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Optical topography measurement of steeply-sloped surfaces beyond the specular numerical aperture limit

Thomas, Matthew; Su, Rong; de Groot, Peter J.; Leach, Richard K.


Matthew Thomas

Rong Su

Peter J. de Groot


Peter J. de Groot

Pascal Picart


Engineered functional surfaces often feature varying slopes on macro- and micro-scales. When surfaces are mirror-like, the highest surface slope that can be measured by a far-field 3D imaging optical surface measuring instrument isthe arcsine of the numerical aperture (NA) of the objective lens, i.e. the acceptance angle of the lens. However, progress in instrument design has allowed for measurement of non-specular surfaces with slopes steeper than this “traditional” NA limit. Nonetheless, there is currently a lack of understanding about the instrument response to surfaces with steep slopes beyond this limit. It is unclear over what surface spatial frequencies we can expect to accurately report fine surface-feature details. Here we present results demonstrating the capability of a commercial coherence scanning interferometer for measuring surface topography of a roughened flat and a blazed grating with tilt angles greater than the NA slope limit. We show that the surface form, i.e. the tilted plane, can be measured correctly. But, while surface texture information that can appear useful is also obtained, tilting significantly influences the measurement accuracy of micro-scale texture, and for asymmetric gratings, can depend on the tilting direction. A simplified surface scattering model suggests that the loss of scattered power captured by the instrument and a low signal-to-noise ratio causes the reduction of measurement accuracy. However, a rigorous three-dimensional instrument model is needed for a full understanding; we will develop this in our future work.


Thomas, M., Su, R., de Groot, P. J., & Leach, R. K. (2020). Optical topography measurement of steeply-sloped surfaces beyond the specular numerical aperture limit. Proceedings of SPIE, 11352,

Journal Article Type Conference Paper
Conference Name Optics and Photonics for Advanced Dimensional Metrology
Acceptance Date Mar 4, 2020
Online Publication Date Apr 1, 2020
Publication Date Apr 1, 2020
Deposit Date Apr 22, 2020
Publicly Available Date Apr 22, 2020
Journal Proceedings of SPIE
Print ISSN 0277-786X
Publisher Society of Photo-optical Instrumentation Engineers
Peer Reviewed Peer Reviewed
Volume 11352
Article Number 1135207
Public URL
Publisher URL


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