The primary of the large optical telescope can be divided into segments. The design breakthroughs the limitation of aperture. It makes the ground-based telescope of 30-meter scale possible using building-block approach, or conversely, launching 10-meter telescope to space by fitting the folded primary mirror into the rocket fairing.
However, according to Gauss theorem egregium, the curved aspherical surface cannot be separated into segments which are identical in shape and size and separated by uniform gaps. Segmentation outcomes significantly impact telescope construction. It will lead to variations in shape and mass distribution among segments to which the support assembly is extremely sensitive. Therefore, the segmentation of primary is not only a theoretical concern, but also a practical difficulty in engineering.
Recently, NIAOT researcher team lead by associate Prof. Zheng Yi presented a novel segmentation approach using inverse map projection. The research is published in renowned international journal “Applied Optics” in July 2021.
First, the curvature of the primary mirror of the telescope is quantitatively studied, and eight patterns of projection are put forward. It concluded that a large optical primary mirror with a solid angle less than (p/6) can be well divided by projecting identical hexagonal tilings from flat surfaces onto curved ones.
Fig. 1. Hexagonal tiling patterns and coverage. (a)Hexagonal tiling in a plane; (b)–(f ) tiling on a conical surface with the number of sectors ranging from 5 to 1; (g) tiling on cylindrical tube; (h) best covering areas on a sphere; (i)Goldberg polyhedron.
Based on cartographic projections, three approaches were presented. The conformal method preserved the angle locally, providing optimal regularity. The equal-area algorithm generated zero area variation partition. The equidistant projection minimized the CD of the segments. They were unified by the newly developed compromise approach.
Numerical analysis using the Thirty Meter Telescope model verified its validity (reference to Fig. 2). It not only integrated the merits of the three conventional projections but also provided the adjustment range necessary for individual preferences. Telescope expert Larry Stepp gave good remarks to the study as “The paper is well-written and well-illustrated with figures. It will be a valuable addition to the literature about design of segmented mirrors.” The importance of study was also recognized by reviewer.
Fig. 2. Row from top to bottom: segments irregularities, area variations, and circumscribed diameters. Column from left to right: the conformalinverse projection, equal-area method, and equidistant approach
The team also devoted to the fabrication of primary segments. Participating the international collaboration program Thirty Meter Telescope (TMT), the team finished the grinding of the Type 63 segment on 5-axis CNC tool machine whose profile is irregular, and interface complicated in space orientation. The test result is evaluated highly by TMT.
Fig. 3. TMT segment Type 63 profile grinding and testing. (a) Fabrication on a 5-axis CNC tool machine. (b) Testing on CMM machine.
The team includes senior engineer Bin Liang, associate researcher Ying Li and doctoral student Lifeng Tang. They are the coauthors of research paper. The work is supported by National Natural Science Foundation of China (11973008, U1731134); International Science and Technology Cooperation Program of China (2015DFG02710).
Thirty Meter Telescope report (https://www.tmt.org/image/tmt20210203a)
