*3.1. Auto-Collimation Method*

First, we used the classical auto-collimation method to measure this OAP. The result can be seen as the real shape distribution of this OAP. According to Figure 1a, this OAP is located on the o ff-axis position. Meanwhile, a Φ150 mm flat mirror was chosen as the aiding optical element. A 6-inch Zygo interferometer (Middlefield, CT, USA) with an F/0.8 transmission sphere (TS) was used. The quality of this TS was 1/10λ (PV), and the shape error of the flat mirror measured via interferometry was about 0.1λ (PV). The corresponding error distribution is seen in Figure 5. According to Equation (1), the testing results can be reckoned as the error of OAP because the errors of TS and flat mirror were both far less than that of the OAP.

Due to its location on an o ff-axis position in Figure 5, the OAP was adjusted to guarantee the position accuracy by a five-dimension adjusting tool. In this measurement system, the adjustment processing is very di fficult because of a lack of alignment marks. Coma, astigmatism, and power aberration always exist because of the misalignment of di fferent optical elements. Therefore, adjusting experience is critical. After repeating the adjusting until there is almost no coma and astigmatism, a credible testing result will be obtained.

**Figure 5.** (**a**) Photo of auto-collimation for this OAP; (**b**) the error of flat mirror (PV = 0.096λ).
