Estimation of Dye Concentration by using Kubelka-Munk and Allen-Goldfinger Reflective Models: Comparing the performance

Abstract

Abstract The problem of primary interest in quantitative analysis of a dye bath or a dyed sample of textile is to determine the concentration with a minimum percentage error. The present study describes the applicability of two reflective models i.e. the Kubelka-Munk and the Allen-Goldfinger here called Geometry, to estimate the concentration of dye from the reflectance data. The performance of the Geometry model in predicting the spectral reflectance factor of dyed polyamide fibers is evaluated by the determination of the unit k/s and the Beer-Lambert absorption extinction coefficient. To examine the models, a reflectance dataset is created by dyeing nylon 6 fabrics with four different acid dyes. The results show that the replacement of the unit k/s for the Beer-Lambert absorption coefficient in the Geometry model causes lower error in the prediction of the spectral reflectance factor. However, it is shown that this model, does not lead to better results. Consequently, the Kubelka-Munk model is still found as the most reliable method while benefiting from more simplicity in comparison to the Geometry model. The analysis of errors shows that the results deeply depend on different factors such as the range of applied concentrations as well as the spectral adsorption behaviors of dyes.