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This paper describes a fabrication process for the hyperboloidal concave mirror of a 46.5-nm telescope. The 180-mm aperture hyperboloidal concave mirror and 70-mm aperture compensator are machined directly from chemical mechanical polishing (CMP) of a spherical surface to a high-accuracy aspherical surface by ion beam figuring (IBF). The aspherical measurement method is the Dall null test. To minimize system errors in the measurement process, the rotational measurement method with six rotations is used in the null test. The results of the analysis for the ME (first solve the machined surface profile, then solve the system errors) and EM (first solve the system errors, then solve the machined surface profile) methods of calculation in the measurement are given. The ME method is a more accurate rotational test method, and the six rotations are appropriate for rotational measurements. After the figuring process, the hyperboloidal concave mirror surface profile reached 8.27 nm RMS and the compensator surface profile is approximately 4 nm RMS. The roughness of the hyperboloidal concave mirror is smooth to 0.160 nm RMS.
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