# A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits
## 3 Experimental Result and Discussion  
### Evaluation of Alignment Errors of the Measurement System  
As described above, the gap width measurement is carried out in the developed micro-CMM by probing one point on each of the surfaces of the micro-slit. The reliability of the measurement results is influenced by the angular alignment errors and motion errors of the moving stages. Figure 5 shows a schematic of the angular alignment errors of the moving stages. The moving axis of the air bearing linear slide is defined as the \(Y\)-axis. The \(X\)-axis and \(Z\)-axis are shown in Figure 5. The length direction of the micro-slit of the slot die and the surface of the gauge block are arranged in parallel with the \(Y\)-axis. The angular alignment errors of the slot die and the calibrations around the \(Z\)-axis are indicated as \(\theta_{gb}\) and \(\theta_{sd}\), respectively. \(\theta_{gb}\) and \(\theta_{sd}\) are calculated based on the \(X\)-directional deviation \(\Delta d_{x}\) obtained by moving the \(Y\)-directional linear slide. \(\Delta d_{x}\) is measured by using an optical fiber displacement sensor with a resolution of 0.49 nm. Therefore, \(\theta_{gb}\) and \(\theta_{sd}\) can be calculated by using the following equations. \[\theta_{gb}=\tan\left(\frac{\Delta d_{x\_gb}}{L_{gb}}\right) \tag{4}\]  
\[\theta_{sd}=\tan\left(\frac{\Delta d_{x\_sd}}{L_{sd}}\right) \tag{5}\]  
where \(\Delta d_{x\_gb}\) and \(\Delta d_{x\_sd}\) are the \(X\)-directional displacements of the gauge block and the slot die due to the tilt around the \(Z\)-axis of the slot die, respectively. \(L_{gb}\) and \(L_{sd}\) are the \(Y\)-directional displacements caused by the linear slide, respectively. \(L_{gb}\) and \(L_{sd}\) are set to be 180 mm and 20 mm, respectively. The alignment errors of the \(X\)-directional moving axis of the PZT stage around the \(Y\)-axis and the \(Z\)-axis are indicated as \(\theta_{y\_X\_PZT}\) and \(\theta_{y\_X\_PZT}\), respectively. Figure 6a shows a schematic diagram of the evaluated angular alignment errors of the \(X\)-directional stages. A right-angle prism mirror is placed on the table of the \(Y\)-linear slide for measurement of the deviations in the \(Y\)- and \(Z\)-directions with the optical fiber displacement sensor. The \(Y\)-\(Z\) plane of the prism mirror is aligned in parallel with the moving axis of the \(Y\)-linear slide. Based on Equations (4) and (5), \(\theta_{y\_X\_PZT}\) and \(\theta_{y\_X\_PZT}\) can be calculated by moving the \(X\)-directional PZT stage. Similarly, for the \(X\)-direction servo motor stages, the alignment errors around the \(Y\)-axis and \(Z\)-axis are defined as \(\theta_{x\_Servo}\) and \(\theta_{z\_X\_Servo}\), respectively. Figure 5: Schematic of the angular alignment errors of the moving axes of the measurement system. The \(Z\)-directional servo motor stage is used to adjust the measurement position inside the micro-slit along the \(Z\)-direction. The alignment errors of the \(Z\)-directional servo motor stage around the \(X\)-axis and the \(Y\)-axis are indicated as \(\theta_{x\_Z\_Serro}\) and \(\theta_{y\_Z\_Serro}\), respectively. As shown in Figure 6b, \(\theta_{x\_Z\_Serro}\) and \(\theta_{y\_Z\_Serro}\) can be evaluated by using the right-angle prism mirror and the optical fiber displacement sensor. Figure 7 shows a schematic of the tilt errors of the reflective mirror with respect to the optical axis of the laser interferometer. Since the gap width of the micro-slit is obtained from the outputs of the laser interferometer, the alignment error of the laser interferometer is also an uncertainty source for the gap width measurement. When the reflective mirror of the interferometer, which is mounted on the opposite side of the micro-probe, is not perpendicular to the \(X\)-axis, a cosine error will occur, as shown in Figure 7. \(\theta_{y\_mirror}\) and \(\theta_{z\_mirror}\) are defined as the tilt errors around the \(Y\)- and \(Z\)-axes with respect to the optical axis, respectively.