Measurement of vibrating modes for a shell resonator by using dual-interferometers.

A shell resonator shaped as a half-toroidal has several vibration modes including wine-glass mode. Coriolis force induces the precession of certain vibrating modes, such as wine-glass vibration under a rotation. Therefore, shell resonators can be used to measure the rotations or rotation rates. The quality factor of the vibrating mode is a key parameter for reducing noise as a rotation sensor or gyroscope. This paper demonstrates how to measure the vibrating mode, resonance frequency, and quality factor of a shell resonator by using dual Michelson interferometers. Interferometers simultaneously measure the x and y motions of the resonator when a vibration mode is excited. A buzzer attached to one of the mounting walls excites vibrations via transferring energy. The n = 2 wine-glass mode is measured when two interferometric phases are in out-of-phase condition. The tilting mode is also measured for the case of in-phase conditions, and one of the interferometers has a smaller amplitude than another. The shell resonator manufactured by the blow-torching method here has 13.4 s (Q = 2.7 × 10) and 2.2 s (Q = 2.2 × 10) in life-time (Quality factor) for n = 2 wine-glass and tilting modes, respectively, at 9.7 mTorr. The resonant frequencies are also measured at 6.53 and 3.12 kHz. We can distinguish the resonator's vibrating mode with a single detection rather than the whole scanning of the resonator's deformation by using this method.