Abstract
The LIGO (Laser Interferometric Gravitational-wave Observatory) project, and other projects around the world, are currently planning to use long-baseline (> 1 km) interferometers to directly detect gravitational radiation from astrophysical sources. In this work we present a framework for lock acquisition, the process by which an initially uncontrolled resonant interferometer is brought to its operating point. Our approach begins with the identification of a path which takes the detector from the uncontrolled state to the operational state. The properties of the detector's outputs along this path, embodied in the sensing matrix, must be determined and parameterized in terms of measureables. Finally, a control system which can compute the inverse of the sensing matrix, apply it to the incoming signals, and make the resulting signals available for feedback is needed to close the control loop. This formalism was developed and explored extensively in simulation and was subsequently applied to the LIGO interferometers. Results were in agreement with expectation within error, typically ±20% on the sensing matrix elements, and the method proved capable of bringing a high-finesse power-recycled Fabry-Perot-Michelson interferometer (a LIGO detector) to its operating point.
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