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

精密透镜和反射镜被用于许多应用——用于天文学的地面望远镜、观测太空或地面的卫星、制造半导体“芯片”的机器（用于计算机到移动电话……）、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分为两个阶段。首先，用硬砂轮研磨玻璃坯，切割材料，将玻璃挤出基本的弯曲形状。然后用某种形式的衬垫摩擦玻璃表面，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。在过去的十年中，光学行业经历了计算机数控（CNC）的磨削和抛光过程的革命。该项目涉及两家在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（最初从UCL在该领域的研究中剥离出来）生产CNC抛光机和测量设备。克兰菲尔德精密有限公司（Cinetic Landis的一个部门）生产数控磨床。这种数控机床几乎总是以标准的前后光栅模式或螺旋路径（通过旋转工件）在表面上移动研磨或抛光工具。栅格或螺旋是一种特殊的情况，因为它没有交叉，这简化了计算如何去除累加。但是，就像拖拉机犁地一样，这些路径在地表留下了规则的“沟”。虽然这些可能只有纳米深（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。有各种各样的平滑表面的方法来去除这些规则特征，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，而这些签名本身必须被删除……有时看起来像是一个无穷无尽的圆圈！新的研究将通过使用先进的数学方法来产生更复杂的刀具路径，这些路径在无数个点上相互交叉，并产生自然的平均效果，从而打破这种模式。我们称之为“超交叉路径”。此外，抛光机能够“在飞行中”改变抛光点的大小。原则上（通过正确的数学计算），当工具在表面上移动时，点的大小可以主动调整，以攻击不同尺寸的表面特征。我们计划开发这个新想法，并相信它将在更短的时间内带来卓越表面的突破。结果如何呢？这些将被纳入合作伙伴公司的标准软件，提高他们的竞争地位。研究结果也将用于北威尔士国家超精密表面设施的机器上，该设施由格林多尔大学与伦敦大学学院合作运营。这将增强光学制造能力，以支持英国科学和我们的海外合作者。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，以合作开发光学领域以外高精度表面应用的应用和原型，例如医疗假体关节。

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.