Spectral resolution in multivariate optical computing

An examination of spectral resolution effects on multivariate optical computing (MOC) and the design of multivariate optical elements (MOEs) is presented. A solution of napthalene and pyrene in CCl4 is used as a test mixture, with spectra recorded in the nominal 2–2.5 μm spectral region at resolutions varying from 1 to 128 cm−1. Spectra were treated in absorption mode and in transmission mode at sample pathlengths of 1, 0.5, and 0.2 cm. Principal components regression is used to provide comparison to MOE models.Conventional model prediction errors using all methods are presented as well as results of applying low-resolution models to high-resolution validation sets. This latter calculation is aimed at understanding the limits of calibration transfer when a model is based on spectra acquired with marginal spectral resolution. A theory is developed describing calibration transfer in the case of linear spectroscopy, which is shown to be consistent with the results observed in absorption mode and to represent the case of the short-pathlength limit in transmission mode. A definition of the necessary spectral resolution as a function of apodization function is given for linear spectroscopy, and a brief discussion of how non-linearity affects the results is provided.