Spectrum Estimation Of FT-IR Data With Sampling Errors

In usual rapid-scan FT-IR systems [1], the sampled interferogram values are recorded at measured positions of the moving mirror, the latter being subject to errors. The laser signal used for generating the reference cosine interferogram, for example, suffers from slight frequency fluctuations due, among other things, to temperature variations. During the zero crossing detection, an error is also introduced due mainly to the background radiation, detector noise electronic noise and mirror drive fluctuations [2] (imperfect delay compensation between HeNe LASER signal and infrared amplification electronics) [3]. It is therefore important to investigate the impact of sampling errors upon the interferogram values. Note that only "soft" zero crossing detection error are here considered, that is, no extraneous detection happens but only a random shift of the zero crossing event being detected. In this paper we consider stochatic as well as deterministic error models. We exploit the fact that the output interferogram results from the average of several scans. Hence it is of interest to investigate the property of the first statistical moment of the interferogram values subject to errors as well as the impact on the related true spectrum to be computed. As stochastic models, we treat the additive uncorrelated normal noise, the correlated normal noise and the uniformly distributed noise. For the systematic error model involving multiple harmonics, we extend the work of Sakai [2] on monochromatic signal to the broadband case.