Kubelka-Munk theory

The Kubelka-Munk theory (named after Paul Kubelka and Franz Munk ) describes the light absorption and light scattering properties of pigmented systems, such as paints or dyes in textile fabrics .

The theory can use measurements of two layer thicknesses to predict how the color will work with other layer thicknesses. This enables paint manufacturers to estimate how much pigment they need to add to a paint so that the paint is opaque for a certain thickness of the order .

With the help of theory, the color effect of the mixture of two dyes can also be predicted if the parameters of the individual dyes have been determined with the help of spectroscopic measurements. The results are better than with naive use of subtractive color mixing.

Requirements and boundary conditions

The theory applies on the assumption that the absorption in a medium is significantly weaker than the scattering and that the reflection on the surface is negligible. This applies, for example, to matt, light colors.

To this end, Kubelka and Munk have described the paths of light within paint coatings in a very simplified manner. In this model, the light can only move vertically through the layer of paint. This is justified with statistical assumptions that apply in the case of isotropy of irradiation and scattering within the color layer. Uncoated papers under diffuse lighting are therefore well described by the Kubelka-Munk theory, whereas coated glossy papers under direct, directed light are worse.

description

The central equation of the theory, the Kubelka-Munk function , is:

{\ displaystyle {\ frac {K} {S}} = {\ frac {(1-R _ {\ infty}) ^ {2}} {2R _ {\ infty}}} <1}

With

an abstract absorption component ${\ displaystyle K}$
an abstract scattering component ${\ displaystyle S}$
the reflectance of an infinitely thick layer of paint. In practice, this can be replaced by the reflectance of a layer that is so thick that measuring instruments can no longer detect any difference. Thus the right side of the equation can be determined by measurement. ${\ displaystyle R _ {\ infty}}$

The theory assumes that the absorption and scattering components remain constant at different thicknesses of a paint layer.

In the Kubelka-Munk theory, these components do not have the meaning of physical probabilities per volume. This is due to the fact that the concrete paths of light in the material are three-dimensional and therefore longer; as the scattering increases, so does the probability that light will actually be absorbed within a volume and converted into other forms of energy.

swell

Paul Kubelka, Franz Munk: A contribution to the appearance of the paintwork. In: Journal for Technical Physics. 12, 1931, pp. 593-601.
Deane B. Judd, Gunther Wyszecki: Color in Business, Science and Industry. 1975.

Web links

Kubelka and Munk. The two constant theory

Individual evidence

↑ Georg Meichsner, Jörg Schröder: Measuring and controlling paint properties . Vincentz Network GmbH & Co KG, 2003, ISBN 3-87870-739-8 , p. 190 .

↑ NEVEN DUVNJAK: Experimental investigation of laser-induced temperature fields and their influence on the optical properties of biological tissues. (No longer available online.) In: Diploma thesis. Faculty of Physics at Freie Universität Berlin, archived from the original on April 2, 2015 ; accessed on March 1, 2015 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

↑ M. Sc. (Chem.) Eveline Ganpo-Nkwenkwa b. Tonfack: Optical on-line method for determining dry weight during fermentation of filamentous mushrooms. Dissertation. Department of Biology at the University of Kaiserslautern, November 27, 2002, accessed on March 1, 2015 .

[1] Georg Meichsner, Jörg Schröder: Measuring and controlling paint properties . Vincentz Network GmbH & Co KG, 2003, ISBN 3-87870-739-8 , p. 190 .