Recent years have seen the introduction of many surface characterization instruments and other spectral imaging systems that are capable of generating data in truly prodigious quantities. The challenge faced by the analyst, then, is to extract the essential chemical information from this overwhelming volume of spectral data. Multivariate statistical techniques such as principal component analysis (PCA) and other forms of factor analysis promise to be among the most important and powerful tools for accomplishing this task. In order to benefit fully from multivariate methods, the nature of the noise specific to each measurement technique must be taken into account. For spectroscopic techniques that rely upon counting particles (photons, electrons, etc.), the observed noise is typically dominated by 'counting statistics' and is Poisson in nature. This implies that the absolute uncertainty in any given data point is not constant, rather, it increases with the number of counts represented by that point. Performing PCA, for instance, directly on the raw data leads to less than satisfactory results in such cases. This paper will present a simple method for weighting the data to account for Poisson noise. Using a simple time-of-flight secondary ion mass spectrometry spectrum image as an example, it will be demonstrated that PCA, when applied to the weighted data, leads to results that are more interpretable, provide greater noise rejection and are more robust than standard PCA. The weighting presented here is also shown to be an optimal approach to scaling data as a pretreatment prior to multivariate statistical analysis.

Spectral imaging in the scanning electron microscope (SEM) equipped with an energy-dispersive X-ray (EDX) analyzer has the potential to be a powerful tool for chemical phase identification, but the large data sets have, in the past, proved too large to efficiently analyze. In the present work, we describe the application of a new automated, unbiased, multivariate statistical analysis technique to very large X-ray spectral image data sets. The method, based in part on principal components analysis, returns physically accurate (all positive) component spectra and images in a few minutes on a standard personal computer. The efficacy of the technique for microanalysis is illustrated by the analysis of complex multi-phase materials, particulates, a diffusion couple, and a single-pixel-detection problem.

Algorithms for multivariate image analysis and other large-scale applications of multivariate curve resolution (MCR) typically employ constrained alternating least squares (ALS) procedures in their solution. The solution to a least squares problem under general linear equality and inequality constraints can be reduced to the solution of a non-negativity-constrained least squares (NNLS) problem. Thus the efficiency of the solution to any constrained least square problem rests heavily on the underlying NNLS algorithm. We present a new NNLS solution algorithm that is appropriate to large-scale MCR and other ALS applications. Our new algorithm rearranges the calculations in the standard active set NNLS method on the basis of combinatorial reasoning. This rearrangement serves to reduce substantially the computational burden required for NNLS problems having large numbers of observation vectors.

Full-spectrum imaging is fast becoming a tool of choice for characterizing heterogeneous materials. Spectral images, which consist of a complete spectrum at each point in a spatial array, can be acquired from a wide variety of surface and microanalytical spectroscopic techniques. It is not uncommon that such spectral image data sets comprise tens of thousands of individual spectra, or more. Given the vast quantities of raw spectral data, factor analysis methods have proved indispensable for extracting the chemical information from these high-dimensional data sets into a limited number of factors that represent the spectral and spatial characteristics of the sample's composition. It is well known that factor models suffer a 'rotational ambiguity', that is, there are an infinite number of factor models that will fit the data equally well. Thus, physically inspired constraints are often employed to derive relatively unique models that make the individual factors more easily interpreted by the practicing analyst. In the present work, we note that many samples undergoing spectral image analysis are 'simple' in the sense that only one or a few of the sample's constituents are present at any particular location. When this situation prevails, simplicity in the spatial domain can be exploited to make the resulting factor models more realistic. In particular, orthogonal rotation of the spatial-domain vectors arising from singular value decomposition (SVD) of the spectral data matrix will be shown to be an effective method for making physically acceptable and easily interpretable estimates of the pure-component spectra and abundances.

SynopsisA new, simplified technique for obtaining the kinetic parameters of an autocatalyzed cure reaction from isothermal DSC measurements is presented. The method is appropriate to reactions that have a zero initial rate and relies solely upon characteristics of the exotherm peak with no assumptions being made about the overall reaction order. This technique is illustrated by obtaining the phenomenological cure kinetics of a commercial epoxy f i l m adhesive. The derived kinetic model reproduces the measured isotherms in their entirety. In addition, the predictive capability of the model is demonstrated by comparison with an independent measurement of the adhesive's low temperature curing behavior. Glass transition temperature measurements are also made on partially cured samples and a good correlation with the degree of cure is found.