A spectroscopic Mueller matrix ellipsometer based on two rotating Fresnel rhomb compensators with a nearly achromatic response and optimal retardance is described. In this instrument, the compensators rotate in a discrete manner instead of continuously rotating, and this allows for a well-conditioned measurement even for low intensity samples. Moreover, in this configuration, the exposure time of the CCD detector can be varied within orders of magnitude without interfering with the dynamics of the compensator rotation. An optimization algorithm determines the optimal set of discrete angles that allows the determination of the Mueller matrix in the presence of noise. The calibration of the instrument is discussed, and examples of experimentally determined Mueller matrices are provided.