GroupdelayFT

A Fourier Transform leads from the intensity derived from the "derotated" recorded images (i.e. those where the instrumental OPD has been taked care of but not the atmospheric delay) to those from which the groupdelay is estimated (see e.g. Eq. (3.11) in Konrad Tristram's thesis or Eq. (2.28) in Leonard Burtscher's thesis). The usual explanation for this step is that you need to transform from frequency / wavelength space (i.e. from the spectra that you recorded) to the delay space to see at which delay the signal is maximal (i.e. what the groupdelay is / the delay function).

An easy-to-grasp explanation for this Fourier transform is the following: In integrating over frequency space you basically sum up the intensity at all wavelengths rotated by some delay d. Now at the true groupdelay, the intensity does not vary with wavelength and you get a peak for this value of d.