# A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits
## 2 Experimental Setup for the Micro-CMM
The positioning accuracy resolution of the servo motor stages are 0.1 \(\upmu\)m. For positioning the probe in the \(Y\)-direction, an air bearing linear slide (TAAT30 SL-19+C, NTN) with a travel stroke of 300 mm is employed. The resolution and positioning accuracy of the \(Y\)-directional linear slide are 20 nm and \(\pm\)0.1 \(\upmu\)m, respectively. The precision slot die with a length of 200 mm is placed on the moving table of the \(Y\)-directional linear slide for measurement. When a typical CMM is employed for measuring the gap distance between two parallel surfaces, at least three points on one surface are probed first to define the surface. A point on the other surface is then probed for obtaining the coordinates of the point. The gap distance between the two surfaces can thus be accurately obtained from the coordinates of the point on the second surface with respect to the defined first surface even if the normal of the surfaces are not parallel/vertical to the coordinate axes of the CMM. However, it is necessary to conduct the probing at least three points on the first surface, which is a time-consuming process. In order to shorten the measurement time, the gap width of the precision slot die is measured in the micro-CMM, as shown in Figure 3, by probing only one point on each of the surfaces forming the micro-slit under the condition that the axes of the \(X\)-directional positioning stages are carefully aligned to be parallel to the normal of the slit surfaces and perpendicular to the \(Y\)-axis of the linear slide. Consequently, the gap width of the slot die \(w_{s}\) can be calculated by the following equation. \[w_{s}=L_{34}+D_{e}+2s_{ts} \tag{1}\]  
where \(L_{34}\) is the distance between the trigger positions \(P_{3}\) and \(P_{4}\) along the \(X\)-direction. \(D_{e}\) is the effective diameter of the probe tip ball. \(s_{ts}\) is the thickness of the water layer on the slot die at the  
Figure 3: Schematic diagram of on-line qualification and length measurement of gap width. Figure 2: Experimental configuration of the micro-CMM (micro-coordinate measurement machine) by using a shear-mode micro-probe. trigger point. The effective diameter \(D_{e}\) is influenced by the water layer on the measured surface, the stiffness of the stylus shaft, and so on. The probing can be carried out by the shear-mode micro-probe through detection of the interaction between the water layer on the measured surface and that on the surface of the probe tip ball. Similar to the authors' previous research [32], on-line qualification of the effective diameter \(D_{e}\) is carried out soon before the gap width measurement to reduce the combined standard uncertainty caused by the variations in the water layer thickness of the water layer, which is dependent on measurement conditions such as temperature, humidity, and surface materials. Firstly, the effective diameter of the probe tip is estimated by using a calibrated artifact. A grade \(K\) gauge block (Mitsutoyo) with a thickness of 100 \(\upmu\)m and a tolerance of \(\pm\)10 nm is used as the calibrated artifact. The tolerance of the gauge block was determined based on the calibration certification. Both the slot die and the gauge block are made of stainless steel. The effective diameter \(D_{e}\) can be estimated by:  
\[D_{e}=L_{12}-w_{b}-2s_{tb} \tag{2}\]  
where \(w_{b}\) is the thickness of the calibrated artifact, \(L_{12}\) is the distance between the trigger points \(P_{1}\) and \(P_{2}\) along the \(X\)-direction, and \(s_{tb}\) is the thickness of the water layer on the calibrated artifact. The stroke of the PZT stage used in the micro-CMM is 100 \(\upmu\)m. It is not enough to move the probe across the calibrated artifact for probing the two sides of the artifact. The \(X\)-servo motor stage is therefore used to move the probe to the opposite side of the artifact for the probing at \(P_{2}\) after the probing at \(P_{1}\).