A measuring apparatus (10) for interferometric shape measurement of a surface (12) of a test object (14) comprises a test optical unit (26; 226-1, 226-2) configured to generate a test wave (28) for irradiating the surface of the test object from measurement radiation (18), a reference element (32; 232) having an optically effective surface (33; 233) for interaction with a reference wave (30, 30r), which is likewise generated from the measurement radiation (18) and which serves for generating an interferogram by superimposition with the test wave after the interaction thereof with the surface of the test object, and a holding device (48; 148) for holding the reference element, said holding device being configured to move the reference element relative to the reference wave in at least two rigid body degrees of freedom in such a way that a marginal point of the optically effective surface of the reference element is displaced by at least 0.1% of a diameter of the optically effective surface, wherein the at least two rigid body degrees of freedom comprise a translational degree of freedom directed transversely with respect to a direction of propagation of the reference wave radiated from the reference element, and a rotational degree of freedom, the axis of rotation of which is oriented substantially parallel to the direction of propagation of the reference wave radiated from the reference element.