LIGO Publication Abstract
Alignment Issues in Laser Interferometric Gravitational-Wave Detectors
Mavalvala, N.
PhD Thesis, MIT (1997)

In this work we present a detailed quantitative study of the effects of angular misalignment in gravitational wave detectors. To analyze complex optical configurations we have developed a mathematical formalism which is powerful enough to accurately predict the effects of misalignment in coupled cavity systems, such as the LIGO (Laser Interferometric Gravitational-wave Observatory) interferometer. The formalism describes misaligned mirrors and free space propagation as operators acting on the eigenmodes of the perfectly aligned system and treats distortion effects as perturbations. Operators representing complicated optical systems are recursively built upon simpler ones, allowing a straightforward generalization to arbitrarily complex optical configurations. This model has been pivotal in determining the sensitivity to misalignment of the LIGO detector and for designing an automatic alignment system for an interferometer with ten angular degrees of freedom. Phase modulated light circulating in the interferometer is used to discriminate different angular degrees of freedom and to accurately measure misalignment angles. This wavefront sensing technique enables sensing of the angular misalignment of the interferometer mirrors relative to the incoming laser beam by spatial sampling of the optical wavefront, thus providing robust error signals for an angular servo system. The wavefront sensing system was successfully implemented on a table-top scale fixed mirror interferometer (FMI) featuring an optical configuration very similar to LIGO: a power recycled Michelson interferometer with Fabry-Perot cavities in the arms. In the FMI experiment four longitudinal degrees of freedom were controlled to maintain resonance and the measured wavefront sensing signals were also used to feedback to the angle acuators on the interferometer mirrors, making this the first interferometer with a LIGO configuration to accomplish closed loop servo control of all ten angular degrees of freedom. Good agreement was found between the model predictions and the measured wavefront sensing signals, with typical experimental errors of order +20%/-20%. Quantiative understanding of the alignment sensitivity and implementation of an automatic alignment system using the wavefront sensing technique marks the significant progress towards achieving the sensitivity goals of LIGO.


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