Tristimulus analysis for sensors set with either positive or negative sensitivities—determination of the relative concentration of an analyte in a binary mixture

We consider the general case of a set of three sensors that show a response proportional to analyte concentration and apply tristimulus analysis to represent the set of responses as tristimulus coordinates in a two-dimensional representation. These coordinates are a signature of the analyte and can be used for analyte identification. We extend the tristimulus analysis for cases where the sensors may present either positive or negative sensitivities, a situation in which the usual tristimulus analysis has limitations. We propose a different approach, taking the coordinates where the tristimulus vector crosses the unitary radius spherical shell, taking the angular coordinates as signature of the analyte. We also consider the case of binary mixtures and derive the set of equations that can be used to determine the relative concentration of each one of the analytes in the binary mixture from the tristimulus coordinates of the mixture.