## 4 Investigations and Measurement Results  
In previous publications, the great potential of the NFM-100 in combination with a tip-based system was shown and statements were made about the accuracy [5; 10; 11; 17]. In the following part, first, only the machine itself is considered in static operation and, subsequently, its performance at high movement speeds. Furthermore, the deviation from the specified trajectory is analysed for both linear and circular motion. In the presented setup of the machine, there is no constraint for the \(x\) and \(y\) direction. Thus, a rotation around the \(z\) axis is allowed in principle. Through the use of air bearings, a higher linearity of the \(x\) and \(y\) movements can be achieved through almost friction- and force-free movement. This is further supported in terms of control technology through precise, permanent measurement and dynamic control of the rotation around the \(z\) axis by means of the three voice coil actuators. Therefore, the position noise of the machine table with a sampling frequency of 10 kHz for a duration of 10 s in the x and y direction as well as the noise of the angle interferometer is first considered. In Figure 6, the recorded position noise in closed-loop control at the origin is depicted. The standard deviation (\(1\sigma\)) of the different values are shown in the following table. As can be seen in Table 2, the values fulfil the requirement of an extremely low positioning noise (\(<\)1 nm), which is necessary for precise AFM measurements. Moreover,this is especially important for the fabrication of nanostructures, because they cannot be corrected afterwards. For the further investigation of the static operation, the machine table was moved to several points on the \(x\) and \(y\) axis, where the position noise was recorded. Figure 7 shows the points where the position noise was recorded within the entire range of motion. Initially, Figure 8 shows how the position stability behaves over the movement range of 100 mm in both the \(x\) and \(y\) direction. For this purpose, the position noise was recorded over a period of 10 s with a sampling frequency of 10 kHz, each at a distance of 2 mm on the \(x\) and \(y\) axis over a maximum distance of 100 mm (see Figure 7). For this purpose, the deviations of the \(x\) and \(y\) axis are plotted in each case. Over the entire examined range, the maximum deviation is below 450 pm (1\(\sigma\)), as can be seen in Figure 8.  
After this static investigation, the focus was placed on the dynamic mode. First, straight-line trajectories were driven at different velocities. For this purpose, this analysis was carried out along the \(x\) axis as well as the \(y\) axis over a length of 50 mm and 100 mm. In this case, a velocity range between 0.5 mm/s and 20 mm/s was selected and investigated. Figure 9 shows that at the maximum velocity of 20 mm/s over a length of 100 mm, the maximum path deviation perpendicular to the moving direction is below 7 nm (6.545 nm). \begin{table}
\begin{tabular}{c c} \hline \hline Position noise in \(x\) direction & 246 pm \\ Position noise in \(y\) direction & 317 pm \\ Angular noise & 3.4855 nrad \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different values of positioning noise (1\(\sigma\)) in closed-loop control of the NFM-100 for a duration of 10 s and a sampling frequency of 10 kHz (see Figure 6). Figure 6: Positioning noise of the NFM-100 of the \(x\) and \(y\) interferometer (left \(y\) axis) as well as of the angle interferometer (right \(y\) axis) in closed-loop control for a duration of 10 s at the origin (0,0). Figure 7: Investigated points for positioning noise over a range of 100 mm in x and \(y\) direction with a distance of 2 mm. In addition, it can be seen that the movements in the \(y\) direction have a smaller deviation than in the \(x\) direction at the same velocity. This can be explained by the fact that when moving in the \(y\) direction, two actuators are used equally due to the symmetry of the actuator arrangement.