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.