Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

A novel phase-step calibration technique is presented on the basis of a two-run-times-two-frame phase-shift method. First the symmetry factor M is defined to describe the distribution property of the distorted phase due to phase-shifter miscalibration; then the phase-step calibration technique, in which two sets of two interferograms with a straight fringe pattern are recorded and the phase step is obtained by calculating M of the wrapped phase map, is developed. With this technique, a good mirror is required, but no uniform illumination is needed and no complex mathematical operation is involved. This technique can be carried out in situ and is applicable to any phase shifter, whether linear or nonlinear. (c) 2006 Optical Society of America.

Calibration of Grassholme Channels, 1982

Adjustment of experimental channels to give any specified pattern of water depth or velocity is complex and tedious because it involves a number of variables. Since some variables are not controllable and variables may interact, valve settings of the Grassholme channels were initially determined on an ad hoc basis to suit individual experiments. This method was used during 1982 but additional observations were made in order to gain more detailed understanding of the channel system and, as far as possible, to develop a guide to future short-cuts in attaining suitable channel settings for any given purpose. This report describes calibration of the Grassholme channels (using water of the Grassholme Reservoir) for the biological experiments of spring - summer 1982. The main variables that are discussed are valve turns and discharge and velocity and depth. It also seeks to establish relationships which will be of value in future managment of the channels for experimental purposes.

Calibration method for a photoelastic modulator with a peak retardation of less than a half-wavelength

A new calibration method for a photoelastic modulator is proposed. The calibration includes a coarse calibration and a fine calibration. In the coarse calibration, the peak retardation of the photoelastic modulator is set near 1.841 rad. In the fine calibration, the value of the zeroth Bessel function is obtained. The zeroth Bessel function is approximated as a linear equation to directly calculate the peak retardation. In experiments, the usefulness of the calibration method is verified and the calibration error is less than 0.014 rad. The calibration is immune to the intensity fluctuation of the light source and independent of the circuit parameters. The method specially suits the calibration of a photoelastic modulator with a peak retardation of less than a half-wavelength. (c) 2007 Optical Society of America.