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.
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