Exploratory chemical imaging made easy

This work reviews different one-sample calibration methods used in multivariate calibration. These methods are fascinating in a sense that they involve only one single calibration sample. This really means that the entire calibration is based on a single sample and measured concentrations on it. No extensive training/calibration set is used in any stage of the calibration. The methods that we cover here are all based on this one-sample calibration concept. As follows, we compare three one-sample multivariate calibration techniques Matched spectral filtering which is also known as science-based calibration (SBC) Direct classical least squares (CLS) Partial least squares discriminant analysis (PLS-DA) To illustrate the benefits of these one-sample calibration techniques, we used an independent test set of 15 different tablets based on a three-component mixture design that consisted of ibuprofen, lactose and microcrystalline cellulose (MCC) in different formulations. The calibration was built on using one hyperspectral image of a single tablet and the corresponding chemical concentrations of this single tablet. Thus the amount of laboratory work is minimized which results in big savings. It appears that all the models were excellent for API. PLS-DA performed well for all analytes. The test set was very challenging for the evaluation of model performance since the chemical concentrations in our mixture design varied between 0...100 % and all the models were trained with a single formulation. Based on the validation with independent test set, the results were very promising. Additionally, the corner points that reflect the pure components suggest that the PLS-DA was the most selective technique in this case. While the results of PLS-DA were quantitative and very accurate for all three analytes in a full concentration range, the results were similar for API in CLS and SBC but slightly worse for the other analytes. There was either some slope deficiency in the predictions of lactose, especially in SBC, or some imprecision in the predictions of MCC. In general, slope deficiency problems in SBC can be taggled by addressing more work on the definition of spectral noise estimates. On the other hand, PLS-DA is very flexible as it does not need any additional a priori spectroscopic first principles knowledge regarding spectral signal or noise. Yet, it seems to be very selective and also fulfils the closure condition. This condition refers to the fact that the predictions of chemical concentrations in a mixture design should add up to 100%. In summary, suggested calibration approaches save a lot of lab work and offer a great opportunity for exploratory chemical imaging. The suggested approaches have also been evaluated with other data sets and with other cameras in other spectral regions. All the results collected so far clearly indicate that this kind of an approach is very versatile as long as the pure components as measurable samples are available. The results may not be accurate enough for quantitative models but they are very useful in troubleshooting and in screening phases in R&D. Though we underlined that the calibration is based on a one-sample, we also wish to emphasize that the model validation should be based on a representative and independent validation and test sets. This latter statement applies especially when the above models are applied in quantitative purposes instead of exploratory qualitative / semi-quantitative purposes.