  We report on a new high resolution apparatus for measuring magnetostriction
suitable for use at cryogenic temperatures in pulsed high magnetic fields which
we have developed at the Hochfeld-Magnetlabor Dresden. Optical fibre strain
gauges based on Fibre Bragg Gratings are used to measure the strain in small
(~1mm) samples. We describe the implementation of a fast measurement system
capable of resolving strains in the order of $10^{-7}$ with a full bandwidth of
47kHz, and demonstrate its use on single crystal samples of GdSb and GdSi.
