Nuclear Magnetic Resonance Gyroscopes

Introduction Gyroscopes measure rotation of a platform with respect to an inertial system [1]. The classic example of a mechanical gyroscope is a spinning massive object in a gravitational field, with one point of the object on its rotation axis held fixed. In this system, rotation ("precession") about the gravitational field axis will be observed at a rate proportional to the field magnitude and inversely proportional to the angular momentum of the object. Changes in the precession frequency indicate rotation with respect to inertial space. As described in previous chapters, atomic spins in a magnetic field precess in a manner analogous to spinning mechanical systems in a gravitational field, with the precession rate proportional to the field magnitude and inversely proportional to the atom's angular momentum. Rotation of a measurement platform within the inertial frame can be detected by monitoring the apparent change in the Larmor frequency of the atoms. In an inertial frame, the equation of motion for the spin polarization P of an ensemble of spins is δP/δt = γB × P. When the laboratory frame containing the instruments used to measure the Larmor precession is rotating with respect to inertial space, the Larmor frequency is shifted by Ω, the rotation rate of the apparatus about the direction of the applied field. In this case, the equation of motion for P becomes The concept of rotation sensing by a measurement of the Larmor frequency is illustrated in Fig. 19.1. The problem therefore becomes one of measuring the rotation-induced precession-frequency shift with high precision, while simultaneously controlling all other effects that lead to precession-frequency shifts.