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.

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Based on the idea of the spectral visual response fitting, the visual difference between the spectral reflectance factor function of the standard and specimen was proposed in this paper. Basic equations used in the recipe formulation as well as recipe correction were derived based on the spectral visual response fitting in matrix form and an algorithm for the least-squares match has been developed. The iterative procedure for the recipe correction has been established in this algorithm. Twenty standards were used in our numerical experiments. The experimental results showed that the average colour difference against for the standards under the five different illuminants (D65, A, F1, F2 and F3) was smaller than one based on other spectrophotometric fittings, balanced the colour differences better and produced lower metamerism.