Colorant formulation based on new two‐constant theory

Abstract

A new two‐constant theory for colour matching has been developed based on the Kubelka–Munk theory. Colorant formulations and algorithms for matching tristimulus, K/S and reflectance values of a standard are presented based on the new theory. The algorithms are suitable for a single‐constant theory as well as a two‐constant theory. The experimental data show that the recipes predicted by the new two‐constant theory are closer to the actual recipes of the standard sample than the recipes predicted by the single‐constant theory, and also show smaller colour difference values for some disperse dyes. The results show that the scattering of some disperse dyes cannot be negligible, and that the recipes that match to textiles coloured by these disperse dyes should be predicted using the new two‐constant theory.

Recipe formulation based on spectral visual response fitting

“…The set of wavelengths that are used in the matching process on the visible spectrum is usually the following: {k i , i = 1, 2, ……, 31} = {400 nm, 410 nm, ……, 700 nm}. For n dyes present, this gives Eqn 11 [4]:…”

“…There are two kinds of strategies for colour matching based on the Kubelka–Munk theory [1–4]. One strategy is called tristimulus colorimetric algorithm and minimises the colour difference between a pair of samples under a given CIE standard observer and a given CIE standard illuminant.…”

Instrumental colourant formulation

“…The method for measuring the two-constant values of a colourant described by He and Zhou (2007) is advantageous over the traditional two-constant method, as the former method is much easier to use. Algorithms for colourant formulation proposed in their study are suitable for the single-constant theory as well as the new two-constant theory.…”

“…where both ( k/S b ) and ( s/S b ) are the new two-constants of each colourant proposed by He and Zhou (2007). They can be determined by measuring the refl ectance R b of substrate without colourant, as well as the refl ectance R ∞ of the combination of the substrate and one colourant with various concentrations.…”

Dye binary mixture formulation by means of derivative ratio spectra of the Kubelka–Munk function

“…2,4,10 However, other types of colorant formulation approaches, using modified forms of K-M based algorithms are also found in the literature. 12,17 In the application of single-constant K-M theory, the usual known method for the determination of dye concentration in multicomponent mixtures is; first of all, to make a selection of dyes likely to produce the target color, then apply each dye to a given substrate with different concentrations covering the range of working concentrations normally used. The reflectance values of the different dyed samples at the different concentrations are measured using a reflectance spectrophotometer.…”