Deep–Frequency Modulation Interferometry for Gravitational Wave Detectors

Abstract

This thesis presents my research on a new type of local displacement sensors proposed to be used in gravitational wave detectors to improve upon the alignment and control noise in the low frequency regime around 3 Hz. Gravitational wave astronomy is an emerging field using large interferometers with km long arms to measure small displacements of less than 10−20 m/√Hz caused by passing gravitational waves. The currently running LIGO and Virgo detectors are limited in the low-frequency region (below 30 Hz) by alignment and control noises of their suspended optics. As a possible path to improve upon these noise limitations, the use of more precise local sensors to measure the local displacement of the optics, counteract their motion and improve upon their alignment has been proposed. This thesis presents my research on local displacement sensors based on “deep–frequency modulation interferometry (DFMI)” which allows for precise measurements down to displacements in the order of∼100fm/√Hz while simultaneously providing an absolute displacement readout allowing for measurements over a large dynamic range over millimeter and centimeter, necessary for some of the suspended optics in gravitational wave detectors. I present an “analytic readout algorithm” developed to extract the displacement parameters of interest from a measured DFMI signal and I conduct a thorough analysis of the achievable precision limits of DFMI using the “Cram´er-Rao bound”. The readout algorithm I present allows for a faster readout than previous experiments using DFMI, significantly increasing the control bandwidth and the number of sensor channels that can be processed. My noise analysis proves that the readout algorithm runs close to optimal precision (given by the Cramer-Rao bound) and provides a displacement readout similar to other interferometry–based displacement sensing techniques. These results show that using “deep–frequency modulation interferometry (DFMI)” based local displacement sensors can help current and future planned ground–based gravitational wave detectors to reach their target/design sensitivity in the low frequencies around 10−21 m/√Hz.