Application of principal component analysis to X-ray photoelectron spectroscopy - The role of noise in the spectra

This communication addresses the application of principal component analysis (PCA) to simulated two-component photoelectron spectra with varying signal-to-noise ratios (SNRs). Two aspects of the analysis are addressed: (a) determination of the number of primary components in spectra with noise levels comparable to the signal, using standard predictor functions; and (b) on determination of the number of primary components, the use of PCA for noise filtering and calculation of the resulting enhancement in SNR. Using standard predictor functions, it was found that, in spectra studied here with SNRs less than or equal to 50, the predictor functions used in the PCA analysis are unable to determine the number of principal components unequivocally. However, a visual examination of the reconstructed spectra with different numbers of factors can lead to a determination of the number of principal components. For higher SNRs, where eigenvalues corresponding to the noise in the spectra can be identified, and in spectra in which the number of primary factors is known a priori, noise removal is possible using PCA. The results of noise removal using PCA are compared with a simple low-pass Fourier noise filter. Fourier noise filtering yields a larger SNR enhancement factor but some distortion of the signal, which does not occur in noise-removed signals with PCA. By way of illustration, the above analysis is then applied to angle dependent C 1s core level spectra of a typical Langmuir-Blodgett film.