The system uses a monochromatic radiation source (1) and an acousto-optic modulator (2), which acts as a Bragg modulator and is driven by a frequency which is caused to periodically vary. The modulator emits a first beam having the same wavelength as the source and a second beam, whose wavelength and emission direction vary with the modulating frequency and which is collimated. For measuring angular displacements, the collimated beam is recombined with the first beam after traversing a plate (5) with parallel and plane faces integral for the rotation with a moving device, and a photodetector (12) generates a beat signal whose frequency depends on the angular position of the plate (5). For measuring linear displacements, the two beams are directly sent onto a detector (12) integral with the moving device.