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

Abstract

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 is the 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.

Maximum Acceptable Tilt Angle for Point Autofocus Microscopy

“…Each offset distance will undergo five repeated measurements to ensure data accuracy. The standard deviation σ of the measurement data and the expanded uncertainty u (k = 2) can be calculated using Formulas (10) and (11), respectively. n represents the number of repeated measurements, and e i represents the measurement error for the ith (1, 2, 3, 4, 5) group at each measurement position.…”

“…Similarly to other microscopic measurement systems, point autofocus microscopy has limitations, including a narrow measurement field of view and a small maximum acceptable tilt angle [ 10 ]. To effectively gather complete surface information from a complex and small component, multiple measurements and data stitching are typically required to keep the tested region within the microscopy’s maximum acceptable tilt angle [ 11 , 12 ]. However, this approach not only decreases the measurement efficiency but also amplifies potential errors [ 13 , 14 , 15 ].…”

Optimisation of Imaging Confocal Microscopy for Topography Measurements of Metal Additive Surfaces

“…Objective magnification refers to the optics under consideration; each has magnification, an NA, and a field of view (FoV) [24]. These values will influence the optical resolution and the slope limitation when measuring a single measurement area and, by extension, the total measurement area.…”

Commented review on refractive microlenses and microlens arrays metrology

“…As shown previously, the microlens surfaces are very smooth, and going above this limit by using scattered light seems to us almost unfeasible even if some work is currently done. 57,58 We have thus to look at the microscope objectives properties that are used in those optical surface profilers to estimate the limitations.…”