为实现自由曲面的定位与位姿高精度测量，提出了“光学-机械”基准定位法，建立了位姿测量模型，并对该方法的定位误差和基准选择展开研究。根据三坐标测量机与计算全息提出了“光学-机械”基准定位法。然后，采用球形安装的回射器（Sphere Mounted Retroreflector ，SMR）、猫眼、基准球作为基准，基于波像差理论与视差效应分别建立了3种基准的位姿测量模型，得到了位置误差与基准区域波前像差的函数关系，并对3种位姿测量模型进行对比。最后，对3种基准位姿测量方法进行仿真及实验验证，实测结果与模型的残差结果均小于0.05λ，相对误差均小于2.43%，验证了模型的准确性。实验结果表明，当检测距离为1 000 mm时，猫眼法的轴向定位误差为24 μm；基准球法的轴向定位误差为50 μm；SMR靶球法的轴向定位误差为16 μm，X，Y方向的定位误差为1 μm，滚转角定位误差为3.26″。SMR靶球法的定位误差最小、检测动态范围最大且检测光学元件的自由度最多，更适用于自由曲面的高精度位姿检测。

We implemented a stitching swing arm profilometer (SSAP) test for the inner and outer regions of a large aspheric surface with a short arm. The SSAP was more capable of improving sampling density of surface and was less sensitive to system error, like vibration noise and air-table noise. Firstly, a calculation model was built to evaluate the sampling density of the SSAP test. Then, sensitivity to system noise was tested when different lengths of arm were used. At the end, an experiment on a 3 m diameter aspheric mirror was implemented, where test efficiency was promoted, and high sampling density was achieved.

The demand for space-borne telescopes with an aperture of 20 m is forcing the development of large diameter diffractive Fresnel zone lenses (FZLs) on membranes. However, due to the fabrication errors of multi-level microstructures, the real diffraction efficiency is always significantly smaller than the theoretical value. In this Letter, the effects of a set of fabrication errors on the diffraction efficiency for a diffractive membrane are studied. In order to verify the proposed models, a 4-level membrane FZL with a diameter of 320 mm is fabricated. The fabrication errors of the membrane FZL are measured, and its diffraction efficiency in the +1 order is also tested. The results show that the tested diffraction efficiency is very close to the calculated value based on the proposed models. It is expected that the present work could play a theoretical guiding role in the future development of space-borne diffractive telescopes.

Null lenses are always used to test large convex aspheric mirrors. For large convex aspheric mirrors with large deviate wavefronts from the aspheric wavefront to its best sphere wavefront, a traditional null lens composed of a flat and a sphere cannot be used to test. An aspheric null lens needs to be designed and manufactured to test a large convex aspheric mirror with a large deviate wavefront. Another traditional null lens is used to guide the manufacture of the aspheric null lens. The accuracy and feasibility of the aspheric null lens are unknown and should be tested by a high precision computer-generated hologram (CGH). In the article, we introduce the principle of a null lens, designed an aspheric null lens to test a Φ338 mm aspheric SIC mirror whose radius of curvature is 1024 mm, the deviate wavefront from the aspheric wavefront to its best fit sphere wavefront is 66.5728λ PV (λ=632.8 nm). The result of the aspheric null lens that is tested by a CGH is 0.018λ RMS and satisfies the need of accuracy. The test result of the aspheric mirror is 0.030λ RMS.