Kubelka–Munk equation

The Kubelka–Munk equation relates diffuse reflectance of an optically thick layer to its absorption and scattering coefficients, commonly as F(R∞) = (1 − R∞)²/(2R∞) = K/S.

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Kubelka–Munk function: The transform F(R) = (1 − R)²/(2R), used to express reflectance in terms of absorption-to-scattering ratio. It is the reflectance transform at the heart of the equation.
Colorimetry: The measurement and quantification of color using physical measurements and standardized observers. Reflectance-derived values can support quantitative comparisons of colored materials.
Beer–Lambert law: A law relating light attenuation in a homogeneous absorbing medium to absorber concentration and path length. Unlike Kubelka–Munk, it models transmission through an absorbing medium rather than diffuse reflection in a scattering layer.
Paul Kubelka: A physicist who, with Franz Munk, developed a two-constant model of light in scattering layers. His work supplied the model from which the reflectance equation is derived.
Diffuse reflectance: Light reflected from a material after scattering within it, rather than reflecting only at its surface. The equation uses diffuse reflectance as its observable input.
Color strength: A measure of a colorant’s ability to produce color at a given concentration or under specified conditions. The K/S ratio is often used as a practical indicator of colorant strength.
Finite-layer Kubelka–Munk model: A Kubelka–Munk formulation that relates reflectance and transmittance to the thickness of a finite layer. It relaxes the optically thick assumption behind the equation’s simplest form.
Franz Munk: A physicist who coauthored the foundational Kubelka–Munk treatment of light in scattering media. His collaboration established the theory underlying the equation.
Absorption coefficient: A measure of how strongly a material removes light from a beam per unit distance. It supplies the K term governing light loss inside the layer.
Tinting strength: The ability of a pigment to alter the color of a mixture when added in a specified amount. Reflectance measurements can compare pigment performance through K/S values.