The apparatus according to the invention comprises an object lens which can operate in at least two different measuring modes. In a first, interference mode a workpiece is measured by means of interference optometry. In a second, imaging measuring mode an optical image is produced, for example, on a camera-like detector array and may be applied to an image processing routine. Switching between the two measuring modes is performed by the type of illumination of the object lens and an element which is disposed preferably in the reference beam path of an interferometer and which activates or deactivates the reference beam path dependent on the spectral composition of the utilized light. In this manner a simple and rapid changeover between the two measuring modes is provided, without the need for replacing or even for moving the object lens. Apart from the rapidity of changeover, a good correlation is achieved between the measuring data which are yielded by the interferometry and by the image processing and which are obtained in one and the same reference coordinate system.