Reducing tilt-to-length coupling for the LISA test mass interferometer

Objects sensed by laser interferometers are usually not stable in position or orientation. This angular instability can lead to a coupling of angular tilt to apparent longitudinal displacement -- tilt-to-length coupling (TTL). In LISA this is a potential noise source for both the test mass interferometer and the long-arm interferometer. We have experimentally investigated TTL coupling in a setup representative for the LISA test mass interferometer and used this system to characterise two different imaging systems (a two-lens design and a four-lens design) both designed to minimise TTL coupling. We show that both imaging systems meet the LISA requirement of +-25 um/rad for interfering beams with relative angles of up to +-300 urad. Furthermore, we found a dependency of the TTL coupling on beam properties such as the waist size and location, which we characterised both theoretically and experimentally