Optical metrology to support the next generation of nanopositioning

Lead Research Organisation: CRANFIELD UNIVERSITY
Department Name: Sch of Aerospace, Transport & Manufact


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.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R511894/1 30/09/2017 29/09/2022
2199198 Studentship EP/R511894/1 30/09/2017 29/09/2021 Angus Bridges
Title strapy (Scattering TRAnsfer matrix model PYthon) 
Description strapy (Scattering TRAnsfer matrix model PYthon) is python package implementing the combined transfer and scattering matrix modelling approach described in A. Bridges, A. Yacoot, T. Kissinger, R. P. Tatam, "Polarisation-sensitive transfer matrix modelling for displacement measuring interferometry", Applied Optics 59, 7694 (2020). 
Type Of Material Computer model/algorithm 
Year Produced 2020 
Provided To Others? Yes  
Impact The combined scattering and transfer matrix model has permitted sources of non-linearities in a range of optical interferometer designs within the NPL to be identified. The ability to identify and model complex non-linearity sources has allowed for improved interferometer designs to be developed. 
URL https://strapy.readthedocs.io/en/latest/introduction.html