A Polynomial-Exponent Model for Calibrating the Frequency Response of Photoluminescence-Based Sensors

Abstract

In this work, we propose a new model describing the relationship between the analyte concentration and the instrument response in photoluminescence sensors excited with modulated light sources. The concentration is modeled as a polynomial function of the analytical signal corrected with an exponent, and therefore the model is referred to as a polynomial-exponent (PE) model. The proposed approach is motivated by the limitations of the classical models for describing the frequency response of the luminescence sensors excited with a modulated light source, and can be considered as an extension of the Stern–Volmer model. We compare the calibration provided by the proposed PE-model with that provided by the classical Stern–Volmer, Lehrer, and Demas models. Compared with the classical models, for a similar complexity (i.e., with the same number of parameters to be fitted), the PE-model improves the trade-off between the accuracy and the complexity. The utility of the proposed model is supported with experiments involving two oxygen-sensitive photoluminescence sensors in instruments based on sinusoidally modulated light sources, using four different analytical signals (phase-shift, amplitude, and the corresponding lifetimes estimated from them).