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

精密透镜和镜子被用于许多应用--用于天文学的地面望远镜、仰望太空或俯视地面的卫星、制造半导体“芯片”的机器（从计算机到移动的手机.），国防系统、激光系统和许多其他应用。精密光学器件的制造基本上是一个两阶段的过程。首先，玻璃坯件用切割材料的硬砂轮研磨，以将玻璃拱出基本的弯曲形式。然后用某种形式的抛光垫摩擦玻璃表面，使用抛光化合物的水浆-旧时代的红色胭脂，今天的白色氧化铈粉末。在过去的十年中，光学行业经历了一场磨削和抛光工艺的计算机数控（CNC）革命。该项目涉及两个合作伙伴公司在这两种类型的机器和工艺卓越。Zeeko有限公司（最初从UCL在该领域的研究中分离出来）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CNC机床几乎总是以标准的来回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。光栅或螺旋线是一种特殊情况，因为它没有任何地方穿过自己，这简化了计算如何删除加起来。但是，就像拖拉机耕地一样，这些路径在表面留下规则的“犁沟”。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中的图像周围产生杂散光。有多种方法可以平滑曲面以去除这些规则特征，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，而签名本身必须被删除。有时似乎是一个无止境的循环！新的研究将打破这种模式，通过使用先进的数学方法来生成更复杂的刀具路径，这些路径在无数点处相互交叉，并产生自然的平均效果。我们称之为“超交叉路径”。此外，抛光机能够“在运行中”改变抛光点尺寸。原则上（并与正确的数学）斑点的大小可以积极调整，以攻击不同大小的表面特征，因为工具在表面上移动。我们计划发展这个新的想法，并相信它将导致在更短的时间内突破上级表面。这些将被纳入合作伙伴公司的标准软件中，以提高其竞争地位。研究结果还将用于北威尔士国家超精密表面设施的机器上，该设施由Glyndwr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界，以合作开发光学领域以外的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.