Radiative Formulation
Mathematical relationships expressing light absorption and diffuse scattering within opaque particulate layers provide the theoretical foundation for industrial colour prediction software. The kubelka-munk theory calculates the ratio of light absorption to light scattering from measured spectral reflectance values on dyed textiles. By treating light flux as two opposing streams moving through an absorbing and scattering medium, the formulation translates surface reflectance percentages into quantitative dye concentrations.
Colorimetry engines calculate relative colour yield across woven and knitted substrates using this continuous mathematical framework. Fabric opacity must remain sufficient to prevent background substrate transmission from distorting the calculated reflectance values.
Optical Scattering
Textile fibres scatter incident illumination through multiple internal reflections and boundary refractions across surface filaments. While absorption coefficients depend strictly on dye chemistry and applied volume, scattering coefficients derive from fibre geometry and yarn texture. Applying the kubelka-munk equation requires baseline optical profiling of uncoloured substrate lots.
Mercerisation shifts scattering dynamics by altering cotton fibre roundness.
Concentration Linearity
Spectrophotometer software correlates absorption ratios to dye bath concentrations across pale and medium depths. The relationship loses linear precision at heavy saturation levels where dyestuff aggregation suppresses light absorption. Dyehouse algorithms correct for high concentration limits to prevent batch tint overshoots.
Commercial Match
Colour formulation laboratories match customer color standards by running digital reflectance curves through automated recipe prediction databases. Formulators verify predicted dye combinations through miniature lab dip dyeings before bulk dyehouse release. The kubelka-munk model remains the standard mathematical backbone for commercial recipe calculation and automated batch colour correction.
