This paper describes the application of loose-abrasive processes to the manufacture of 1.4 meter, off-axis aspheric, hexagonal mirror-segments. These are prototypes for the 39 m European Extremely Large Telescope (E-ELT). The application of active forces to correct the overall form of segments in the telescope, means that the overall form-accuracy achieved in polishing can be less critical than for a non-active mirror. However, it is a requirement that the base-radii and conic constants of mirror-segments are very closely matched, so that the combined image is not degraded. This means that abrasive processes have to operate with respect to an absolute rather than relative datum. Furthermore, there are stringent requirements on mid-spatial frequency defects on segment surfaces, and on edge-roll. These control stray-light, and ultimately detectability of faint astronomical targets. We describe the CNC abrasive techniques we have developed in response. We then demonstrate the success of the approach, which represents the first time ever that segments have been processed entirely in the hexagonal shape:- a milestone in loose-abrasive processing. Finally, we address up-scale for the unprecedented number of segments required for the E-ELT build-phase.
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