Angle-constrained alternating least squares.

When resolving mixture data sets using self-modeling mixture analysis techniques, there are generally a range of possible solutions. There are cases, however, in which a unique solution is possible. For example, variables may be present (e.g., m/z values in mass spectrometry) that are characteristic for each of the components (pure variables), in which case the pure variables are proportional to the actual concentrations of the components. Similarly, the presence of pure spectra in a data set leads to a unique solution. This paper will show that these solutions can be obtained by applying angle constraints in combination with non-negativity to the solution vectors (resolved spectra and resolved concentrations). As will be shown, the technique goes beyond resolving data sets with pure variables and pure spectra by enabling the analyst to selectively enhance contrast in either the spectral or concentration domain. Examples will be given of Fourier transform infrared (FT-IR) microscopy of a polymer laminate, secondary ion mass spectrometry (SIMS) images of a two-component mixture, and energy dispersive spectrometry (EDS) of alloys.

Loopy MSC: a simple way to improve multiplicative scatter correction.

Multiplicative scatter correction (MSC) is a widely used normalization technique. It aims to correct spectra in such a way that they are as close as possible to a reference spectrum, generally the mean of the data set, by changing the scale and the offset of the spectra. When there are other differences in the spectra than just a scale and an offset, the mean spectrum changes after MSC. As a result, another MSC, with the new mean spectrum as the reference, will result in an additional correction. This paper studies the effect of multiple applications of MSC.

Multivariate curve resolution applied to infrared reflection measurements of soil contaminated with an organophosphorus analyte.

Multivariate curve resolution (MCR) is a powerful technique for extracting chemical information from measured spectra of complex mixtures. A modified MCR technique that utilized both measured and second-derivative spectra to account for observed sample-to-sample variability attributable to changes in soil reflectivity was used to estimate the spectrum of dibutyl phosphate (DBP) adsorbed on two different soil types. This algorithm was applied directly to measurements of reflection spectra of soils coated with analyte without resorting to soil preparations such as grinding or dilution in potassium bromide. The results provided interpretable spectra that can be used to guide strategies for detection and classification of organic analytes adsorbed on soil. Comparisons to the neat DBP liquid spectrum showed that the recovered analyte spectra from both soils showed spectral features from methyl, methylene, hydroxyl, and P=O functional groups, but most conspicuous was the absence of the strong PO-(CH2)3CH3 stretch absorption at 1033 cm(-1). These results are consistent with those obtained previously using extended multiplicative scatter correction.

Determining sample differences in a sample series of complex liquid chromatography-diode array detector data using chemometrics.

In analytical laboratories, one often has to deal with sample series that have minor differences between them. For example, different batches of the same material may cause manufacturing problems, and quality control is an important issue. Another example is decomposition studies, where changes may or may not occur in a sample. To extract the differences between such highly related samples from LC-DAD (liquid chromatography-diode array detector) data is a time-consuming and subjective task. This paper describes an algorithm that efficiently extracts such differences.

Combined use of conventional and second-derivative data in the SIMPLISMA self-modeling mixture analysis approach.

Simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) is a successful pure variable approach to resolve spectral mixture data. A pure variable (e.g., wavenumber, frequency number, etc.) is defined as a variable that has significant contributions from only one of the pure components in the mixture data set. For spectral data with highly overlapping pure components or significant baselines, the pure variable approach has limitations; however, in this case, second-derivative spectra can be used. In some spectroscopies, very wide peaks of components of interest are overlapping with narrow peaks of interest. In these cases, the use of conventional data in SIMPLISMA will not result in proper pure variables. The use of second-derivative data will not be successful, since the wide peaks are lost. This paper describes a new SIMPLISMA approach in which both the conventional spectra (for pure variables of wide peaks) and second-derivative spectra (for pure variables of narrow peaks, overlapping with the wide peaks) are used. This new approach is able to properly resolve spectra with wide and narrow peaks and minimizes baseline problems by resolving them as separate components. Examples will be given of NMR spectra of surfactants and Raman imaging data of dust particle samples taken from a lead and zinc factory's ore stocks that were stored outdoors.