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

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.