an interferometric measuring device , especially for measuring the shape of a surface of an object , includes a radiation source emits a short coherent electromagnetic radiation , a component , in particular a beam splitter , to form an object beam that is guided to the object via an object light path , and a reference beam guided to a reference plane via a reference light path , and a pickup element , by the use of which an electromagnetic radiation , that is reflected by the object and the reference plane and brought to interference , is able to be picked up . in this context , an adaptive optical element is provided , with the aid of which the imaging of the object on the pickup element and / or the wave front of the reference beam and / or the optical path length in the reference light path and / or in the object light path may be influenced .