Improved Data Processing by Application of Brault's Method to Ultra-Rapid-Scan FT-IR Spectrometry

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In Fourier transform infrared spectrometry, the use of analog-to-digital converters clocked at a constant rate leads to interferograms the data points of which are evenly spaced in time. An interpolation step is generally required to resample these data to equal intervals of retardation. Three methods of resampling the data were compared: Fourier interpolation (i.e., zero-filling), cubic interpolation, and digital filter interpolation as described by Brault. These approaches were investigated using both simulated data and interferograms acquired from an ultra-rapid scanning Fourier transform infrared spectrometer. In both cases, the optical path difference varied sinusoidally with time and interferograms were sampled at equal time intervals. It was shown that the data processing time can be reduced significantly, relative to previous methods, through the application of Brault's method, which can be considered as three separate steps involving a first-, second-, and third-order correction. If only the first-order correction for the local phase relationship between the sampling grids is applied, the noise level of resulting spectra is similar to that obtained by cubic fitting, but the data processing time is reduced significantly. If the second-order correction for the variation of velocity is also used, the data processing time is approximately the same as the first-order correction, while the signal-to-noise ratio of the spectra is increased significantly. The implementation of the third-order correction for channel delay mismatch appears to be unnecessary for this instrument because the detector channel delays are small.
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