*Article* **The Methods and Experiments of Shape Measurement for O** ff**-Axis Conic Aspheric Surface**

**Shijie Li 1,2,\*, Jin Zhang 1,2, Weiguo Liu 1,2, Haifeng Liang 1,2, Yi Xie 3 and Xiaoqin Li 4**


Received: 26 March 2020; Accepted: 27 April 2020; Published: 1 May 2020

**Abstract:** The o ff-axis conic aspheric surface is widely used as a component in modern optical systems. It is critical for this kind of surface to obtain the real accuracy of the shape during optical processing. As is widely known, the null test is an e ffective method to measure the shape accuracy with high precision. Therefore, three shape measurement methods of null test including auto-collimation, single computer-generated hologram (CGH), and hybrid compensation are presented in detail in this research. Although the various methods have their own advantages and disadvantages, all methods need a special auxiliary component to accomplish the measurement. In the paper, an off-axis paraboloid (OAP) was chosen to be measured using the three methods along with auxiliary components of their own and it was shown that the experimental results involved in peak-to-valley (PV), root-mean-square (RMS), and shape distribution from three methods were consistent. As a result, the correctness and e ffectiveness of these three measurement methods were confirmed, which are very useful in engineering.

**Keywords:** off-axis conic surface; shape accuracy; auto-collimation; single CGH; hybrid compensation
