G. Balcerowska

Spurious principal components in the set of spectra subjected to disturbances: I. Presentation of the problem

Abstract It has been shown that a kind of imperfections which can be met in spectrometers, or small shifts of the recorded lines, can influence properties of spectra sets in such a way that the number of principal components (PCs) necessary to describe the non-noisy part of the total variance of the set increases compared to the number when the disturbances are absent. The number of additional (spurious) PCs depends on the magnitude of disturbances and on the signal-to-noise ratio (SNR). The mechanism which generates spurious PCs is discussed, and a criterion enabling an evaluation when the effect becomes important, is given. Numerical simulations of the effect enabled the inference of an empirical relationship between the number of PCs, the magnitude of imperfections, and SNR. Finally, a procedure is proposed to check if a spectrometer is free of the kind of disturbances discussed.

Comparison of the usability of different spectral ranges within the near ultraviolet, visible and near infrared ranges (UV-VIS-NIR) region for the determination of the content of scab-damaged component in blended samples of ground wheat

Soft wheat grain samples of the same variety were obtained from a plot where the crop grew under natural conditions (control material) and from a plot where the crop was inoculated with Fusarium culmorum. The grain was ground and sieved with the finest fraction (a particle size less than 0.18 mm) of both materials being used for the preparation of samples in which the content of damaged constituent varied from zero to approximately 84%. Diffuse reflectance spectra of the absorbance from the blended samples were recorded in the 200–2500 nm spectral range and multivariate calibration PLS (Partial Least Squares) models were built within three spectral ranges: 200–2500, 200–1400 and 1400–2500 nm. Before modelling, several variants for spectra pre-processing were tried: multiple scatter correction, single and double differentiation, in all cases with and without centring. Single differentiation followed by centring was found to be the best method for spectra pre-processing in all spectral ranges. Very good calibration models were obtained for the whole and shorter wavelengths spectral ranges, allowing the detection of 1.50 and 0.76% of the content of scab-damaged constituent, respectively. Two-dimensional correlation spectroscopy applied to the set of spectra enabled the assignment of spectral bands and an analysis of changes in the chemical composition caused by scab damage. It was found that the content of protein and lipids increased with an increase of the scab-damaged constituent, whereas the content of moisture and starch decreased.

Inelastic background subtraction from a set of angle-dependent XPS spectra using PCA and polynomial approximation

Abstract The contribution describes an application of the window principal component analysis (WPCA) to determine precisely the energy subregions in a set of angle-dependent XPS spectra where only the inelastic background exists. Localisation of the subregions enables to approximate the background with polinomial and to subtract the approximated background from the spectra. The reconstructed shapes of the lines obtained in this way were evaluated using several criteria. Application of the procedure to sets of simulated spectra proved that the optimal degrees of approximating polynomials ranged between the 2 and the 5°, depending on the signal-to-noise ratio (SNR) and on the structure of the spectra.

Grain boundary diffusion of Pd through Ag thin layers evaporated on polycrystalline Pd in high vacuum studied by means of AES, PCA and FA

Abstract This work investigates the process of palladium diffusion through grain boundaries of thin polycrystalline silver films. Auger electron spectroscopy (AES) is employed to determine the composition of the topmost layers. Because of the overlapping of Ag and Pd Auger lines, principal component analysis (PCA) and factor analysis (FA) were used to decompose the series of Auger spectra recorded during annealing into contributions coming from particular constituents. These techniques also allowed us to confirm the presence of carbon and to evaluate the amount of this element in the investigated system. The consequences of carbon contamination of the Pd–Ag structures and its effect on the grain boundary diffusion data are put forward.

On the application of principal component analysis and factor analysis in electron spectroscopy : the limit of detectability of factors in a set of noisy spectra

Based on the geometrical look on the mathematical structure of a set of noisy spectra composed of two factors, some general properties of any set of noisy spectra are derived and discussed. It is then pointed out that the ability to detect the presence of lower contributing factor depends on the choice of the criterion applied together with principal component analysis (PCA). The efficiency of two particular criteria were compared by the application to sets of simulated spectra of known composition. The comparison showed that the detection limit can be improved by a factor of 2 or 3 by a proper choice of the criterion. Removing the less informative parts of the spectra results in an additional improvement of the detection limit.

Effect of particle size and spectral sub-range within the UV-VIS-NIR range using diffuse reflectance spectra on multivariate models in evaluating the severity of fusariosis in ground wheat

Control (crops grown in natural conditions) and Fusarium head blight (FHB) damaged (crops inoculated with Fusarium culmorum conidia) grain of four wheat cultivars was ground and sieved into three fractions of different particle size. A series of blended samples differing in content of damaged material were prepared within fractions and cultivars, and diffuse reflectance spectra recorded within the 200–2500 nm wavelength range. Partial least-squares (PLS) models for the percentage of damaged material in blended samples were built for each of twelve series within different spectral ranges, and the root-mean-squared error of cross-validation (RMSECV) was used for the assessment of model performance. Errors using the models were lowest for the finest fraction independent of spectral range; however, their values depended on the cultivar. RMSECV for the finest fraction averaged over cultivars ranged from a little below 3.0 (when the ultraviolet light sub-range was used or participated with another one) to 8.1% (when only the near infrared (NIR) sub-range was used). For the medium and coarse fractions, averaged errors showed the same tendency of dependence on the sub-range(s); however, with higher values that increased with an increase in particle size. In conclusion, within the different fractions of particle size and spectral ranges, the most sensitive to the presence of damaged material were models developed for the finest fraction and when the ultraviolet light sub-range was used in modelling.

PCA-Based Analysis of X-Ray-Excited Auger Spectra from Non-ordered Ag(110)

Principal-components analysis (PCA) followed by factor analysis enables one to decompose the structure of Auger lines originating from large effects such as energy shifts induced by chemical effects. The aim of the present contribution is to show that PCA can also be effectively used for detection of composed structure in a set of Auger spectra even if the observed changes in line shape are very subtle. The analysed set of X-ray-excited MNN Auger spectra from Ag(110) shows a clear correlation between peak shifts and peak widths. This correlation can be explained as a result of the composed structure of the recorded Auger lines. It is suggested that the resultant Auger lines may consist of a number of constituents, each referred to Ag atoms differing in the value of their co-ordination number.