Novel Mathematical Techniques for Advanced Tool-paths to Transform High-value Optical Fabrication

Precision lenses and mirrors are used for a host of applications - ground-based telescopes for astronomy, satellites looking up at space or down at the ground, machines to make semiconductor 'chips' (for computers to mobile phones...), defence systems, laser-systems and numerous other applications.

The manufacture of precision optics is basically a two-stage process. First a glass blank is ground with a hard grinding wheel that cuts the material, to hog out the glass to the basic curved form. The glass is then polished using some form of pad that rubs the surface, using a water-slurry of a polishing compound - red rouge in the old days, white cerium oxide powder today.

Over the last decade, the optics industry has experienced a revolution in computer numerical control (CNC) of both the grinding and polishing processes. The project involves two partner companies pre-eminent in both types of machine and processes. Zeeko Ltd (originally spun out of UCL research in this field) manufactures CNC polishing machines and measurement equipment. Cranfield Precision Ltd (a division of Cinetic Landis) produces CNC grinding machines.

Such CNC machines almost always move the grinding or polishing tool across the surface in a standard back-and-forth raster pattern, or in a spiral path (by rotating the work-piece). A raster or spiral is a special case, because it crosses itself nowhere, and this simplifies calculating how the removal adds up. But, just like a tractor ploughing a field, these paths leave regular 'furrows' in the surface. Whilst these might be only nanometres deep (just tens of atoms) they cause stray light around an image in a telescope or camera.

There are various ways of smoothing surfaces to remove these regular features, but this takes additional times. Moreover, each extra process leaves its own signature, which itself has to be removed ... in what sometimes seems like an endless circle!

The new research will break out of this mould by using advanced mathematical methods to generate more complex tool-paths, which cross each other at myriads of points, and give a natural averaging effect. We call these 'hyper-crossing paths'. Furthermore, the polishing machines are able to change the polishing spot size 'on the fly'. In principle (and with the right mathematics) spot-size could be actively tuned to attack different sizes of surface-feature as the tool moves across a surface. We plan to develop this new idea, and are confident it will lead to a break-through in superior surfaces in less time.

And what of the results? These will be incorporated in the standard software of the partner companies, enhancing their competitive position. The results will also be used on the machines at the National Facility for Ultra-precision Surfaces in North Wales, operated by Glyndwr University in partnership with University College London. This will give enhanced capability for manufacturing optics to support British Science and our overseas collaborators. Beyond this we plan to disseminate the findings to the wider UK academic and and manufacturing communities to collaborate on and develop applications and prototypes for applications in high precision surfaces outside of the optics sector e.g. medical - prosthetic joints.