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

The arm length and the isolation in space enable the Laser Interferometer Space Antenna (LISA) to probe for signals unattainable on the ground, opening a window to the subhertz gravitational-wave universe. The coupling of unavoidable angular spacecraft jitter into the longitudinal displacement measurement, an effect known as tilt-to-length (TTL) coupling, is critical for realizing the required sensitivity of $\mathrm{picometer}/\sqrt{\mathrm{Hz}}$. An ultrastable interferometer test bed has been developed in order to investigate this issue and validate mitigation strategies in a setup representative of LISA and in this paper it is operated in the long-arm interferometer configuration. The test bed is fitted with a flat-top beam generator to simulate the beam received by a LISA spacecraft. We demonstrate a reduction of TTL coupling between this flat-top beam and a Gaussian reference beam via the introduction of two- and four-lens imaging systems. TTL coupling factors below $\ifmmode\pm\else\textpm\fi{}25\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}/\mathrm{rad}$ for beam tilts within $\ifmmode\pm\else\textpm\fi{}300\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{rad}$ are obtained by careful optimization of the system. Moreover, we show that the additional TTL coupling due to lateral-alignment errors of elements of the imaging system can be compensated by introducing lateral shifts of the detector and vice versa. These findings help validate the suitability of this noise-reduction technique for the LISA long-arm interferometer.