Fluctuation scaling of colour variability in automotive metallic add-on parts
CIELAB lightness L*, red-green a*, and blue-yellow b* coordinates were calculated by using multi-angle spectrophotometric reflectance measurements from a broad range of metallic coatings from different manufacturers.
Colour coordinates of finishes follow fluctuation scaling
The scientists found that trial-to-trial L* variations are related to a self-similar stochastic process. The sample variance and the sample mean value of L* calculated over different viewing angles are correlated across painted pieces. A power function model describes the data quite well. This power function corresponds to a wide spread phenomenon known as fluctuation scaling in many engineering process. They also found that the sample skewness and the sample kurtosis of L*, a*, and b* follow a U-shaped pattern and a generalised version of fluctuation scaling.
Better prediction of lightness flop variations
The exponent of fluctuation scaling in the skewness-kurtosis plane depends on the cardinal directions, L*, a*, and b*. This suggests that different flake-shaped pigments mediate trial-to-trial correlations of colour coordinates. The researchers conclude that fluctuation scaling provides a powerful approach for better prediction of lightness flop variations and for better colour quality control between car manufacturers and suppliers of add-on parts.
The study is published in: Progress in Organic Coatings, Volume 104, March 2017, Pages 118-124.