## 3 Results and Discussion
Although a Gaussian high-pass filter with a cut-off value of 0.1 mm could be used to suppress the longer wavelength components for determining the surface features, this could also remove the surface features due to the presence of unmelted and partially melted Ti64 metal powder particles sintered to the surface. Note that in this study, the length scale of FOV was similar to the minimum cut-off value of 0.1 mm, and therefore by using small sampling lengths during measurement, it should be possible to obtain accurate values of the S\({}_{\mathrm{sk}}\) and S\({}_{\mathrm{ku}}\)[24]. For this reason, this study primarily focused on the areal surface texture parameters via the measured surface in the absence of a Gaussian high-pass filtering to address the effect of heat treatment of SLM printed Ti64 specimens on cell attachment. ### Surface Morphology and Roughness Analysis  
Figure 6a-f respectively show the height signals, contour plots of the wavelet transform of the height signals, and the average wavelet spectra of untreated/heat-treated Ti64 specimens, where the height signals were directly obtained along the horizontal axis from the symmetry center of the position (a) and position (g) (see Figure 3). In Figure 6b,e, the  
Figure 5: 3D surface texture parameters, including (a) S\({}_{\mathrm{a}}\), (b) S\({}_{\mathrm{q}}\), (c) S\({}_{\mathrm{sk}}\), and (d) S\({}_{\mathrm{ku}}\), for untreated and heat-treated Ti64 specimens. abscissa is the sampling length, the ordinate represents the characteristic length scales, and the color bar indicates the magnitude of the wavelet coefficient \(W(a,\,b)\). As can be seen from these two figures, there are multi characteristic scales that reveal periodic oscillations for the height signals. For the case of untreated Ti64 specimen (Figure 6c), there existed a small characteristic period around 14 \(\upmu\)m, which is smaller than the mean particle size of the Ti64 powders. Besides, there existed characteristic scales around 29 and 45 \(\upmu\)m, respectively, which were in the range of 1-2 powder sizes. Besides, there also existed a large periodic characteristic scale around 84 \(\upmu\)m, which is more than twice of the mean particle size of the Ti64 powders. As discussed in Figure 2a, unmelted Ti64 metal powder particles were sintered to the structure's surface during manufacturing. We speculated that there might exist powder-size subpopulations. When these subpopulations are uniformly distributed and sintered to the surface, periodic characteristic scales appeared and could be decomposed via the wavelet transform of the height signals. For the case of heat-treated Ti64 specimen (Figure 6f), there existed characteristic scales around 19 and 47 \(\upmu\)m, respectively, where the former was smaller than the powder diameter and the latter was in the range of 1-2 powder sizes. Therefore, we focus on calculating periodic characteristic scales that appear in the range of 1-2 powder sizes, and define the mean value of the periodic characteristic scales as the primary peak. The results showed that for heat-treated specimens, the value of the primary peak statistically significantly increased from 37.4 \(\pm\) 3.8 to 45.6 \(\pm\) 6.9 \(\upmu\)m (\(n\) = 5, \(p\) = 0.048), which revealed that an increase in the periodic characteristic length scale was primarily due to the formation of large-scale aggregations of Ti64 metal powder particles on the heat-treated surface, as discussed in Figure 2d,e. Figure 6: Wavelet-based multi-resolution analysis for the characteristic length scales of untreated and heat-treated Ti64 substrates. (**a–c**)/(**d–f**) respectively show the height signals, contour plots of the wavelet transform of the height signals, and the average wavelet spectra of untreated/heat-treated Ti64 specimens, where the height signals were directly obtained along the horizontal axis from the symmetry center of the position (a) and position (g) (see Figure 3).