Arm locking for the Laser Interferometer Space Antenna

Abstract

The Laser Interferometer Space Antenna mission is a planned gravitational wave detector consisting of three spacecraft in heliocentric orbit. Laser interferometry is used to measure distance fluctuations between test masses aboard each spacecraft to the picometer level over a 5 million kilometer separation. Laser frequency fluctuations must be suppressed in order to meet the measurement requirements. Arm-locking, a technique that uses the constellation of spacecraft as a frequency reference, is a proposed method for stabilizing the laser frequency. We consider the problem of arm-locking using classical optimal control theory and find that our designs satisfy the LISA requirements.

Arm locking performance with the new LISA design

“…Following the work by Sheard et al [20], there have been several works ( [18,21,23]) on optimizing arm locking by constructing a sensor signal using frequency dependent linear combinations of signals from both arms. This resulted in sensor signals that allow for more aggressive controllers.…”

“…However, the long light travel times and the relative motion of the end points require tailored sensor and controller designs which have been developed during the first decade of this century for the original 5 Gm LISA mission. This has been summarized very well in [18,21]. In this paper, we apply the lessons learned to the new LISA design with its shorter arms, different orbits, improved clock noise, and LISA Pathfinder (LPF) based model for the residual spacecraft motion to supply a baseline for follow up studies.…”

“…The paper is organized as follows: section 2 briefly reviews arm locking, the challenges involved in the arm locking sensor and controller design and how clock noise, shot noise and residual spacecraft motion is included in the model (see [18,21] for a detailed study). Section 3 discusses the new LISA mission parameters and noise ASDs that are relevant to the arm locking performance.…”

LISA long-arm interferometry

“…There is some design freedom in determining how best to combine the information from the two long-arm measurements. The goal is to generate a sensor with a flat, broadband response to laser phase noise and minimal coupling of phase noise from other sources, a problem that can be approached using optimization techniques [25] or traditional control design methods. The current baseline arm-locking sensor is the modified dual arm-locking sensor, described by McKenzie, et al [26].…”