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China is planning to construct a new space-borne gravitational-wave (GW) observatory, the TianQin project, in which the spaceborne telescope is an important component in laser interferometry. The telescope is aimed to transmit laser beams between the spacecrafts for the measurement of the displacements between proof-masses in long arms. The telescope should have ultra-small wavefront deviation to minimize noise caused by pointing error, ultra-stable structure to minimize optical path noise caused by temperature jitter, ultra-high stray light suppression ability to eliminate background noise. In this paper, we realize a telescope system design with ultra-stable structure as well as ultra-low wavefront distortion for the space-based GW detection mission. The design requirements demand extreme control of high image quality and extraordinary stray light suppression ability. Based on the primary aberration theory, the initial structure design of the mentioned four-mirror optical system is explored. After optimization, the maximum RMS wavefront error is less than λ/300 over the full field of view (FOV), which meets the noise budget on the telescope design. The stray light noise caused by the back reflection of the telescope is also analyzed. The noise at the position of optical bench is less than 10-10 of the transmitted power, satisfying the requirements of space gravitational-wave detection. We believe that our design can be a good candidate for TianQin project, and can also be a good guide for the space telescope design in any other similar science project.

Computing a source-target map that yields integrable surface normal field is quite challenging for freeform illumination design. Here, we propose a least-squares ray mapping method to calculate a superior ray mapping by iteratively correcting an integrable map to approach the energy conservation and boundary condition. The process is implemented via solving three minimization problems. The first two problems can be figured out pointwise and the third can be converted to two decoupled Poisson equations with Robin boundary conditions. We demonstrate the robustness and high efficiency of the proposed method with several design examples.

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