Identification and correction of Sagnac frequency variations: an implementation for the GINGERINO data analysis

Ring laser gyroscopes are top sensitivity inertial sensors used in the measurement of angular rotation. It is well known that the response of such remarkable instruments can in principle access the very low frequency band, but the occurrence of nonlinear effects in the laser dynamics imposes severe limitations in terms of sensitivity and stability. We report here general relationships aimed at evaluating corrections able to effectively account for nonlinear laser dynamics. The so-derived corrections are applied to analyse thirty days of continuous operation of the large area ring laser gyroscope GINGERINO leading to duly reconstruct the Sagnac frequency ω _s . The analysis shows that the evaluated corrections affect the measurement of the Earth rotation rate _⊕ at the level of 1 part in 1.5× 10^3 . The null shift term ω _ns plays a non negligible role. It turns out proportional to the optical losses μ of the ring cavity, which are changing in time at the level of 10% within the considered period of thirty days. The Allan deviation of estimated _⊕ shows a remarkable long term stability, leading to a sensitivity better than 10^-10 rad/s with more than 10 s of integration time, and approaching (8.5± 0.5)× 10^-12 rad/s with 4.5× 10^5 s of integration time.