Determination of suitable wavelengths in dye concentration estimation by spectral analysis of K/S’s scalability

Abstract

K/S and reflectance graphs are essential tools in characterizing the dyeing behavior. In textile coloration, estimating the dye concentration is poor using the Kubelka-Munk model due to its low scalability and deviation of the reflectance function from linearity after low dye concentrations, particularly in the wavelengths where the gradient of K/S against dye concentration is noticeable. This paper focused on extending the validity of the Kubelka-Munk function, which originates from the linearity of reflectance function against higher dye concentration. A data set of dyed polyester specimens with three disperse dyes in a dye concentration range was prepared. At the present work, K/S was analyzed by describing the scalability property, and the suitable wavelengths in the visible spectrum where K/S benefits from minor deviation from linearity were also discussed. It was observed that the K/S function is not always scalable and deviates in λ max after a specific dye concentration for K/S > 17. Accordingly, the wavelengths other than λ max were found that could be as important as λ max. For the K/S values > 25, no practical region was achieved.