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

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.