Modeling the instrument line shape of Fourier-transform spectrometers within the framework of partial coherence

The instrument line shape (ILS) of Fourier-transform spectrometers is modeled within a framework that enables us to take into account the partial coherence of optical fields. The cross spectral density and the angular coherence functions are used to develop a global ILS model including all possible geometric defects that can be introduced by a realistic two-beam interferometer. Tilt and shear no longer only reduce the modulation efficiency but are presented as contributors to the ILS. The case of an incoherent secondary planar source is covered and agrees with previously known results. However, it shows a coupling among tilt, shear, and optical path difference (OPD). A quasi-coherent source is also studied. Differences between the incoherent and the quasi-coherent cases are highlighted. The relative localization of the reference laser beam in the interferometer is shown to be of significance to provide a sampling scale that minimizes the OPD, or phase, induced by angular misalignment.