tuned away from the resonance frequency of the resonator 25 in the cw direction the energy from the cw beam does not enter the optical fiber and the light is reflected off the highly reflective mirror 22 to produce a maximum intensity at the cw photodetector 26 when f 0 is tuned at the resonance frequency of the resonator 25 in the cw direction the cw beam enters the optical fiber coil 24 and the light striking the cw photodetector 26 has a minimum output i e a resonance dip thereby indicating the resonance center similarly for the ccw light beam the energy of the ccw beam enters the optical fiber coil 24 when the ccw beam is tuned to the resonance frequency of the resonator 25 in the ccw direction in the absence of rotation the round trip path lengths of the cw and ccw beams inside the resonator 25 in the cw and ccw direction respectively are substantially equal thus u03b4f is tuned to zero by the frequency shifter 20 in the presence of rotation the round trip path lengths differ between the cw and the ccw directions producing a resonance frequency difference between the two directions that is proportional to the rotation rate by tuning the frequency f 0 to track the ccw resonance and the frequency u03b4f to track the ccw resonance center the rotation rate is determined in a preferred exemplary embodiment of rfog 10 frequency shifting is obtained using a serrodyne method whereby a phase ramp is applied to an input light beam e g cw and ccw beams by driving a phase modulator such as the wave modulators 16 18 with a.