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.

Modeling the Draper machine for finishing optical surfaces.

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Publications

B1999

Bennett, T.L.: Best approximation in quotient spaces with application to the finishing of optical surfaces. PhD, University of Pittsburgh, Pittsburgh, PA (1999). [link].

NAOJ

Photos of Construction Work of Subaru Telescope. National Astronomical Observatory of Japan. (1999). Accessed: 2016-08-16. [link].

PH1996

Porsching T.A. and Hall C.A.: Computationally directed axisymmetric aspheric figuring (after N. J. Brown). Appl. Optics, 35(22), 4463-4470 (1996). [link].

PHB1998

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].

PHBE1993

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].