In a Michelson interferometer used as a Fourier spectrometer, whenever the detector system is nonlinear, then the self-convolution of the spectrum occurs enroute to the correction for distortion. In that event, it is important to treat phase data carefully, especially when the interferogram is asymmetric, as in the commonplace cases of imperfect compensation or mild chirping due to electronics and filters. We investigate the distinction between the inverse transform of the interferogram and the original spectrum with phase; in general, asymmetric interferograms show a phase discrepancy that becomes important whenever the self-convolution of the spectrum is involved. Examples of correct and erroneous calculations illustrate this point.
Thomas P. Sheahen and Thomas O. McCanney, "Phase discrepancies in asymmetric interferograms and application to nonlinearities in Fourier spectroscopy," J. Opt. Soc. Am. 65, 825-828 (1975)