Systems and methods for reducing rotation sensing errors in a resonator fiber optic gyroscope. An example method propagates a primary light wave through a resonator having an optical fiber and a plurality of optical surfaces for directing the light wave exiting a first end of the optical fiber back into an opposite end of the optical fiber. The optical fiber is wound onto a piezo-electric transducer (PZT) tube. A sinusoidal voltage is applied to the PZT tube to modulate a length of a fiber cavity within the optical fiber. The amplitude and frequency of the fiber cavity length modulation is selected to produce a relative phase modulation between the primary light wave and a double-back reflected light wave, such that the rotation sensing errors resulting from double backscatter of light is at a frequency above a frequency band of interest. This allows the associated error to be filtered out of the rotation rate signal.