On point-ahead angle control strategies for TianQin

Pointing-related displacement noises are crucial in space-based gravitational wave detectors, where point-ahead angle control of transmitted laser beams may contribute significantly. For TianQin that features a geocentric concept, the circular high orbit design with a nearly fixed constellation plane gives rise to small variations of the point-ahead angles within $\pm 25$ nrad in-plane and $\pm 10$ nrad off-plane, in addition to a static bias of 23 $\mu$rad predominantly within the constellation plane. Accordingly, TianQin may adopt fixed-value compensation for the point-ahead angles and absorb the small and slow variations into the pointing biases. To assess the in-principle feasibility, the far-field tilt-to-length (TTL) coupling effect is discussed, and preliminary requirements on far-field wavefront quality are derived, which have taken into account of TTL noise subtraction capability in post processing. The proposed strategy has benefits in simplifying the interferometry design, payload operation, and TTL noise mitigation for TianQin.