A method for reducing the Kerr effect in an interferometric measuring device including a light signal generator configured to emit a periodic input light signal having at least two non-zero input power values (Pe1, Pe2), and a Sagnac interferometer comprising an optical loop, a splitter configured to couple the periodic input light signal to the optical loop in order to split the light signal into mutually counter-propagating first signal and second signal, which each have at least two power values each corresponding to an input power value and which propagate in opposite directions in the optical loop and to combine said counter-propagating signals (15, 16) after their propagation in the loop in order to form a periodic output signal having at least two output power values each corresponding to an input power value, the method comprising a periodic modulation with at least two opposite states (Δφ1, Δφ3; Δφ2, Δφ4) of the phase shift between the two counter-propagating signals (15, 16) and, over a same modulation period, a. a first series of measurements that includes at least two output power measurements at points of the output signal that have first output power values corresponding to a first input power value and that correspond to opposite modulation states; b. a first phase-shift determination between the two counter-propagating signals each having a power value corresponding to the first input power value, and a cancellation of this phase shift that includes adjusting the modulation depending on the cancellation of a first calculated demodulation term that is function of said at least two measurements of the first series of measurements and that is representative of said phase shift, then c. a second series of measurements that includes at least two measurements at points of the output signal that have second output power values corresponding to a second input power value and that correspond to opposite modulation states; d. a second phase-shift determination between the two counter-propagating signals (15, 16) each having a power value corresponding to the second input power value, and a cancellation of this phase shift, depending on the cancellation of a second calculated demodulation term that is function of said at least two measurements of the second series of measurements and that is representative of the phase shift. a. a first series of measurements that includes at least two output power measurements at points of the output signal that have first output power values corresponding to a first input power value and that correspond to opposite modulation states; b. a first phase-shift determination between the two counter-propagating signals each having a power value corresponding to the first input power value, and a cancellation of this phase shift that includes adjusting the modulation depending on the cancellation of a first calculated demodulation term that is function of said at least two measurements of the first series of measurements and that is representative of said phase shift, then c. a second series of measurements that includes at least two measurements at points of the output signal that have second output power values corresponding to a second input power value and that correspond to opposite modulation states; d. a second phase-shift determination between the two counter-propagating signals (15, 16) each having a power value corresponding to the second input power value, and a cancellation of this phase shift, depending on the cancellation of a second calculated demodulation term that is function of said at least two measurements of the second series of measurements and that is representative of the phase shift.