*3.2. Single CGH Method*

Second, we tested this OAP with the single CGH method. Depending on the conditions of our laboratory, silica (Φ58 mm, n = 1.457081 and d = 6.028 mm) was chosen as the CGH basement. Before processing the CGH, this silica basement was processed by IBF (ion beam figuring) to guarantee that its shape error was less than 5 nm (RMS) and its wedge angle was less than 10 s. The geometry parameters of this measurement system are defined in Figure 6, from which the designing result of a customized single CGH could be conducted and is demonstrated in Figure 7. The CGH wavefront was designed using Zemax software and the etching map was generated by the specialized MATLAB program (Figure 3).

**Figure 6.** The geometry parameters of measuring this OAP with a single CGH.

**Figure 7.** (**a**) Simulated residual wavefront of the single CGH method (test CGH) in Zemax (PV = 0.0257λ, RMS = 0.0023λ); (**b**) simulation pattern of the customized CGH; (**c**) CGH photograph.

After obtaining the design result of the customized CGH seen in Figure 7b, photoetching was used to fabricate the CGH with high manufacturing precision. Even so, CGH still had some errors and the real error of CGH was very difficult to calibrate directly. According to the corresponding estimation method of the CGH error, the total CGH error was about 7.8 nm (RMS), which is a negligible value compared with the error of the OAP [19,20]. The customized single CGH includes three parts: the test CGH (the inner part), reflection CGH (the outer part), and three crosshairs (three orthogonal rectangular couples), which are attributed to different functions. The test CGH, which is a transmission CGH using first order diffraction, was fabricated by a grating groove depth of 692.2 nm. It can be seen that the test CGH is the most important because it was adopted to measure the shape of the OAP. As shown in Figure 7a, the residual wavefront of test CGH was only 0.0257λ (PV) and 0.0023λ (RMS). With a grating groove depth of 158.2 nm, the reflecting CGH, which made use of the third order diffraction, was used to align the interferometer and CGH. With a grating groove depth of 692.2 nm, three crosshairs, which were transmission CGHs using first order diffraction, were applied to align the OAP and CGH. The combined CGH was fabricated by photoetching, as shown in Figure 7c. The measurement experiment is shown in Figure 8 with an obvious crosshair. Relying on these crosshairs, it was easy to adjust the various optical elements to its own correct position.

**Figure 8.** Photo of measuring the OAP with the single CGH method.
