Limitations in predicting dyebath exhaustion using optical spectroscopy

There are practical limitations in predicting dyebath concentrations and dyebath exhaustion using absorbance measurements from optical spectroscopy. The purpose of this paper is to examine the common assumptions of prediction models that cause prediction errors, and especially when multiple dye combinations are used. If a linear model is used to map absorbance to concentration, then five assumptions must hold: measurement repeatability, linear scaling, spectral additivity, linear independence of the constituent spectra and the absence of spectral morphing. Violation of one or more of these assumptions will lead to errors in predicting the concentrations of dyes in a dyebath and subsequent exhaustion calculations.