When measuring very small ellipticities or rotations induced on a polarized beam of light, Fabry–Pérot cavities are often used to increase the number of passes within the region of interest. In this paper we show that due to the intrinsic birefringence of the reflective surface of the cavity mirrors, a cross talk between dichroism and ellipticity is induced. We also show how such a cross talk may be measured and kept under control by means of an adequate phase locking scheme of the laser to the cavity.