ESTIMATION AND ERROR ANALYSIS IN MULTIMODAL SPECTROSCOPY

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This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Raman spectroscopy provides quantitative spectral information about sample composition. The presence of noise and multiple overlapping components complicates attempts to use Raman peak intensities for accurate quantitative analysis. Thus, multivariate analysis is often implemented to extract quantitative information from Raman spectra. The concentration errors resulting from chemometric analysis are typically assessed by comparison to a reference measurement. Reference measurements have the disadvantage of introducing an additional source of error, contained in the reference concentration. Further, in many biologic samples, such as tissue, obtaining reference concentrations is not straightforward. We have derived an analytical formula that estimates the uncertainty in concentrations predicted by linear multivariate calibration, particularly ordinary least-squares (OLS). The expression is a function of the signal to noise ratio and the model spectral overlap. The first term is the signal to noise ratio of the target chemical. It is determined by the integrated signal (norm) of the component of interest at unit concentration and the noise (standard deviation) in the data set. The second term describes the effect of overlap in model basis spectra. The spectral overlap is affected by the similarity of the components in the model, the resolution of the spectral data, and the spectral range of the data. The analytical formula is expressed in terms of easily quantifiable experimental parameters and is straightforward to evaluate. To test this formula, we performed OLS analysis upon simulated spectra and upon experimental Raman spectra of dissolved biological analytes in water. In each instance, the root-mean-squared error of prediction was compared to the estimate from the formula. We observe excellent agreement between the formula and data for these simple systems. The ability to make predictions concerning the concentration error is valuable to the process of developing and refining analytical measurements.