Apparatus is described for measuring torsional displacement between ends 32 and 35 of a hollow rotating shaft 28. Polarised light from the source 12 enters the shaft through apertures 30 and is reflected by a mirror 34 to a retardation plate 38. Plate 38 has a fast axis 42 positioned at an angle A relative to the plane of polarisation 46 of the light when the shaft is positioned with one of the pairs of apertures 30 in alignment with the received light beam 24. The retardation plate produces 0 degree and 90 degree components from the light whose relative intensities depend on any torsional displacement between end 35 of the shaft and end 32. The components are reflected by a mirror 40 and a mirror 34 to a beam splitter 20. A polarisation splitter 54 separates the 0 degree and 90 degree components which are respectively detected by detectors 58 and 62 and their relative intensities measured to determine the torsional displacement.