Estimation of dye concentration by using Kubelka–Munk and Allen–Goldfinger reflective models: comparing the performance

If the relationship between the reflectance function (K/S) and dye concentration (C) is known, the color of the dyed textile (R(∞)) and C could be predicted from each other. In the present work, the concentration value estimated from the reflectance data using two reflective models, i.e. the Kubelka–Munk and the Allen–Goldfinger is compared. First, the Allen–Goldfinger model was run by using the absorption coefficient of dyes in fiber, i.e. the unit k/s values instead of that in the solution. The results showed that the replacement of the unit k/s for the Beer–Lambert absorption coefficient in the Allen–Goldfinger model causes lower error in the prediction of the spectral reflectance factor as well as the dye concentration. However, this model did not lead to better results. Then, an inverse form was used to estimate the concentration of dyes from the corresponding spectral reflectance. Consequently, it was observed that the Kubelka–Munk model is still a more reliable method while benefiting from more simplicity than the Allen–Goldfinger model. The analysis of errors showed that the results deeply depend on different factors such as the applied concentration range as well as the dye spectral adsorption behavior.