A Nonlinear Quantitative Model for Measuring Concentration Ratios From Raman Intensities

ABSTRACT Raman spectroscopy is a valuable tool for detecting trace compounds over wide ranges of concentrations but is usually limited to qualitative analysis (e.g., identification) due to the difficulty of determining concentration from Raman peak intensity except under very controlled conditions. This study presents a new quantitative model, derived from first principles, that can be used to estimate the concentration ratio of binary mixtures from their Raman intensities over several orders of magnitude, fully accounting for any nonlinear behaviors introduced by factors such as overlapping peaks and self‐absorption. By training the model on experimental data of mixtures with known concentrations, the empirical parameters describing a particular mixture can be ascertained and then used to predict concentrations in further samples. The efficacy of the model is explored using synthetic datasets representing four scenarios depending on which compounds contribute to each peak. Bootstrapped model training can be used to consider the effects of noise, determine uncertainties for future predictions, and estimate the limits of detection and quantification for any given measurement. Finally, the model's efficacy is tested on experimental data for aqueous solutions of different organic nucleotides at concentration ratios between 0.1 and 1000 ppm, showing that the model works over 4 orders of magnitude and can be used to reliably predict the concentration ratio of test samples to within 0.1 orders of magnitude. This advanced model will improve our ability to estimate and assess concentrations in a wide range of mixed samples, even when their peaks overlap significantly.