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J. Eur. Opt. Society-Rapid Publ. 21, 30( 2025)
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2. Two examples of polishing flowers and the covered area.
close to production. Nevertheless, a targeted evaluation of the data should take priority over a machine learning model.
7.3 Error estimation
The overall uncertainty in this investigation arises from three main sources: the calculation of relative velocity, the interferometric measurement of material removal, and the spatial registration between both datasets. Each of these contributes differently to the final correlation and must be considered separately.
The relative velocity field is derived from machine kinematics, assuming ideal rotational and oscillatory motion. The workpiece rotation is considered constant and known( e. g., 5 rpm), and the oscillation amplitude and frequency of the lever arm are estimated from machine settings and video analysis. The spatial resolution of the velocity field is limited by the frame rate and pixel size of the recording camera, resulting in a quantization of approximately 1 mm / pixel. Uncertainties in rotation speed(± 0.5 rpm), pivot length(± 2 mm), and angular amplitude(± 1 °) propagate into a local velocity uncertainty of approximately ± 4.7 mm / s, corresponding to a relative error of ~ 8 %.
Material removal is assessed by comparing interferometric surface measurements before and after polishing. As in-situ measurement is not possible, the part must be removed from the machine and re-clamped in the interferometer. Due to the limited size of the measurement cavity, large components must be measured in multiple positions, requiring rotational or lateral shifting. This introduces the risk of alignment error, curvature mismatch, and stitching artifacts. Additionally, the mismatch between the cavity and the surface curvature causes reference wavefront distortion, especially near the edges of the measurement field. The resulting shape deviation error is estimated between ± 50 and ± 100 nm. In combination with re-clamping, the spatial registration uncertainty is approximately ± 0.5 – 1mm.
The removal map is manually overlaid onto the velocity map. Due to the independent origins of both datasets, any translational or angular misalignment during overlay will directly affect local correlations. Given the abovementioned spatial registration error and the pixel resolution of the velocity field, the effective correlation window is subject to positional uncertainty. The error introduced in the assignment of removal to velocity vectors is estimated to be on the order of one to two pixels.