Optimal Estimation of Tilt-to-Length Noise for Spaceborne Gravitational-Wave Observatories

The proposed Laser Interferometer Space Antenna (LISA) mission features a three-satellite constellation realizing a long-arm interferometer designed to observe gravitational waves emitted by a multitude of stellar, galactic, and possibly cosmic sources not accessible to ground-based detectors. In support of maximizing LISA’s scientific return, this paper presents an on-orbit excitation and estimation strategy for tilt-to-length coupling noise, a fundamental limitation of the detection sensitivity of spaceborne long-arm interferometers. Tilt-to-length coupling describes the distortion of measurements through the relative attitude jitter of the spacecraft. In operation, inevitable instrument imperfections and misalignments will cause the effect to scale proportionally with the jitter strength, the proportionality factor being referred to as the tilt-to-length coupling factor. For the first time, analytical equations are derived modeling the impact of tilt-to-length coupling on the scientific observations. These equations are shown to define the optimal on-orbit excitation needed to estimate this noise source, enabling the correction of the recorded gravitational wave signals and achievement of LISA’s required detection sensitivity.