The analysis accuracy and precision of any multivariate calibration method will be severely degraded if unmodeled sources of spectral variation are present in the unknown sample spectra. A synthetic method for correcting errors generated by the presence of unmodeled components or other sources of unmodeled spectral variation has been developed. If the spectral shape of the unmodeled spectral component can be obtained and mathematically added in variable amounts to the original calibration spectra, then a new synthetic multivariate calibration model can be generated from the augmented data to accommodate the presence of the unmodeled source of spectral variation. The new method is demonstrated for a case where unmodeled temperature variations are present in the unknown sample spectra of dilute aqueous solutions of urea, creatinine, and NaCl. When constant-temperature partial least-squares (PLS) models are applied to spectra of variable-temperature samples, the standard errors of prediction (SEP) are approximately an order of magnitude higher than those of the original cross-validated SEPs of the constant-temperature PLS models. Synthetic models based upon constant-temperature data augmented with a classical least-squares (CLS) estimate of the spectral effect of temperature obtained from variable-temperature aqueous sample spectra are demonstrated to significantly reduce errors when predicting concentrations from spectra of solutions at variable-temperature. We demonstrate that the prediction precisions approach the original calibration precisions when the new synthetic PLS models are applied to variable-temperature solution spectra. Although spectrometer drift added bias errors to the analyte determinations, a method is demonstrated that can minimize the effect of long-term drift on prediction errors through the measurement and use of spectra obtained from a small subset of samples measured during both calibration and prediction. In addition, sample temperature can be predicted with high accuracy (± 0.13 °C) with this new synthetic PLS modeling method without the need to recalibrate using actual variable-temperature sample data. Therefore, the synthetic method eliminates the need for expensive generation of new calibration samples and collection of their spectra. The method is quite general and can be applied by using any known source of spectral variation and used with any multivariate calibration method.
David M. Haaland, "Synthetic Multivariate Models to Accommodate Unmodeled Interfering Spectral Components during Quantitative Spectral Analyses," Appl. Spectrosc. 54, 246-254 (2000)