In this article, the measurement method of convex hyperboloid using Hindle sphere is further studied. Firstly, the precise analytical formulas for solving radius of curvature, the diameters of outer edge and inner hole of Hindle sphere mirror are developed. The formula can be degenerated to the common approximate formula under certain conditions. In addition, the semi exact analytical formulas for solving the parameters of auxiliary Hindle sphere mirror are derived under some conditions, and the approximate formula is further extended to other occasions of aspheric mirror test, and a feasible stitching detection scheme for the secondary mirror of the CFGT (China Future Giant Telescope) is given. Then, based on the aberration theory, using Hindle auxiliary sphere, the relationships and formulas of the measurement error of vertex radius of curvature of convex hyperboloid mirror caused by the adjustment of interferometer position, the mirrors spacing, and machining error of radius of curvature of the Hindle sphere mirror are obtained, and the Zemax optical software is used for simulation verification.
The primary mirrors of several large ground-based astronomical telescopes currently in the research or planning phases, such as TMT (Thirty Meter Telescope), ELT(Extremely Large Telescope) and LOT (Large Optical /infrared Telescope), take the form of a segmented array telescope. The fabrication of hundreds of off-axis aspheric segments is one of the key technologies for their development. Our proposed stressed mirror continuous polishing (SMCP) method combines the stressed mirror polishing (SMP) and continuous polishing (CP) technologies. The combined technologies deliver high-quality surface smoothness of the SMP technique with the high efficiency of continuous polishing. Nanjing Institute of Astronomical Optics & Technology (NIAOT) and TMT have carried out in-depth cooperation in the segment fabrication of the primary mirror. NIAOT is currently working on the development of off-axis aspheric segments. In this article, the progress for the 5m continuous polishing machine and ancillary equipment, the stress loading test on a 1.52 meter segment, the calibration of our 2-dimensional contact-metrology device and the reference mirror calibration are introduced here in detail.
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