Tilt-To-Length coupling in LISA Pathfinder: model, data analysis and take-away messages for LISA

Abstract

In the mid-2030s, the laser interferometer space antenna (LISA) is planned to be launched and will be the first gravitational wave detector in space. One of the major noise sources in LISA will be tilt-to-length (TTL) coupling, i.e. the coupling of lateral and angular spacecraft motion into the interferometric readout. Likewise, TTL coupling was a significant noise in LISA’s technology demonstrator mission LISA Pathfinder (LPF), operating from March 2016 until the end of June 2017 with a performance that exceeded the expectations. During this mission, TTL coupling was the main noise contributor between 20 and 200 mHz. It was successfully subtracted via a fit model in post-processing. However, each analytical model existing at that time failed to describe the TTL coupling consistently. The lack of such a physical model limited the ability to minimise the TTL noise via realignments of the optical system a priori. Therefore, I present in this thesis, on the one hand, a detailed description of the TTL mechanisms in general cases and a derivation of the corresponding analytical equations if possible. On the other hand, I interpret these findings for the LPF case, followed by an analysis of the TTL noise during this mission. The analytical models introduced in the first part describe TTL coupling in general interferometric detectors. This analysis covers geometric and non-geometric TTL coupling contributions from lateral and angular jitter of either a mirror or a receiving system. The models can be applied to different interferometric setups modelling the found TTL noise and developing strategies for the TTL coupling suppression. The model predictions have been verified in simulation and, in the case of LPF, by the comparison to data taken during the mission. In particular, the new LPF TTL model successfully describes how the measured coupling depends on the alignment of the test masses hosted by the LPF satellite and, therefore, how they could have been realigned for an optimal TTL suppression. Also, the TTL coupling coefficients match the results from the fit used during the LPF mission in a TTL coupling experiment. Based on this data, I present how a comparable physical model can be derived using the fit results. In addition, the long-term analysis shows that TTL coupling is not stable over the entire mission duration. The individual TTL contributors are affected by a small distortion of the optical bench and its components, mainly due to temperature changes. However, the TTL coupling provides an additional measure for the actual alignment of the full optical system. In summary, I demonstrate within this thesis that modelling TTL noise in space interferometers while complex is possible. Likewise, this result boosts our confidence that the suppression techniques planned for LISA will enable the successful gravitational wave measurement.