Mechanism and measurement of second-order backscattering error in closed-loop hollow-core photonic crystal fiber optic gyroscopes

Second-order backscattering (SOBS) error is an important source of bias error in closed-loop hollow-core photonic crystal fiber (HC-PCF) gyroscopes, but its generation mechanism and measurement method have not been fully clarified. We establish a SOBS-error model and analyze its dependence on the square-wave and step-wave modulation phases introduced through the Y-branch waveguide, as well as on environmental phase fluctuations. Simulations show that the SOBS error exhibits two periods of variation as the step-wave phase varies from 0 to π. We further propose a dual-fiber-coil interference method for experimentally measuring the SOBS error. For a 260-m-long, 140-mm-diameter HC-PCF coil, the measured SOBS-error amplitude is 0.453 °/h, providing an experimental reference for the SOBS-error magnitude under the tested conditions.