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TianQin is a planned Chinese space-based gravitational wave (GW) observatorywith a frequency band of 10-4 to 1Hz. Optical telescopes are essential for thedelivery of the measurement beam to support a precise distance measurementbetween pairs of proof masses. As the design is driven by the interferometricdisplacement sensitivity requirements, the stability control of optical pathlength (OPL) is extremely important beyond the traditional requirement ofdiffraction-limited imaging quality. In a telescope system, the recurringtilt-to-length (TTL) coupling noise arises from the OPL variation due to thewavefront deformation and angular misalignment. The pupil aberrations arepreferred option to understand the OPL specifications and further suppress TTLcoupling noise. To correct the pupil aberrations, we derive primary pupilaberrations in a series expansion form, and then refine the formulation ofmerit function by combining the pupil aberration theory and traditional imageaberration theory. The automatic correction of pupil aberrations is carried outby using the macro programming in the commercial optical software Zemax,leading to a high performance telescope design. The design results show that onone side the pupil aberrations have been corrected, and on the other side, itsoptical performance meets the requirements for TianQin project. The RMSwavefront error over the science field of view (FOV) is less than {\lambda}/200and the maximum TTL coupling noise over the entire 300 urad FOV is0.0034nm/urad. We believe that our design approach can be a good guide for thespace telescope design in any other space-based GW detection project, as wellas other similar optical systems.

Pupil aberrations correction of the afocal telescope for the TianQin project