TianQin is a future space-based gravitational wave (GW) observatory targeting the frequency window of 10⁻⁴–1 Hz. A large variety of GW sources are expected in this frequency band, including the merger of massive black hole binaries, the inspiral of extreme/intermediate mass ratio systems, stellar-mass black hole binaries, Galactic compact binaries, and so on. TianQin will consist of three Earth orbiting satellites on nearly identical orbits with orbital radii of about 10⁵ km. The satellites will form a normal triangle constellation whose plane is nearly perpendicular to the ecliptic plane. The TianQin project has been progressing smoothly following the ‘0123’ technology roadmap. In step ‘0’, the TianQin laser ranging station has been constructed and it has successfully ranged to all the five retro-reflectors on the Moon. In step ‘1’, the drag-free control technology has been tested and demonstrated using the TianQin-1 satellite. In step ‘2’, the inter-satellite laser interferometry technology will be tested using the pair of TianQin-2 satellites. The TianQin-2 mission has been officially approved and the satellites will be launched around 2026. In step ‘3’, i.e. the TianQin-3 mission, three identical satellites will be launched around 2035 to form the space-based GW detector, TianQin, and to start GW detection in space.

The arm length of the space-based interferometer for gravitational wave detection is 10⁸–10⁹ m , and picometer precision is required. The wavefront error in the far-field coupled with the pointing jitter is a major noise source, which raises higher requirements of the wavefront quality of the telescope. By extending the analytical solutions of the far-field phase to 21 Zernike aberrations, this paper demonstrates that the far-field phase could be regarded as the sum of the effects of the individual aberrations and a phase plane with its slope related to the wavefront RMS. For individual aberrations, only low-order aberrations have a significant effect on the far-field phase, but high-order aberrations will contribute to the coupling terms which is shown as a phase slope. So there is a definite corresponding relationship between the aberrations and the far-field phase, and it can be easily illustrated graphically. Based on the analytical solutions of the far-field phase, we proposed to consider the tilt-to-length (TTL) error together with the far-field phase. The TTL error is also one of the main noise sources in space-based laser interferometry, which presents big difficulties in the optical system. We found that TTL error could be added to the far-field phase as a piston term during pointing, which then help to bring the stationary point closer to the z-axis and reduce the phase noise detected at the stationary point. By considering the TTL together with the far-field phase, the requirement of the telescope could be λ/25 wavefront RMS (λ = 1064 nm ). And there will be a large tolerance range for the TTL error, so it is only necessary to evaluate the TTL error and limit it to a suitable range, not to eliminate it.

Space-based gravitational wave detection aims to measure gravitational waves with strains of down to 10 ⁻²⁰ in 10 ⁻⁴ Hz ∼ 1 Hz frequency band. In order to achieve this measurement sensitivity, inter-satellite laser interferometry with picometer precision for an armlength of 10 ⁸ ∼ 10 ⁹ m is required. However, the coupling of the transmitting-beam misalignment and the wavefront distortion results in a non-negligible measurement error of intersatellite laser interferometry. Considering a wavefront distortion model composed of the first 55 terms of Zernike polynomials, we analyze the coupling effect of beam misalignment and wavefront distortion in both analytical and numerical methods. Calculation results show that the position of the stationary point is mainly determined by defocus, astigmatism and coma of the wavefront distortion of the transmitting beam. Moreover, a large defocus and small coma are preferred to achieve a better alignment of the stationary pointing direction with the inter-satellite line-of-sight, such that the coupling noise and received laser power can be optimized.

Optical path length (OPL) noise resulting from stray light significantly constrains interferometry displacement measurements in the low-frequency band. This paper presents an analytical model considering the presence of stray light in heterodyne laser interferometers. Due to the cyclic nonlinear coupling effect, there will be some special OPLs of stray light, minimizing the frequency-mixing impact to zero. Consequently, we propose a noise suppression scheme that locks the OPL of stray light at the zero coupling point. Therefore, we significantly enhanced the interference displacement measurement noise within the low-frequency band. Experimental results show that the interferometer achieves a displacement noise level lower than 6 pm/Hz^1/2 covering 1 mHz.

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 ±25 nrad in-plane and ±10 nrad off-plane, in addition to a static bias of 23 µrad 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.

As ground-based gravitational wave (GW) detection has opened a new window for exploring the Universe, space-based GW detection will be the next frontier to deepen the understanding of galaxy evolution and massive black holes merging. TianQin-1 is a technology verification satellite for the space-based GW detector TianQin. One of the key technologies demonstrated in TianQin-1 is a high-precision and ultra-stable interferometer, with a noise floor lower than 100 pm / Hz 1 / 2 @ 0.1 Hz . In this paper, we report the long-term stability of the interferometer in the TianQin-1 satellite, which contains a quasi-monolithic optical bench made through hydroxide catalysis bonding (HCB). According to the results of the ground and in-orbit tests, the long-term stability of the interferometer for 13 months after launch has been evaluated. The resolution of the interferometer is better than 30 pm. The noise level of the interferometer is about 30 pm / Hz 1 / 2 @ 0.1 Hz and 10 pm / Hz 1 / 2 above 1 Hz, fulfilling the mission requirement of TianQin-1. The successful in-orbit operation has demonstrated the interferometer’s high precision and long-term stability based on the quasi-monolithic optical bench.