Abstract: An optical gyroscope is provided for measuring a small angular difference. The gyroscope includes a laser, a pre-selection polarizer, a first beam splitter, a coil of optical fiber, a second beam splitter, a post-selection polarizer, a spectrometer and an analyzer. The laser emits a pulse beam of coherent photons. The beam has pulse duration ?. The pre-selection polarizer pre-selects the photons, and the first beam splitter separates the photons by their horizontal |? and vertical |? polarization eigenstates. These beams are launched into a fiber optical coil of radius r, which preserves polarization. The coil rotates by a difference rotation angle ??. The second beam splitter recombines the polarized photon beams as they exit the coil. The post-selection polarizer post-selects the photons. The spectrometer captures the post-selected photons and measures the associated frequency translation ??.