## 3 Calibration Artefacts
### Microforce Calibration Standard  
To calibrate the probe's force and stiffness, a convenient method is to apply a reference spring, whose spring constant has been calibrated by, e.g., means of a compensation balance before usage [42]. An application example was introduced in [36]; however, it is only suitable for calibrating the \(z\) probing axis due to its size limit. To overcome this problem, a new artefact has been fabricated as shown in Figure 6. The artefact consists of three cantilevers marked as \"\(x\)\", \"\(y\)\" and \"\(z\)\" used as reference springs, whose spring constant has been calibrated _in prior_. The cantilevers and their substrates are made from silicon using etching techniques. The substrates are glued to an aluminium cube with a glass plate (thickness: 0.2 mm) inserted as a spacer. This glass spacer ensures that the cantilever will not contact the aluminium  
Figure 5: (**a**) Probing repeatability of a 3D-ACP probe along the \(z\)-axis; and (**b**) probing repeatability of a 3D-ACP probe in full 3D. cube in its free standing and bent states. Near the free end of the cantilever, a trapezoid-shaped tip is fabricated. It is used for loading the probing forces at a known position. As the spring constant of the reference cantilever depends on the position where the force is loaded, the cantilever should be calibrated and used for calibration with forces loaded at the given position. Using such a device, we calibrated the \(x\)-, \(y\)- and \(z\)-stiffness of a boss-membrane 3D probe to be 208.8 N/m, 313.8 N/m and 5642.9 N/m, respectively, as mentioned earlier. Adhesive forces are observed during the probing process resulting in sticking between the probing sphere and the sample [20]. Such adhesive forces may be attributed to several factors such as atomic/molecular interaction forces, capillary forces, electrostatic forces etc. Since the probing forces of micro/nano-CMMs are only in the order of milli- or micronewtons, the adhesive forces may impact the CMM's measuring/scanning performance significantly. Such adhesive forces can also be characterized using the force calibration standard. Figure 7 shows an example where the adhesive force of an ACP probe is characterized. Figure 7a shows a typical probing curve, which depicts the cantilever bending signal vs. the probing distance. For ease of explanation, the curve is marked with letters \"A\" to \"F\" to indicate different probe-sample interaction states as shown in Figure 7b. B is the point where the probing sphere begins to contact the sample. This point is calculated as the zero force contact point. In B \(\rightarrow\) C, the probe moves towards the sample. The probing force leads to a positive change of the probing signal, which is quasi-linear with respect to the probing distance. At point C, the motion is stopped and the probing sphere begins to retract from the sample. In C \(\rightarrow\) D, the probing sphere undergoes the reverse trajectory to that of B \(\rightarrow\) C and no hysteresis is found. During D \(\rightarrow\) E, the probing sphere sticks to the sample. The adhesive forces lead to a negative change of the probe signal. At point E, the probing sphere begins to separate from the sample. In E \(\rightarrow\) F, a type of damped oscillation can be seen, which is caused by the release of the adhesive forces on the bent probe. The adhesive forces \(F_{a}\) can be calculated as the probing forces at point E according to [PERSON]'s law:  
\[F_{a}=k_{x}\cdot L_{r} \tag{1}\]  
Here, \(k_{x}\) is the spring constant of the probe in the \(x\)-direction and \(L_{r}\) is the probing distance needed for separating the probing sphere and the sample. In this study (sample: sapphire sphere with \(\O\) = 2 mm; probing sphere: sapphire sphere, \(\O\) = 0.12 mm; relative humidity: 46% \(\pm\) 2%; temperature: 20.5 \(\pm\) 0.5 \({}^{\circ}\)C), we measured \(L_{r}\) = 1.31 \(\upmu\)m and estimated adhesive forces of 2.06 \(\upmu\)N according to the calibrated reference spring constant \(k_{x}\) = 1.575 N/m.