Abstract: An apparatus is proposed for making absolute, two-dimensional measurements of the position of an object (10) with reference to a measuring arrangement (11), with the surface of the object (10) being configured as a hologram. The information contained in the hologram is red out by means of a measuring wave (13) that is directed onto the hologram (18), is diffracted there and interferes with a reference wave (14). The interfered-with waves (13, 14) are picked up by an optical sensor arrangement (20) including at least two sensors (21, 22). In a signal processing arrangement (23), the absolute position is determined either from the radiation intensities picked up by the sensors (21, 22) or from the phase relationship between the signals emitted by the sensors (21, 22), in each case by a comparison with a value stored in a memory.