The invention relates to a method and an optical-fiber measuring device including a light source with a light power P, a Sagnac ring interferometer in which propagate two counter-propagating waves, a detector receiving a light flux from the interferometer and converting it into an electrical signal representing the total phase difference δφt between the counter-propagating waves. It also includes an electronic element receiving the electrical signal from the detector and providing a first signal S1 function of the measured parameter. The electronic element includes a demodulator contributing to provide the first signal function of the measured parameter and provide a second signal S2 function of the power P of the light flux measured by the detector. The optical phase modulator generates a disturbance component δφcp adding to the phase difference δφm=δφb+δφcr.