Laser Frequency Stabilisation and Interferometer Path Length Differences during the LISA Pathfinder Satellite Mission

Abstract

This thesis focusses on laser frequency stabilisation and interferometer path length differences on LISA Pathfinder (LPF). LPF was a satellite mission, in operation from December 2015 until July 2017, to demonstrate key technologies for the future spaceborne gravitational wave observatory, the Laser Interferometer Space Antenna (LISA). It successfully showed that the undesired disturbances, the so-called residual acceleration noise, of a pair of free-falling test masses (TMs) could be limited to less than 2 fm/s^2/sqrt{Hz} at mHz Fourier frequencies and thus paved the way for LISA.

This level of residual acceleration noise could only be reached by the interaction of several key subsystems. One of these, the Optical Metrology System (OMS), provided the LPF science measurement: a heterodyne interferometry readout of the relative positions of the free-floating TMs. The OMS showed excellent performance over the mission and is studied here in detail to make the best use of this unique measurement data and to learn as much as possible for future interferometer development.

The OMS is subject to several noise sources. This thesis focusses on one of these: laser frequency fluctuations. In the design phase of the OMS, a laser frequency stabilisation technique via a dedicated interferometer measurement and a nested control loop was developed. In this thesis, we show the in-flight results of the planned loop characterisation experiments and noise measurements. We prove that the stabilisation worked as expected from ground tests and was reliable over the mission duration. We also identified periods of slightly increased laser frequency fluctuations whose origin could not yet be identified. This analysis was restricted by the limited number of laser telemetry channels and their low sampling frequency.

The coupling of laser frequency noise depends on the optical path length difference between the measurement and the reference beam. Two experiments optimised for determining this quantity have been designed and executed on LPF and are analysed here. The evidence collected in the offset experiment allows us to associate a change in measured path length mismatch to a commanded offset at a 3\sigma uncertainty level, both in direction and amplitude. In addition, we confirmed that the estimated path length mismatch is independent of the laser frequency modulation amplitude and frequency. In general, we find the path length mismatch is only a few hundred μm, which is a sign of excellent integration. We also provide an example where these experiments were used as a means to measure absolute distances on LPF.

During these experiments, we also observed short term path length mismatch variations which are not believed to be caused by a true TM motion, as well as spurious signals in the angular measurements of the OMS. Within the scope of this work, a definite reason could not be found for either of these two observations but different cross-coupling hypotheses to explain the signals in the angular measurements could also not be fully rejected. However, we have found no reason to believe that these angular signals could be an indication of a mechanism that impacts the longitudinal measurements and thus adds a systematic error to the path length mismatch numbers reported.