A division-of-amplitude photopolarimeter is described that uses multiple reflections inside a coated dielectric slab at oblique incidence. The first four parallel reflected beams pass through suitably oriented, but fixed, linear analyzers and are intercepted by linear photodetector arrays for spectroscopic polarimetry and ellipsometry. A particular design is presented that uses a parallel-plane fused-silica slab which is coated with an opaque reflecting layer of Ag or Al on the back side and with a transparent ZnS thin film on the front side. Sufficient power is available in the high orders and the instrument matrix is non-singular, so that all four Stokes parameters of the input light can be measured simultaneously, over the visible and near-visible spectral range.