A fiber optic rotation sensing interferometer based on the Sagnac effect in which mechanical rotation introduces measurable shifts in the phase of optical signals transversing a closed path. The interferometer includes the closed optical path made up of a multi-turn fiber optic loop, a directional coupler or couplers, and an amplifier. A pulse of electromagnetic radiation is fed into the optical path by means of a pulsed electromagnetic source such as a laser and a beam splitter. The beam splitter splits the pulse into two pulses which undergo multiple circulations about the optical path in opposite directions. The directional couplers non-destructively sample the two pulses after each pass therethrough and send the pair of pulse samples to the beam splitter once each circulation. The beam splitter sends these pulse pair samples to a detector and signal processor once each circulation. The detector measures the instantaneous relative phase shift between the two pulse samples in each of the multiple pulse pairs and outputs phase information once each circulation. This phase information is converted by the signal processor into the angle of rotation or into rotation rate of the interferometer.