K, the absorption coefficient, and S, the scattering coefficient. For a semi-infinite, diffusely reflecting layer, the Kubelka–Munk function F(R∞) = (1 − R∞)^2 / (2 R∞) equals K/S.

This relationship allows converting measured reflectance into a quantity proportional to pigment concentration and is widely used for color matching and quality control in paints, pigments, paper, plastics, and textiles. The theory rests on a two-flux approximation, assuming diffuse illumination, homogeneous planar layers, isotropic scattering, and no significant specular reflection or back reflections from underlying substrates. It neglects nonlinear optical effects, strong anisotropy, or highly translucent layers where the assumptions break down.

Extensions include equations for finite thickness layers and multi-layer systems, as well as methods to separate absorption and scattering contributions. In practice, researchers calibrate K and S with standard samples and apply the Kubelka–Munk function across wavelengths to predict or match colors.

History and impact: published in 1931 by Kubelka and Munk, the theory became a standard tool in color science and paint technology, influencing color measurement methods and pigment specifications. Limitations include its assumptions of homogeneity, isotropic scattering, and semi-infinite layers, which can limit accuracy for highly glossy, layered, or highly translucent materials. Variants and more advanced models have since extended its applicability.