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Incoherent broadband light sources are used in interferometric fibre optic gyroscopes (IFOGs) to mitigate the deleterious effects of Kerr and polarisation nonreciprocity, and backscattering effects in gyroscopes. However, incoherent broadband sources suffer from excess noise or relative intensity noise (RIN), caused by the beating of different spectral components on the photodetector. Unless RIN noise is suppressed, IFOG performance cannot be improved once light on the photodetector exceeds one photon per coherence time (~~W~s). Demonstrated is a low RIN light source capable of significantly improving angle random walk of an IFOG by 12 dB.