An arrangement for building a compact Fourier transform interferometer for optical radiation according to the Michelson principle or a principle derived therefrom. According to the invention, this arrangement is characterized in that the optical modulation of the radiation in at least one of the interferometer arms is produced by the translational displacement of micromechanical translation mirrors that are optically accessible on one side or on both sides, with an effective oscillation amplitude of at least 50 .mu.m and a usable mirror surface area of at least 1 mm.sup.2. In doing so, the micromechanical mirror components according to the invention assume the function of known movable mirrors so that by using an almost massless microcomponent in comparison to conventional systems, a much smaller size and a mirror modulation frequency that is several orders of magnitude higher can be achieved. The arrangement according to the invention is used especially for optical spectroscopy.