Compact advanced pure tilt actuator for testing tilt-to-length coupling in space-based gravitational wave detection

Tilt-to-length (TTL) coupling, caused by the jitter of test masses or satellites, is a major noise source in space-based gravitational wave detection. Calibrating and suppressing TTL coupling noise at the sub-nanometer level is essential. A key challenge in current ground-based TTL coupling testing is the residual translational movement of the tilt actuator. This paper presents the development of a compact advanced pure tilt actuator (APTA) specifically designed for testing TTL coupling. The APTA enables precise tilt motion, monitored by a four-beam interferometer measuring the displacement of attached retroreflectors. Detailed theoretical models and experimental setups are given. Experimental results demonstrate that the APTA test bed can achieve sub-nanometer-level TTL coupling calibration. Additionally, a typical test-mass interferometer tested by the APTA test bed demonstrated that the imaging system effectively suppresses TTL coupling errors. The TTL coupling coefficients were reduced from over +/- 30 mu m/rad to within +/- 5 mu m/rad across a range of +/- 200 mu rad. The APTA test bed offers a compact, high-precision solution for ground-based TTL coupling tests and has the potential for broader application in related experimental setups.