*3.4. Surface Roughness*

A detailed examination of the resulting surface roughness is carried out based on a systematic analysis of WLI data for each set of process parameters investigated. Figure 10a shows the surface roughness Sa as a function of the spatial wavelength (Sa spectrum) for the laser fluences investigated. Several observations are directly apparent for the smallest laser beam size Q100. The high standard deviation is due to the large number of craters on the surface (Figure 7b–e), so that the evaluation strongly depends on the number and the geometrical dimensions of the craters. Since the WLI data were measured at five randomly selected positions, this very high standard deviation results from large differences in the measured surface topographies. Furthermore, for fluences up to about 10–11 J/cm2, only a small reduction in micro-roughness up to a spatial wavelength of approximately 10 μm was obtained. In contrast to the other fluences, a high number of craters were formed for these fluences, which even led to a significant increase in macro-roughness. A significant reduction in micro-roughness up to a critical wavelength of approximately 80 μm was achieved only for the highest fluence of *F* = 12 J/cm2. However, this laser remelting process was accompanied by a significant evaporation of material. Furthermore, a characteristic stripe structure is visible in the micrograph (Figure 7f), which indicates that the remelting process had changed from a discrete pulsed process to a continuous remelting process. Nonetheless, the lowest surface roughness was achieved for *Fpol* = 12 J/cm2, so that this was determined as laser polishing fluence *Fpol*.

**Figure 10.** (**a**) Sa spectrum for Q100 and (**b**) Sa spectrum for Q400 each for fluences ranging from 4 to 12 J/cm2.

The Sa spectrum for Q400 is significantly different in comparison (Figure 10b). At a fluence of approximately 4 J/cm2, remelting of the surface started, and a reduction of micro-roughness was achieved for spatial wavelengths up to 10 μm. The reduction in micro-roughness and the critical wavelength were continuously increased for larger fluences. The critical wavelength was increased up to approximately 80 μm for fluences in the range of approximately 8–10 J/cm2. However, at 10 J/cm2, the visible evaporation of material already accompanies the remelting process, and characteristic stripes in the distance of the track offset are visible again on the remelted surface (Figure 7q). Laser polishing fluence at which the minimal roughness was achieved is approximately at *Fpol* = 8 J/cm<sup>2</sup>

The series of Sa spectra is completed by Q200 (not shown) and exhibits qualitatively the same interdependencies as the Sa spectrum for the larger laser beam Q400. For Q200, the minimal roughness was achieved at *Fpol* = 9 J/cm2. To conclude the analysis by Sa spectra, the lowest surface roughness for their respective beam dimensions and laser polishing fluence are compared in Figure 11a, while Figure 11b shows roughness evolution as a function of area rate for different spatial wavelength intervals. These comparisons reveal several insights. Firstly, it is revealed that the critical wavelength (*λcr* = 80 μm) is almost the same for all laser beam dimensions investigated. Secondly, laser polishing fluence increases for decreasing laser beam dimensions. Thirdly, for the larger laser beam size, a greater reduction particularly in micro-roughness was achieved. Fourthly, the achieved surface roughness for Q200 and Q400 are almost the same. Finally, macro-roughness was not reduced by any combination of process parameters, but process-inherent surface features were generated, which led even to an increase in macro-roughness. Furthermore, Figure 11b demonstrates explicitly that the minimal roughness achieved does not depend on area rate. This result is principally the same for each specific spatial wavelength interval up to 40 μm. Therefore, the results indicate that the area rate can be increased without an increase in resulting surface roughness after LμP. In this study, the area rate was increased by a factor of 16 from 1.2 cm2/min to 19.2 cm2/min (Figure 11b), while the required laser polishing fluence was reduced from approximately 12 to 8 J/cm<sup>2</sup> at the same time (Figure 11a). This led to an overall reduction of energy input by approximately 33%.

**Figure 11.** (**a**) Sa spectrum for the lowest surface roughness and laser polishing fluences achieved with each tool Q100, Q200, and Q400; (**b**) roughness Sa as a function of area rate and spatial wavelength at laser polishing fluence.

Sa spectra analyze the areal surface roughness but do not allow for any differentiation regarding a reduction in roughness depending on the orientation of surface features, such as grinding or milling grooves. The initial surface showed a strong heterogeneity regarding the directional roughness, since the milling grooves had a dominant direction, so that the roughness perpendicular to the grooves was significantly higher than parallel to them (cf. Figures 4 and 5). Therefore, a representative WLI measurement of the surface showing the lowest roughness after laser polishing was analyzed by 1D FFT analysis along two perpendicular sections (Figure 12a). The 1D FFT analysis provides a frequency spectrum for each section, which was then compared to a similar analysis of the initial surface (Figure 5).

**Figure 12.** (**a**) WLI image of LμP surface exhibiting the lowest surface roughness (Q400, *F* = 8 J/cm2); (**b**) cross-section along the marked line in WLI image and corresponding (**c**) Fourier analysis; (**d**) longitudinal section along marked line in WLI image and corresponding (**e**) Fourier analysis; in direct comparison to a representative (**f**) cross-section, (**h**) longitudinal, and their corresponding Fourier analyses (**g**,**i**).

Figure 12a shows a WLI image of the surface with the lowest micro-roughness (Q400; *F* = 8 J/cm2). A cross-section along the white dashed line is shown in Figure 12b, while the profile of a representative longitudinal section is shown in Figure 12d. The corresponding frequency spectra are displayed in Figure 12c,d, respectively. A similar analysis is shown in Figure 12f,g for a representative cut-out of the initial surface (Figure 5).

A comparison of sections and their corresponding FFT analyses clearly visualizes the effect of LμP on surface roughness. Micro-roughness is significantly reduced along both sections down to spatial frequencies of approximately *fy* ≈ 83 mm<sup>−</sup><sup>1</sup> (*λcr,y* ≈ 12 μm) for the cross-section (Figure 12c) and even down to *fy* ≈ 33 mm<sup>−</sup><sup>1</sup> (*λcr,y* ≈ 30 μm) for the longitudinal section (Figure 12e). The comparison of an LμP surface (Figure 12b) and initial surface (Figure 12f) along the cross-section perpendicular to the milling grooves shows that these could not be completely smoothed out. This is also visualized and quantified in the corresponding FFT analyses (Figure 12c,g), which show that the amplitudes of characteristic spatial frequencies in the range of approximately 1–10 mm<sup>−</sup><sup>1</sup> could not be reduced. The profiles and FFT analyses for the comparison along the longitudinal section show that these low spatial frequencies were not only not reduced but significantly increased (Figure 12d,e,h,i). Therefore, roughness at low spatial frequencies (long spatial wavelengths) undergoes a directional homogenization, so that the amplitudes for the corresponding spatial frequencies in the x and y direction are almost equalized after LμP (Figure 12c,e).
