# A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits
## 2 Experimental Setup for the Micro-CMM  
Figure 1a shows the photographs of the shear-mode micro-probe. The micro-stylus is composed of a glass micro-stylus shaft and a glass micro-sphere. The stylus shaft is made of a capillary glass tube which is thermally pulled by using a commercially available glass pipette puller. A micro-glass sphere with a nominal diameter of 52.6 \(\pm\) 3.2 \(\upmu\)m (Certified size standard Cat No. 9050, Duke Scientific Corporation, California, CA, USA) [31] is attached on one end of the glass micro-stylus by thermosetting resin. The diameter of the commercially available glass micro-sphere was selected based on the nominal gap width of the precision slot die. Figure 1b shows the schematic of a shear-mode micro-probe. The micro-stylus is then attached on a tuning fork quartz crystal resonator (TF-QCR). A PZT transducer is employed to vibrate the assembly, which is composed of the TF-QCR, the micro-stylus, and the micro-sphere at the resonance frequency of the TF-QCR. The variation of the vibration frequency is detected by the TF-QCR based on the piezoelectric effect of the quartz crystal. The vibration of the TF-QCR is detected and amplified by current-to-voltage (I-V) converter. The output  
of the I-V converter is then utilized to keep the vibration frequency constant by using a self-excitation circuit that consists of a phase locked loop circuit (PLL). It should be noted that the actual resonance frequency of the TF-QCR used in the assembly is confirmed to be approximately 30 kHz, which is smaller than that of the single TF-QCR element of 32.768 kHz, due to the influence of the masses of the micro-stylus and the micro-sphere attached on the TF-QCR. The vibration direction is set in parallel with the measuring surface. To determine the trigger point for the probing of the micro-probe to the measured surface, the interaction force of the water layer on the measured surface against the probe is detected through detecting the change of the probe vibration with the TC-QCR [26]. When the tip ball of the vibrating probe contacts with the water layer of the measured surface, the frequency of the probe vibration is shifted due to the adhesion force of the water layer. The output of the TF-QCR is input to a phase locked loop (PLL) circuit for detection of the amount of frequency shift. The PLL circuit output is then employed as the trigger signal for the probing of the micro-probe to the measured surface. The PLL output signal is fed into analog-to-digital (A/D) converter of a personal computer (PC). A certain frequency shift amount is set to be a threshold of the trigger signal. Figure 2 shows a schematic diagram of the micro-CMM by using the shear-mode micro-probe. The probe is mounted on the PZT-driven linear stages (P-621.2 CL and P-621.1 ZCL, PI), which can be moved in the \(X\)- and \(Z\)-directions independently, for fine positioning of the probe. The stroke and resolution of the PZT stages are 100 \(\upmu\)m and 1 nm, respectively. The positioning accuracy in the \(X\)- and \(Z\)-directions are \(\pm\)2 nm and \(\pm\)1 nm, respectively. Since the gap width of the slot die is calculated based on the \(X\)-directional probe displacement, a commercial laser interferometer (RLE10, RENISHAW) with a resolution of 0.39 nm is employed for the measurement of the \(X\)-directional probe displacement. A plane mirror is mounted on the opposite side of the probe on the \(X\)-direction PZT stage as a moving mirror for the laser interferometer. In order to reduce the influence of the Abbe error, the optical axis of the laser interferometer is aligned with the center of the probe tip. The PZT stages are mounted on the DC servo motor driven positioning stages (M-111.1 DG, PI) for coarse positioning of the probe in the \(X\)- and \(Z\)-directions. The stroke and resolution of the servo motor coarse stages are 25 mm and 6.9 nm,  
Figure 1: Configuration of shear-mode micro-probe. (**a**) Photograph of shear-mode micro-probe; (**b**) Schematic diagram of shear-mode micro-probe. respectively.