Laser Self-Mixing Interferometry for Precision Displacement Measurement in Resonant Gyroscopes

Laser self-mixing interferometry (SMI), as an alternative contactless displacement measurement method, has extremely high resolution (pico-meter), large dynamic range and wide bandwidth. Comparing to electrostatic capacitive sensing, its detection accuracy does not depend on the gap size, electrode area, or bias voltage, which are bottlenecks for high-performance vibrating sensors. This paper presents our initial study in measuring vibrations of 3D shell resonators by laser self-mixing interferometry for application in high-performance gyroscopes. Our measurement of vibrations of a shell resonator using a VCSEL shows a noise-equivalent displacement resolution of 329pm with 100Hz bandwidth for resonator vibration amplitudes of less than 100nm, which can be improved down to $\pmb{2.2}\mathbf{pm}/\surd\mathbf{Hz}$ using low noise voltage amplifiers. If used with a fused silica shell resonator gyroscope, a rate resolution of 0.45 mdeg/hr with 1Hz bandwidth can be expected. To expand sensor dynamic range, a real-time, high-accuracy phase unwrapping technique is proposed. The scale factor of the SMI can be optimized in real time through mid-fringe point tracking by a positioning actuator.