A polarised thermal neutron beam passes through a precession coil. The intensity after an analyser is measured as a function of the magnetic induction in the coil. Fourier transformation of the recorded intensity yields the spectrum of the neutron beam emerging from the analyser. This method is used in a quantitative way in two examples. First, we measure the transmission of a-SiO 2 to determine its scattering cross section as a function of wavelength. In the second example, the transmission of a polarising mirror system consisting of coated curved silicon wafers is determined. Because the neutron beam emerging from the analyser is polarised, we are able to determine the polarising power of the mirror system as a function of wavelength by comparing the transmitted polarised and depolarised spectra.