Improving coherence scanning interferometry signal modelling and topography measurement for complex surfaces

Thomas, Matthew (2022) Improving coherence scanning interferometry signal modelling and topography measurement for complex surfaces. PhD thesis, University of Nottingham.

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This thesis presents work on advanced optical surface metrology methods that enable extending the range of surface slopes that can be reliably measured by optical surface topography measurement instruments, and on investigating the reliability of the current capability. Optical instruments can only capture a limited portion of light scattered from an object’s surface, determined by the instrument’s numerical aperture. As the surface measured becomes steeper, less scatter is captured until all specular scatter is lost, referred to as the specular reflection limit (SRL). While surface measurement of slopes beyond the SRL by modern instruments is possible via the capture and detection of non-specular scatter, the instrument response to these slopes is not well understood. In addition, as the non-specular scatter has a low signal-to-noise ratio, data dropout can occur. Topography measurement of steep and complex surfaces using optical methods can therefore be challenging and have an unknown reliability, and can have significant errors when multiple scattering is present.

The instrument modelling and experimental work focussed on coherence scanning interferometry (CSI). Through use of an approximate linear model the instrument response of a CSI instrument to various slope angles and spatial frequencies was described by a three-dimensional (3D) surface transfer function (STF). This theory was experimentally verified by demonstrating that an experimental 3D STF obtained from measurement of microspheres can be used to generate a filter that can compensate for the effect of lens aberration at a fundamental level and consequently reduce errors in the topographies obtained, especially from surface slopes just below the SRL. Second, a rigorous two-dimensional boundary element method (BEM) model of electromagnetic surface scatter was verified through multiple comparisons including an exact analytical Mie scatter solution and through experimental comparison to measurement data from a laser scatterometer, providing evidence of the BEM model’s capability to accurately predict scatter from complex surfaces, including those that linear models cannot accurately model. A CSI model based on this BEM scattering model was then developed and verified, demonstrating the model’s capability to accurately model the CSI signal for complex surfaces which contain steep surfaces, including those that produce multiple scattering. Using this BEM-CSI model and experimental measurement, the capability of optical surface topography measurement methods for measurement of steep surfaces was investigated, illustrated for the first time with both fringe data and the resulting height estimates for a series of surfaces at slopes steeper than the SRL. At high tilt angles it was found that sharp edges with undercuts still provide strong signals which appear as plateaus in the topography data, with a width corresponding to the width of the point spread function of the instrument. While phase information was lost, part of the topography could still be obtained from the non-specular scatter. The BEM-CSI model’s results were accurate even for challenging surfaces beyond the capabilities of linear models, providing a tool for future investigation of other complex surfaces and providing progress towards evaluating the measurement uncertainty of complex surface measurements by optical instruments.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Leach, Richard
Su, Rong
Keywords: Surfaces; Optical measurements; Interferometry; Boundary element methods
Subjects: Q Science > QC Physics > QC350 Optics. Light, including spectroscopy
T Technology > TA Engineering (General). Civil engineering (General)
Faculties/Schools: UK Campuses > Faculty of Engineering > Department of Mechanical, Materials and Manufacturing Engineering
Related URLs:
Item ID: 71686
Depositing User: Thomas, Matthew
Date Deposited: 24 Aug 2023 07:23
Last Modified: 24 Aug 2023 07:50

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