The intensity as a function of the path length difference (also denoted as retardation) in the interferometer  and wavenumber  is 
where  is the spectrum to be determined.  Note that it is not necessary for  to be modulated by the sample before the interferometer.  In fact, most FTIR spectrometers place the sample after the interferometer in the optical path.  The total intensity at the detector is
This is just a Fourier cosine transform.  The inverse gives us our desired result in terms of the measured quantity :