Contraves Inc. our industrial partner needed mathematical guidance to efficiently fabricate the world’s largest single-piece optical element, an 8.3-meter telescope primary mirror. This component now serves as the principal optical component for the Subaru Telescope, sponsored by the National Astronomical Observatory of Japan [NAOJ].
Operator controlled abrasive finishing of aspherical optical surfaces applies a general mathematical theory of abrasive material removal developed by Porsching and Hall in [PHBE1993] to determine non-negative dwell times for polishing machine settings [PH1996], [PHB1998], [B1999].
The Draper machine is configured as depicted in the following schemeatic. We modelled the dynamics of the Draper machine, ultimately leading to software implementing the operator controlled fabracation process.
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- Bennett, T.L.: Best approximation in quotient spaces with application to the finishing of optical surfaces. PhD, University of Pittsburgh, Pittsburgh, PA (1999). [link].
- Photos of Construction Work of Subaru Telescope. National Astronomical Observatory of Japan. (1999). Accessed: 2016-08-16. [link].
- Porsching T.A. and Hall C.A.: Computationally directed axisymmetric aspheric figuring (after N. J. Brown). Appl. Optics, 35(22), 4463-4470 (1996). [link].
- Porsching T.A., Hall C.A., and Bennett T.L.: Minimax Approximation of Optical Profiles. SIAM J. Appl. Math., 58(6), 1951-1968 (1998). [link].
- Porsching T.A., Hall C.A., Bennett T.L., and Ernsthausen J.M.: A mathematical model of material removal with application to CNC finishing. Mathl. Comput. Modeling, 18(7), 25-40 (1993). [link].