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

精密透镜和反射镜的用途非常广泛--地面天文望远镜、仰视太空或俯视地面的卫星、制造半导体芯片的机器(从电脑到手机……)、国防系统、激光系统和许多其他应用。精密光学的制造基本上是一个两个阶段的过程。首先，用切割材料的硬砂轮研磨一块玻璃毛坯，将玻璃磨出基本的曲面形状。然后用某种形式的衬垫来摩擦表面，使用抛光化合物的水浆--过去是红色的胭脂，现在是白色的氧化铈粉末--来抛光玻璃。在过去的十年中，光学行业经历了一场磨削和抛光过程的计算机数字控制(CNC)革命。该项目涉及两家在这两种类型的机器和工艺方面都非常出色的合作公司。Zeeko有限公司(最初是从UCL在这一领域的研究中剥离出来的)制造数控抛光机和测量设备。Cranfield Precision Ltd(Cinetic Landis的一个部门)生产数控磨床。这类数控机床几乎总是以标准的来回栅格图案或螺旋路径(通过旋转工件)在表面上移动磨削或抛光刀具。栅格或缓和曲线是一种特例，因为它不会在任何地方穿过自身，这简化了删除累加的计算。但是，就像拖拉机犁地一样，这些小路在地面上留下了规则的“犁沟”。虽然它们可能只有纳米深(只有几十个原子)，但它们会在望远镜或相机的图像周围产生杂散光。有多种平滑曲面的方法可以删除这些常规特征，但这需要额外的时间。此外，每个额外的进程都会留下自己的签名，而签名本身必须被删除……在有时看起来像是无穷无尽的循环中！这项新的研究将打破这种模式，使用先进的数学方法来生成更复杂的刀具路径，这些路径在无数个点上相互交叉，并产生自然的平均效果。我们称这些为“超交叉路径”。此外，抛光机能够‘动态’改变抛光点的大小。原则上(在正确的数学计算下)，当工具在表面上移动时，可以主动调整光点大小以攻击不同大小的表面特征。我们计划开发这一新想法，并相信它将在更短的时间内在更高的表面上取得突破。结果如何？这些将被纳入合作伙伴公司的标准软件，增强它们的竞争地位。这一结果也将被用于北威尔士国家超精密表面设施的机器上，该设施由格林德沃大学与伦敦大学学院合作运营。这将增强制造光学器件的能力，以支持英国科学公司和我们的海外合作伙伴。除此之外，我们计划将研究结果传播给更广泛的英国学术界和制造业，以合作开发应用程序和原型，用于光学领域以外的高精度表面应用，例如医疗假肢关节。

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.