Methods and apparatus are provided for attenuating rotation rate errors in a resonator gyro. The gyro includes a ring resonator having a hollow core optical fiber coil and optical elements that are selected and/or oriented to reduce stray light that may be present in input light beams introduced to the ring resonator. The resonator has a predetermined mode. One of the optical elements partially transmits a portion of the input light beam to a first end of the fiber coil while partially transmitting a portion of the input light beam to a filter. Light having the predetermined mode is accepted into the first end of the fiber coil, and the filter accepts light of the input light beam having a corresponding mode. Transmission components of the circulating light beams indicates resonance peaks of the counter-propagating directions of the ring resonator.