Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies

This paper addresses computer numerical control (CNC) polishing of aspheric or freeform optics. Prior CNC grinding of the asphere tends to produce mid-spatial frequencies (MSFs) at some level. Precessions polishing can rectify these, but the very ability of the bonnet tooling to adapt to the local asphere enables it to do so, at least in part, to similar spatial frequencies in the MSFs. To accelerate smoothing, hard tools can, in principle, be used, but aspheric misfit is often assumed to preclude this. In this paper, we explore new insight into the role of abrasive particle size in accommodating misfit. First, we report on a glass-bending rig to produce a continuous range of complex surfaces, while withstanding process forces. Then, we describe how this was used to evaluate the triangle of misfit, abrasive size, and MSFs produced for hard rotating tools. This has revealed a regime in which such tools can be used without introducing significant new MSFs, as evidenced by manufacture of prototype off-axis aspheric segments for the European Extremely Large Telescope project.