## 3 Experiments on the 3D Quartz Tuning-Fork Probe
### Experimental Results  
Noise level, sensitivity, trigger resolution, probing force, and unidirectional repeatability are all important parameters used to evaluate the quality of a positioning trigger probe. In our previous research [30], the working surface of an ultra-precision gauge block was used as the target to obtain the approaching curves of the probe in the \(X\), \(Y\), and \(Z\) directions (the approaching curve shows the relationship between the vibrating amplitude of the probe and the displacement of the stage). In Figure 9, when the probe is in the nanocontact area, the sensitivity of the tip-sample--which is  
Figure 8: Schematic of the experimental system for the quartz tuning fork. Figure 7: (**a**) Schematic diagram of the structure of the probe system; (**b**) Enlarged picture of the quartz tuning fork and the integrated fiber microstem and microsphere tip. determined by the curve slope of the linear segment obtained through the linear regression method--is 2.62 V/\(\upmu\)m in the \(X\) direction. The trigger resolution of 0.38 nm is determined via the system noise level of 1 mV. In the same way, the sensitivity is 2.21 V/\(\upmu\)m and the resolution is 0.45 nm in the \(Y\) direction. In the \(Z\) direction, the sensitivity is 2.24 V/\(\upmu\)m and the resolution is 0.45 nm. The results show that this probe has a sensitivity of less than 0.5 nm in all directions. This probe is proven to have sub-nanometer resolution. Figure 9 shows the approaching curve in the \(X\) direction. The horizontal axis represents the relative displacement that the positioning stage moves, and the longitudinal axis represents the amplitude voltage of the microsphere. Before the nanocontact regions, the microsphere of the probe remains resonant with constant amplitude. When the tip-sample interaction goes into the repulsive region of section A in Figure 3, the amplitude significantly attenuates because of the interfacial resultant force of \"needle point force field\"--a result that is consistent with the model analyzed. This finding indicates that the proposed model qualitatively explains the interaction between the microsphere of the 3D resonant trigger probe and the sample surface. When the oscillation amplitude of the probe decreases to 80 percent of the initial value, this position of the nanostage is recorded as a trigger point. The probing force of the system is also calculated. In the lateral direction, assuming that the contact between the microsphere and the sample surface is rigid, the contact force can be calculated simply by the blending force of the micro-stem. In Figure 9, the distance between the start-decreasing point and the trigger point represents the blending distance (over travel) of the micro-stem which is less than 50 nm. With the stiffness of 143 N/m of the micro-stem, the calculation of the probing force is about 7 \(\upmu\)N. In the \(Z\) direction, the microsphere is in contact with the sample surface in tapping mode, which is not rigid contact. Besides, the approaching speed is in sub micrometer per second, which is very low. So, according to the model we established, the probing force in the \(Z\) direction is in a similar magnitude to the van der Waals force. Repeatability is an important evaluation parameter of a trigger positioning system. Several factors may influence repeatability, such as voltage fluctuations caused by unstable factors of the driving signal, Abbe error resulting from the mechanical structure and positioning accuracy of the nanostage in the process of testing, changes in environmental conditions, external vibration, and other random errors. To verify the reliability of the probe system, the repeatability of the triggering process of the probe has been evaluated by approaching the probe repeatedly at the same measurement point in the working surface of an ultra-precision gauge block. Figure 10a shows the repeatability tests for 10 times in the \(X\), \(Y\), and \(Z\) directions.