The paper describes a new measuring system, using 100 line/in optical gratings, which contains no moving parts and has been incorporated in both continuous-path and co-ordinate-setting control systems.By a method of cyclic switching of four photocells and subsequent filtering of the combined photocell signals, an a.c. waveform is produced which can be compared in phase with a reference waveform, to determine the magnitude and direction of relative displacement between two gratings, and to provide linear interpolation within the pitch of the gratings.Details of the optical, mechanical and electronic design are given, and the effects of variables on the accuracy of the system are discussed.Interpolation accuracy within ±2 × 10−4in using 100 lines/in gratings has been achieved in practical systems.