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Abstract

This paper is the second in a set of two investigating tilt-to-length (TTL)
coupling. TTL describes the cross-coupling of angular or lateral jitter into an
interferometric phase signal and is an important noise source in precision
interferometers, including space gravitational wave detectors like LISA. We
discussed in 10.1088/2040-8986/ac675e the TTL coupling effects originating from
optical path length changes, i.e. geometric TTL coupling. Within this work, we
focus on the wavefront and detector geometry dependent TTL coupling, called
non-geometric TTL coupling, in the case of two interfering fundamental Gaussian
beams. We characterise the coupling originating from the properties of the
interfering beams, i.e. their absolute and relative angle at the detector,
their relative offset and the individual beam parameters. Furthermore, we
discuss the dependency of the TTL coupling on the geometry of the detecting
photodiode. Wherever possible, we provide analytical expressions for the
expected TTL coupling effects. We investigate the non-geometric coupling
effects originating from beam walk due to the angular or lateral jitter of a
mirror or a receiving system. These effects are directly compared with the
corresponding detected optical path length changes in 10.1088/2040-8986/ac675e.
Both together provide the total interferometric readout. We discuss in which
cases the geometric and non-geometric TTL effects cancel one-another.
Additionally, we list linear TTL contributions that can be used to counteract
other TTL effects. Altogether, our results provide key knowledge to minimise
the total TTL coupling noise in experiments by design or realignment.