On the effect of tilted roof reflectors in Martin-Puplett spectrometers

In this paper we analyze theoretically and experimentally the effect of tilt of the roof mirrors in a double pendulum Martin-Puplett Polarizing Interferometer (MPI), focusing on the polarization of the interfering beams. In principle, the tilt affects the efficiency and polarimetric properties of the interferometer. The case of a moderate resolution spectrometer is analysed in detail. Using the Stokes formalism we recover the analytical expressions for the orientation angle and the ellipticity of the beam reflected from a metallic surface, and we compute these quantities for the roof-mirror of a MPI. We find that the polarization rotation and depolarization are small. Using the Jones formalism we propagate their effect on the measured interferogram and spectrum, and demonstrate that the performance degradation is small compared to other systematic effects.