Optical metrology to support the next generation of nanopositioning

可追溯位移测量对许多制造过程和研究任务至关重要，可以追溯到任何有意义的测量比较所需的米的SI定义。一系列技术能够实现亚纳米不确定度的可追溯测量；然而，所有这些最终都可以追溯到光的波长，因此可以追溯到测量位移的光学干涉法。在纳米尺度上，位移测量光学干涉仪的测量不确定度主要受非线性影响，即被测相位（以及位移）的误差与照明光波长的谐波呈周期性变化。目前，商用干涉仪可以实现1 - 0.1 nm的非线性，一些最先进的干涉仪设计在理想情况下可以达到个位数皮米的非线性。目前能够实现个位数皮米非线性的所有干涉仪设计在测量范围，成本或光学复杂性方面都有局限性，并且如果没有针对高度线性的x射线干涉仪进行仔细优化，是否可以实现这种低非线性仍然不清楚。因此，能够实现皮米非线性的现有干涉仪设计不太适合许多实际的位移测量任务，特别是下一代纳米定位设备的表征和校准。本项目将研究：通过模拟理想的涂层设计和改进对涂层过程的控制来改进相正交薄膜涂层。将研究具有偏振无关相位响应的相积涂层的制备。一个模型能够评估复杂的非线性源产生由于干涉光学内部的多重反射将被开发。该模型将允许研究高阶多次反射的影响，以及极化泄漏引起的高阶效应。将研究当前国家物理实验室干涉仪设计中非线性的来源。这将涉及实际测量和先前描述的建模方法的应用。将研究改进干涉仪的设计，消除先前确定的非线性源。最后，改进的干涉仪设计将应用于纳米定位阶段的表征和校准。为了回答这些问题（学生将实际做什么），相位正交薄膜涂层用于NPL干涉仪，在干涉仪的正交输出之间引入90的相位变化。通过优化镀膜设计和镀膜工艺，可以使干涉仪的信噪比最大化，使干涉仪之间的非线性变异性最小化。薄膜涂层工艺也必须优化，以生产所需的极薄（2 - 20nm）薄膜。为了改进干涉仪的设计，必须了解现有设计中非线性的来源。要做到这一点，需要一种建模技术，既可以处理吸收薄膜涂层，也可以处理偏振光学，同时处理多次反射和多次通过偏振光学的高阶效应，而不需要求助于有限的n阶计算。这样一个模型的发展允许研究不完善的光学涂层和元件对干涉仪最终非线性的影响，这是传统的琼斯微积分方法无法做到的。一旦确定了非线性的来源，该模型还可以用于研究消除来源的潜在方法。

Traceable displacement measurement is of vital importance to many manufacturing processes and research tasks, with traceability back to the SI definition of the metre required for any meaningful comparison of measurements to be made. A range of technologies are capable of traceable measurements with sub-nanometre uncertainties; however, all are ultimately traceable back to the wavelength of light and therefore to displacement measuring optical interferometry. At the nanoscale, the measurement uncertainty of displacement measuring optical interferometers is dominated by non-linearities, errors in the measured phase (and therefore displacement) that are periodic with harmonics of the wavelength of the illuminating light. Commercial interferometers currently achieve non-linearities of 1 - 0.1 nm, with some state of the art interferometer designs reaching single digit picometre non-linearities under ideal circumstances. All interferometer designs currently capable of achieving single digit picometre non-linearities have limitations, in measurement range, cost or optical complexity, and whether such low non-linearities can be achieved without careful optimisation referenced against a highly linear X-ray interferometer remains unclear. Existing interferometer designs that are capable of picometre non-linearities are therefore poorly suited to many practical displacement measurement tasks, in particular the characterisation and calibration of the next generation of nanopositioning devices.This project will investigate: Improved phase-quadrature thin film coatings through the modelling of ideal coating designs and improvement of control over the coating process. The fabrication of phase-quadrature coatings with a polarisation independent phase response will be investigated. A model capable of assessing the complex non-linearity sources that arise due to multiple reflections within interferometer optics will be developed. This model will allow investigation of the effects of higher order multiple reflections, and higher order effects due to polarisation leakage. Sources of non-linearity in current NPL interferometer designs will be investigated. This will involve both practical measurements, and the application of the previously described modelling approach. Improved interferometer designs will be researched, eliminating the non-linearity sources previously identified.Finally, improved interferometer designs will be applied to the characterisation and calibration of nanopositioning stages. The approach that will be taken to answer these questions (what the student will actually be doing) Phase-quadrature thin film coatings are used in NPL interferometers to introduce a phase change of 90 between the quadrature outputs of the interferometer. By optimising the coating design and coating process the signal to noise ratio of the interferometer will be maximised, and the variability of the non-linearities between interferometers minimised. The thin film coating process must also be optimised for the production of the very thin (2 - 20 nm) films required. In order to improve upon interferometer designs, the sources of non-linearity in existing designs must be understood. To do this, a modelling technique is required that can handle both absorbing thin film coatings, and polarising optics, whilst treating the higher order effects of multiple reflections and multiple passes through polarising optics without recourse to limited nth order calculations. The development of such a model permits the investigation of the effects of imperfect optical coatings and components on the final non-linearity of the interferometer in a way that would not be possible with a conventional Jones calculus approach. Once the sources of non-linearities are identified, the model can also be used to investigate potential ways to eliminate the source.