High precision, compact inertial sensors for use in gravitational wave detectors

Abstract

Operating a gravitational wave detector requires a suite of high-performance inertial and displacement sensors. These sensors are part of a complex control system which isolates optics from seismic disturbances. Despite the state-of-the-art sensors deployed in current gravitational wave detectors, noise from the control system continues to be a problem for the Laser Interferometric Gravitational Wave Observatories (LIGO). This problem will worsen for the next generation of terrestrial gravitational wave detectors and, hence, needs technological developments in all sensing and control scheme aspects. One of these needs is for better precision inertial sensors in places that currently can not be probed, such as the suspension chains of the optics. We therefore need to develop high precision, compact inertial sensors.

Compact inertial sensors have limited test masses and higher resonance frequencies than their bulkier equivalents. Both of these degrade the performance of the sensors. In order to counteract this effect, a high mechanical Quality factor (Q factor) is required. High Q factors can be achieved with fused silica oscillators but require careful design of test mass suspensions to produce useful oscillation modes. Furthermore, to make a good inertial sensor, these oscillators must be integrated with a precise method of reading out the inertial motion of the test mass.

This thesis discusses the design and testing of such compact inertial sensors. Part I of this thesis begins with a discussion of inertial sensor design. The noise terms of relevance to these sensors are evaluated for their mechanical behaviours. The effect of every design parameter on the mechanical behaviour of oscillators is calculated using a combination Finite Element Analysis and analytical modeling. The responses to these design parameter changes can then be used to optimise the mechanical behaviours for noise performance.

Part II explores the development and testing of sensors. This part covers both the oscillating optic and optical readout methods. The tools for designing inertial sensors were put into practice. Several oscillator designs were produced and tested. The resulting designs achieve mQ products of 2000\,kg, high enough for the gram scale designs to reach thermal noise levels comparable to state-of-the-art sensor available today. Furthermore, methods achieving high-reflectivity on the oscillators without degrading the Q factor is shown.

A high-precision optical readout scheme is developed. The scheme uses an optical resonator to achieve sub f\msqrthz\,\,performance at frequencies above 80\,Hz. It is shown that a frequency reference using an ultra-low expansion glass spacer can achieve satisfactory performance such that the laser's frequency noise is no longer a limiting factor. Huddle tests are used to evaluate the performance of some initial samples. The scheme does not quite reach the thermal noise floor due to some issues controlling the sensors, but promising initial results are shown.

This thesis makes the case that compact optical inertial sensors are a viable solution for seismic isolation systems in the next generation of gravitational wave detectors. Oscillators have been produced with excellent mechanical performance that can be combined with high-precision readout methods to produce state-of-the-art inertial sensors in a compact design. These are excellent candidates for use in gravitational wave detectors due to their compact size, vacuum compatibility, and excellent performance.