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Scattering and three-dimensional imaging in surface topography measuring interference microscopy

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journal contribution
posted on 01.04.2021, 07:35 by Rong Su, Jeremy Coupland, Colin Sheppard, Richard Leach
Surface topography measuring interference microscopy is a three-dimensional (3D) imaging technique that provides quantitative analysis of industrial and biomedical specimens. Many different instrument modalities and configurations exist, but they all share the same theoretical foundation. In this paper, we discuss a unified theoretical framework for 3D image (interferogram) formation in interference microscopy. We show how the scattered amplitude is linearly related to the surface topography according to the Born and the Kirchhoff approximations and highlight the main differences and similarities of each. With reference to the Ewald and McCutchen spheres, the relationship between the spatial frequencies that characterize the illuminating and scattered waves, and those that characterize the object, are defined and formulated as a 3D linear filtering process. It is shown that for the case of near planar surfaces, the 3D filtering process can be reduced to two dimensions under the small height approximation. However, the unified 3D framework provides significant additional insight into the scanning methods used in interference microscopy, effects such as interferometric defocus and ways to mitigate errors introduced by aberrations of the optical system. Furthermore, it is possible to include the nonlinear effects of multiple scattering into the generalized framework. Finally, we consider the inherent nonlinearities introduced when estimating surface topography from the recorded interferogram.

Funding

Metrology for precision and additive manufacturing

Engineering and Physical Sciences Research Council

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Revisiting optical scattering with machine learning (SPARKLE)

Engineering and Physical Sciences Research Council

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History

School

  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of the Optical Society of America A

Volume

38

Issue

2

Pages

A27 - A42

Publisher

Optical Society of America

Version

VoR (Version of Record)

Rights holder

© The Authors Journal © Optical Society of America

Publisher statement

This is an Open Access Article. It is published by the Optical Society of America under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

12/01/2021

Publication date

2021-02-01

Copyright date

2021

ISSN

1084-7529

eISSN

1520-8532

Language

en

Depositor

Prof Jeremy Coupland. Deposit date: 29 March 2021

Licence

Exports