*4.1. Surface Roughness Evolution*

In general, surface roughness reduction is achieved, particularly a reduction of microroughness. This reduction depends among others on the initial roughness, which is clearly visible if the spatial frequency profile along a longitudinal and a cross-section are compared to each other (cf. Figure 12). Due to the mechanical preparation of the surfaces, characteristic grinding grooves were created on the surface (cf. Figures 4 and 5). The roughness perpendicular to these grooves (cross-section) was considerably higher than that parallel to these grooves (longitudinal section). Accordingly, the smoothing effect is different for these two directions. Although roughness spectra enable an evaluation of surface roughness, directional differences are not visible in these spectra. The

spectral analysis along a longitudinal section shows that almost all spatial frequencies larger than approximately *fy* ≈ 33 mm<sup>−</sup><sup>1</sup> (*λcr,y* ≈ 30 μm) are completely reduced to almost zero. In contrast, only spatial frequencies larger than approximately *fy* ≈ 83 mm<sup>−</sup><sup>1</sup> (*λcr,y* ≈ 12 μm) were effectively smoothed out along the cross-section. The main reason for this is that the initial surface features are much more pronounced perpendicular to the milling grooves than parallel to them. Furthermore, the scanning strategy creates surface features perpendicular to the scanning direction, such as a stripe-like structure due to the track offset (Figure 7l,q). Therefore, although it seems that spatial frequencies smaller than approximately *fy* ≈ 83 mm<sup>−</sup><sup>1</sup> and *fy* ≈ 33 mm<sup>−</sup><sup>1</sup> were not completely smoothed, it is more likely that the initial roughness within this range was actually smoothed, but additional process-inherent surface features were created. This would explain the heterogeneity in the micro-roughness for these specific spatial frequencies.
