An interferometer for areally measuring an optically smooth surface is presented, said interferometer comprising means for illuminating a surface region with a plurality of discrete object waves from different directions and comprising means which, on a detector, superimpose object waves reflected at the surface onto a reference wave that is coherent with a plurality of object waves in order to form an interferogram. The interferometer is distinguished by virtue of it being configured to illuminate the surface with a plurality of object waves at the same time and produce the reference wave by way of a Fizeau beam splitter plate or a Fizeau objective, and by virtue of the interferometer comprising an interferometer stop (12) that is arranged in the beam path upstream of the detector (14), and imaging optics, wherein the interferometer stop is situated within, or slightly outside of, the Fourier plane of the imaging optics and said interferometer stop filters the object waves reflected by the surface. An indepe
