Disclosed is a system for the interferometric measurement of a physical parameter, including an amplified spontaneous emission light source, optically connected to a Sagnac ring interferometer, and two detectors, each supplying a measurement signal representative of the light output from the interferometer, and a reference signal representative of the light output emitted by the source, which is impaired by an excess relative intensity noise. This measurement is obtained from a difference between the measurement and reference signals, weighted by a weighting coefficient which is controlled to minimise the statistical deviation of an additional weighted difference between signals obtained by demodulating the measurement and reference signals by way of an additional digital demodulation sequential code insensitive to the parameter. Also disclosed is a gyroscope including such a measuring system.