## 3 Experiments
### Verifying the Characteristics of Each Filter When Spikes Are Included in the Primary Profile
If the width of the spike is wide, it becomes a step. The results of calculating the ideal mean line are different; in the case of the spike, the effect should be removed, whereas for the step, it should be extracted as a shape component. In this paper, anything difficult to judge as a spike or a step is labeled as an outlier. The width boundary between the spike and step is not defined; however, the width of the boundary for each filter, whether it is removed as a spike or extracted as a step, is also verified. Figure 4 is the primary profile with three different widths of step added to Figure 1, and the mean line is calculated using each filter. The height of the steps is unified, and the width of the steps are 0.1\(\lambda\)c, 0.5\(\lambda\)c, and 1\(\lambda\)c, from left to right. From Figure 4, for a width of 0.1\(\lambda\)c outlier, the mean line of RL2-RSF and FMSF is calculated without the effect of it as a spike. On the other hand, for a width of 0.5\(\lambda\)c outlier, RL2-RSF calculated the mean line without the effect of it as a spike; however, FMSF was extracted as the step. For a width of 1\(\lambda\)c outlier, both RSFs try to extract the shape component as a step. The FMSF extracts the shape components without blunting the step boundary area. On the other hand, the output of RL2-RSF has no overshoot compared to the output of SF; however, near the step boundary area is blunter than SF. It is verified with a wider step whether the RL2-RSF can extract the step shape component if the width of the step is wider. Figure 5 shows the primary profile, including the step component of width 2\(\lambda\)c and the mean line calculated using each filter. It can be observed that the FMSF extracts the shape components without blunting the step boundary area, same as 0.5\(\lambda\)c and 1\(\lambda\)c, whereas the output of RL2-RSF blunts the step boundary area, similar to when the step width is 1.0\(\lambda\)c. From this result, it can be concluded that the RL2-RSF cannot extract the step shape component accurately even when the width of the step is widened. Figure 4: Primary profile (Step pattern 1: 0.1\(\lambda\)c, 0.5\(\lambda\)c, 1.0\(\lambda\)c) and mean line of each filter. The width boundary of whether the FMSF removes as a spike or extracts the shape component as a step is verified. Figure 6 shows the primary profile after adding the step components with widths \(0.2\lambda c\), \(0.25\lambda c\), and \(0.3\lambda c\), from left to right, and the mean line calculated using each filter. The RL2-RSF removes all of them as spikes. On the other hand, the FMSF is removed as a spike for width \(0.2\lambda c\) outlier. However, the FMSF outputs the values of the upper side of the step only near the center for a width \(0.25\lambda c\) outlier. For the width \(0.3\lambda c\) outlier, the FMSF has a wider range of outputting the upper side value of the step; however, the extracted width of the step is narrower than the width of the step. The results shown in Figure 6 are discussed here. In the case of FMSF, when the width of the outlier is less than \(0.2\lambda c\), the FMSF outputs only from the data on the lower side because the cumulative sum of weights of the lower side is larger for all points. Therefore, the FMSF removed this as a spike. As the width of the outlier becomes wider, the point appears where the cumulative sum of the upper side weights is larger than the cumulative sum of the weights on the lower side. First, it appears in the middle of the upper side, and as the width of the outlier becomes wider, the output points of the upper side increase. Eventually, it will extract the same width as the outlier (step) width. The boundary's width value of the outlier depends on the roughness components' distribution. As a result of the verification, all of them were removed as spikes when the width of the outlier was less than \(0.2\lambda c\), and all of them were extracted as steps when the width of the outlier was more than \(0.5\lambda c\).