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The arm length and the isolation in space enable LISA to probe for signalsunattainable on ground, opening a window to the sub-Hz gravitational-waveuniverse. The coupling of unavoidable angular spacecraft jitter into thelongitudinal displacement measurement, an effect known as tilt-to-length (TTL)coupling, is critical for realizing the required sensitivity ofpicometer$/\sqrt{\rm{Hz}}$. An ultra-stable interferometer testbed has beendeveloped in order to investigate this issue and validate mitigation strategiesin a setup representative of LISA, and in this paper it is operated in thelong-arm interferometer configuration. The testbed is fitted with a flat-topbeam generator to simulate the beam received by a LISA spacecraft. Wedemonstrate a reduction of TTL coupling between this flat-top beam and aGaussian reference beam via introducing two- and four-lens imaging systems. TTLcoupling factors below $\pm 25\,\mu$m/rad for beam tilts within $\pm300\,\mu$rad are obtained by careful optimization of the system. Moreover weshow that the additional TTL coupling due to lateral alignment errors ofelements of the imaging system can be compensated by introducing lateral shiftsof the detector, and vice versa. These findings help validate the suitabilityof this noise-reduction technique for the LISA long-arm interferometer.

Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer