A scanning unit comprises offset scanning gratings and light receivers disposed behind respective gratings. The scanning unit is moved past an incremental scale and the receivers are illuminated through the scale and the gratings. Carrier frequency signals which are displaced in phase and are amplitude-modulated in dependence on the pitch of the scale are generated in response to the scanning movement. The phase displacement of the modulation of the carrier signal is evaluated to determine the instantaneously scanned fraction of a scale increment in that a proportional number of clock pulses are counted by a counter. The use of a simple and reliable circuit arrangement and a reliable evaluation are permitted in that the illumination is modulated at the carrier frequency so that the light receivers constitute means for effecting an amplitude modulation of the carrier frequency signal. The amplitude-modulated signal is then processed further. The modulating signals corresponding to full scale increments may be separately detected and may be used to detect the direction of the scanning movement and to measure the full scale increments which have been scanned.