## 3 Experiments
### Verifying the Characteristics of Each Filter When Spikes Are Included in the Primary Profile  
In this section, the characteristics of each filter to spike that is the most major outlier are verified. The spikes are caused by speckles or fine dust. The spikes are added to the primary profile in Figure 1 for verification. Figure 2 shows the primary profile after the addition of spikes with four different heights and the mean line calculated using each filter; the heights of the spikes, from left to right, are two, three, five, and ten times that of the reference value. The width of the spikes is set to 0.02\(\lambda c\). Figure 3 shows the deviation between the mean line in Figure 1 (before the addition of the spike) and the mean line in Figure 2 (after the addition of the spike). Figures 2 and 3 shows that the mean line calculated using SF is affected by the spikes, and the effect depends on the height of the spikes. The region between the spikes is also affected in the direction opposite to the spikes, and the influence of the spikes can be observed throughout. In contrast, the mean lines calculated using RL2-RSF and FMSF are less affected by the spikes. Comparing the size of the deviation from Figure 3, the deviation of RL2-RSF is lower when the height of the spike is low, whereas that of FMSF is lower when the height of the spike is high. This is because the 2 nd-order B-spline basis function used in FMSF can eliminate the effect of high-height spikes. However, low-height spikes cannot be eliminated entirely, and some marginal effect occurs. Figure 1: Important profiles of surface roughness (Measurement data): (**a**) primary profile and mean lines calculated using each filter; (**b**) deviation of the mean line calculated using SF and each filter. On the other hand, the RL2-RSF changes the weights according to the deviation between the mean line and the primary profile; however, the first mean line is affected by the spikes same as the mean line calculated using SF. Therefore, the effect of spikes decreases with each repetition of the calculation. However, if the first mean line is highly affected by the spike, the effect of the spike cannot be eliminated even if the number of repetitions is increased, which is why this result was shown. The roughness parameter Ra of SF is 0.9339 \(\upmu\)m, RL2-RSF is 0.7576 \(\upmu\)m, and FMSF is 0.7583 \(\upmu\)m (For reference, Pa of the primary profile is 0.8258 \(\upmu\)m). Compared with Ra before the spike was added, all filters significantly increased. Even if the mean line is calculated without the effect of the spike, the roughness profile will still be affected by the spike because the roughness profile is the subtraction of the primary profile and the mean line [22]. To properly evaluate the roughness without the effect of a spike, only the range of spikes from the roughness profile calculated by the robust filter is removed [22]. Calculating Ra excluding the range of spikes, SF is 0.6917 \(\upmu\)m, RL2-RSF is 0.4954 \(\upmu\)m, and FMSF is 0.4961 \(\upmu\)m. When compared with Ra before the addition of the spike, the Ra of SF increased by approximately 37.6%. In comparison, RL2-RSF and FMSF remained within an increase of less than 1.5%, confirming that both these RSFs can be evaluated properly when spikes are included in the primary profile. From these results, it can be said that the RL2-RSF and FMSF can derive a mean line that excludes the effect of spikes that are more than twice the height of the normal roughness component to a practical use level. Figure 3: Deviation of the mean line between Figures 1 and 2. Figure 2: Primary profile (Spike height pattern) and mean line of each filter. Verifying the Characteristics of Each Filter When the Step (Rectangular Wave) Is Included in the Primary Profile  
This section verifies the characteristics of each filter to step (rectangular wave). Steps are commonly found in semiconductors and standard specimens. The step is a shape component; however, in ISO 16610-30, the step is classified as an outlier.