**4. Conclusions**

Shape accuracy, as a key parameter of the o ff-axis conic aspheric surface, has an important e ffect on the imaging quality of the optical system, so it is necessary to guarantee the shape is accurate during the measuring process. In this study, we provided three methods to test the shape accuracy of the off-axis conic aspheric surface with high precision. The first was auto-collimation, which belongs to a classical and simple method with a requirement of a flat mirror or a sphere mirror as the aiding element. However, this method has some limitations to the surface type and the aperture of o ff-axis surface under testing. The second was the single CGH, which is widely used as an e ffective method with alignment marks to reduce the adjustment di fficulty. However, this method requires a customized CGH, which varies with changes in o ff-axis aspheric surfaces, making it an expensive option. With the need of a fold sphere mirror and a customized CGH, the third is hybrid compensation, which belongs to a more complex measurement technology. The method has a stronger aberration compensation ability and is more suitable for the o ff-axis aspheric surface of large aperture and large asphericity. Unfortunately, its adjustment is more di fficult. Therefore, we recommend not using this method unless absolutely necessary.

In this study, an OAP was measured via these three methods. By the means of auto-collimation, a Φ150 mm flat mirror was used as the aiding element, and the result was PV = 0.583λ and RMS = 0.092λ; by the means of the single CGH, a customized CGH was designed and fabricated, and the result was PV = 0.572λ and RMS = 0.089λ; by the means of hybrid compensation, a fold sphere mirror was chosen, and another customized CGH was also designed and fabricated where the result was PV = 0.615λ and RMS = 0.096λ. These three measurement methods brought forth approximate results, in the meantime, the shape distributions were also close to each other, which proves that these three measurement methods can all obtain comparatively accurate testing results. Furthermore, these three methods can also cross-check the correctness of each other and other available methods.

**Author Contributions:** Methodology, S.L.; software, Y.X.; investigation, X.L.; resources, H.L.; data curation, J.Z.; writing of the original draft preparation, S.L.; writing of review and editing, W.L., H.L. and X.L.; visualization, Y.X.; supervision, J.Z. and W.L.; project administration, W.L. and H.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (No. 61505157), the Xi'an Science and Technology Board (No. 201805031YD9CG15(2)), the Science and Technology Program of Shaanxi Province (No. 2020GY-045), and the Xi'an Key Laboratory of Intelligent Detection and Perception (No. 201805061ZD12CG45).

**Conflicts of Interest:** The authors declare no conflicts of interest.
