same reference symbols in the figures fig1 a shows an interferometric system 1 for measuring surfaces of a measured object 2 interferometric system 1 being shown is an interferometer that measures surfaces in this case a white light interferometer the structure includes a system 3 for aligning the angular position of measured object 2 relative to a detector 5 which includes a ccd chip 4 of a digital camera in order to be able to perform exact interferometric measurements of the surface of measured object 2 surface 6 of measured object 2 must be aligned parallel to the surface extension of ccd chip 4 of detector 5 in the illustrated exemplary embodiment for tilting swiveling measured object 2 about an axis of rotation 7 actuating means 8 are provided which are actuable manually or automatically depending on the embodiment and are shown merely schematically as swivel arrows actuating means 8 are acting on a support 9 on which measured object 2 is fixed in place system 3 for aligning measured object 2 relative to detector 5 includes illumination means 10 as can be gathered from fig1 b these are developed in the form of a four led chip having four leds 11 a 11 b 11 c 11 d leds 11 a 11 b disposed on top in the drawing plane jointly form first partial illumination means 12 and leds 11 c 11 d disposed underneath in the drawing plane form second partial illumination means 13 this means that upper leds 11 a 11 b and lower leds 11 c 11 d are able to be triggered as a unit in each case it is also possible to realize an embodiment.