Different measures of sensitivity of the recipe colour to random and proportional dye concentration error. Part 1: Definitions, mutual relations and estimates of maximal colour errors

Abstract

The general concept of predicting the colour sensitivity to random colorant concentration errors and the colour correctability of a colour matching recipe are reviewed and generalised in this paper. The treatment of both quantities is unified either in the concentration space or, equivalently, in colour space. The concept of the recipe's colour balance is revised. Oulton's concept of recipe colour sensitivity to proportional concentration errors is also briefly reviewed and extended to obtain another measure of recipe sensitivity to random concentration errors. The differences and connections among the two measures of recipe sensitivity to random errors and Oulton's measure of recipe sensitivity to proportional errors are discussed and illustrated by numerical examples. Estimates of maximal colour error, caused by given maximal weighing and strength errors, are developed.

The total colorant sensitivity of a color matching recipe: An approach to colorant weighting and tinctorial strength errors

“…Reasoning, similar to that presented in articles, 2,4 leads to the definition of partial strength sensitivities and their numerical estimates.…”

“…Further, he showed that the impact of random weighing error is highest at low concentrations and that it decreases rapidly with any increase in colorant concentration. Sluban 4 various measures of weighing and strength error sensitivity of recipe color. In the article, Sluban et al 5 reported a weak correlation between weighing sensitivity and repeatability for the case of less saturated light-shade recipes.…”

Different measures of sensitivity of recipe colour to random and proportional dye concentration error. Part 3: Observed repeatability in regard to predicted sensitivity

“…In each three‐dye recipe ( c 1 , c 2 , c 3 ) considered, the perturbations Δ c 1 , Δ c 2 , Δ c 3 of the initial dye concentrations c 1 , c 2 , c 3 corresponding to a 1.7% strength error were determined: Δ c 1 = 0.017 c 1 , Δ c 2 = 0.017 c 2 , Δ c 3 = 0.017 c 3 . The dye concentrations c 1 , c 2 , c 3 in the recipe were simultaneously changed according to the pattern (see Table 2 in Part 1 [4]) to get 27 different combinations of perturbations Δ c i , i = 1, 2, 3. The 27 colour changes and corresponding CMC(2:1) colour differences Δ E k ,pred resulting from this pattern were predicted.…”

“…In Part 1 of this study, various measures for the sensitivity of the recipe colour to random and proportional dye concentration errors were defined and explained [4]. In the calculation of various sensitivity values it was implicitly assumed that dyes obey the Kubelka–Munk equations independently and that they do not interact or block.…”

Different measures of sensitivity of recipe colour to random and proportional dye concentration error. Part 2: An example of target‐position dependence and span

“…In the fi rst part of this study, various sensitivities of the recipe c = (c 1 , c 2 , c 3 ) to dye concentrations c 1 , c 2 , c 3 were defi ned [1]. Let us note, that in the particular case treated (exhaust dyeing of acrylic fabric with basic dyes) the concentrations c 1 , c 2 , c 3 are meant as percentages of dry fi bre weight, and that the relative strength (see Baumann et al [2]) of various batches of the used basic dyes varies within standardisation limits of ± 5% (assured by the producer).…”