Loughborough University
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On tilt and curvature dependent errors and the calibration of coherence scanning interferometry

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journal contribution
posted on 2017-05-19, 12:24 authored by Rong Su, Yang Wang, Jeremy CouplandJeremy Coupland, Richard K. Leach
© 2017, OSA - The Optical Society. All rights reserved.Although coherence scanning interferometry (CSI) is capable of measuring surface topography with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterize the performance of surface measuring instruments and offers considerable insight into the origins of these errors. Furthermore, from the measurement of a precision sphere, a process to calibrate and partially correct instruments has been proposed. This paper presents, for the first time, a critical look at the calibration and correction process. Computational techniques are used to investigate the effects of radius error and measurement noise introduced during the calibration process for the measurement of spherical and sinusoidal profiles. Care is taken to illustrate the residual tilt and curvature dependent errors in a manner that will allow users to estimate measurement uncertainty. It is shown that by calibrating the instrument correctly and using appropriate methods to extract phase from the resulting fringes (such as frequency domain analysis), CSI is capable of measuring the topography of surfaces with varying tilt with sub-nanometre accuracy.


This research was funded by the Engineering and Physical Sciences Research Council (EPSRC) (EP/M008983/1).



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Optics Express






3297 - 3310


SU, R. ...et al., 2017. On tilt and curvature dependent errors and the calibration of coherence scanning interferometry. Optics Express, 25(4), pp. 3297-3310.


© The Authors. Published by the Optical Society of America


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This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

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




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