7 - Phase corrections and their significance

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A true spectrum is real and positive, and can be represented by a symmetric function and by a cosine transform of a symmetric interferogram. The sine transform representing the complex part is zero. The phase is also zero. But in fact the measured interferogram is not a real symmetric function, because experimental, instrumental, and computational limitations introduce asymmetries into it. Complete reconstruction of the spectrum requires a complex Fourier transform, from which the true spectrum must be recovered. If only the real part of an uncorrected complex spectrum (phase not equal to zero) is used as the representation of the true spectrum, there can be serious errors in line shapes, sizes, positions, and signal–to–noise ratios. Therefore, to get spectra from the Fourier transform spectrometer (FTS) that are limited in quality only by source or detector noise, the phase must be determined and corrected with a precision that greatly exceeds its day-to-day reproducibility. These corrections must be done separately for each interferogram, or coadded set of interferograms, and must be deduced from the data contained within the interferograms. When an interferogram is truncated while its amplitude is appreciable, apodization is frequently employed. Asymmetric truncation together with apodization is frequently encountered because the interferogram is not symmetrical to begin with. This asymmetry compounds the difficulties of obtaining a true representation of the spectrum. The process of phase correction turns the complex spectrum into a real function by multiplying it by the rotation function.