An optical fibre-based goniometer is described. This instrument was designed to measure the angular position of patients' limbs within the core of a magnetic resonance body scanner, via a 40 m remote fibre-optic link. The sensor exploits the advantages of optical fibre-based sensing, which include immunity to electromagnetic interference, intrinsic safety and chemical immunity. The detection electronics and signal processing are based on the principles of chromatic modulation, an inexpensive, intensity-independent technique in which a change in the spectral power distribution is measured over a broad bandwidth, by photodetectors with differing spectral responses. The optical fibre goniometer has an angular range of 90 degrees, with an average resolution of 2'. The long-term accuracy is within +/- 1 degree, the specified accuracy for the physiological application.