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The optimisation of noise properties is demonstrated in an interferometric fibre Bragg grating defined Fabry-Perot sensor system. The signal-to-noise ratio is maximised by matching the spectra of the two gratings and the path length differences of the two tandem interferometers. The environmental effects on the interrogation interferometer are monitored with a reference wavelength. A phase resolution close to the theoretical noise limit of -85 dB above 60 Hz is achieved with a corresponding strain resolution of 1.52 pε/Hz1/2 using a 4 m-long cavity.