# A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup for the Micro-CMM

_{s}can be calculated by the following equation.

_{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 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 μm and a tolerance of ±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:

_{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.

_{2}after the probing at P

_{1}. In order to prevent the motion error induced by the Z-servo motor stage, it is desired to move the probe in the X-direction without lifting the probe up in the Z-direction. For this purpose, the artifact is moved by the Y-slide table in the negative Y-direction until the moving path of the probe along the X-direction is not blocked by the artifact. After the probe is moved across the artifact by the X-servo motor stage, the artifact is moved back to its original position by the Y-slide table in the positive Y-direction. Finally, the probing at P

_{2}is carried out by using the X-directional PZT stage. As a result, Equation (1) can be rewritten as follows.

_{tb}is almost the same as s

_{ts}, the influence of the water layer thickness can be cancelled. Figure 4 shows the vibration frequency shifts when probing the slot die and the gauge block, respectively. The vertical axis in Figure 4 indicates the frequency shift ∆f and the horizontal axis indicates the probe displacement in the X-direction. When the frequency shift is extended to the trigger threshold, the probe position in the X-direction is measured by the laser interferometer to determine the trigger point of the probing. The probe tip is then retracted back from the measured surface immediately. As shown in Figure 4, if the frequency shift ∆f of 0.1 Hz is set to be the trigger threshold for the probing, the difference of the probe displacements for the two results in Figure 4 is less than 2 nm. Consequently, the gap width of the slot die can be measured accurately by the on-line qualification of the effective diameter of the tip ball.

## 3. Experimental Result and Discussion

#### 3.1. Evaluation of Alignment Errors of the Measurement System

_{gb}and θ

_{sd}, respectively. θ

_{gb}and θ

_{sd}are calculated based on the X-directional deviation ∆d

_{x}obtained by moving the Y-directional linear slide. ∆d

_{x}is measured by using an optical fiber displacement sensor with a resolution of 0.49 nm. Therefore, θ

_{gb}and θ

_{sd}can be calculated by using the following equations.

_{x_gb}and ∆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.

_{y_X-PZT}and θ

_{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), θ

_{y_X-PZT}and θ

_{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 θ

_{_X-Servo}and θ

_{z_X-Servo}, respectively.

_{x_Z-Servo}and θ

_{y_Z-Servo}, respectively. As shown in Figure 6b, θ

_{x_Z-Servo}and θ

_{y_Z-Servo}can be evaluated by using the right-angle prism mirror and the optical fiber displacement sensor.

_{y_mirror}and θ

_{z_mirror}are defined as the tilt errors around the Y- and Z-axes with respect to the optical axis, respectively. Figure 8 shows a schematic of the cosine error between the laser interferometer and X-directional moving axis. L is the distance measured by the laser interferometer. L' is the actual displacement of the probe tip along the X-direction. L'/L can be expressed by the following equation.

_{gb}is the distance between the probing points on the calibrated artifact. h is the distance between the moving axes of the X-directional PZT stage on the both sides of the gauge block. D

_{s}is the X-directional displacement of the servo motor stage. The thickness of the calibrated artifact w

_{b}can be expressed by the following equation.

_{b}of the calibrated artifact width, which is also extended in the Y-Z plane, can be calculated by the following equation.

_{s}of the slit gap width can be calculated by the following equation.

_{1}indicates the X-directional distance between the probe tip and the reflective mirror. a

_{2}is the Z-directional difference between the center of the probe tip and that of the laser spot on the reflective mirror. θ

_{Abbe}is the tilt error of the X-directional stages. The Abbe errors L

_{y_Abbe}and L

_{z_Abbe}can be expressed as follows.

_{slide_rolling}and the tilt error about the X-axis (Yawing) θ

_{slide_yawing}. The gap width measurement error ∆w

_{y_slide}caused by the tilt errors of the Y-linear slide can be indicated as follows.

_{z-servo_rolling}about the Y-axis (Rolling) and the tilt error θ

_{z-servo_pitching}about the X-axis (Yawing). The gap width measurement error ∆w

_{z-servo}caused by the tilt errors of the Y-linear slide can be indicated as follows.

#### 3.2. Experiments of On-Line Qualification and Gap Width Measurement

_{2}by the X-directional servo motor stage for another 5 times of probing at P

_{2}after 5 times of probing at P

_{1}. It took approximately 50 s for the set of the operation. The same set of the operation was repeated 5 times to evaluate the repeatability of probing at the trigger points. Figure 14 shows the results of the on-line qualification. The X-directional positions of the trigger points at P

_{1}and P

_{2}, which is a contact points between the probe tip ball and the inside surface of the slot die, are shown in Figure 14a,b, respectively. The vertical axes shown in Figure 14a,b show the X-directional probing positions calculated by the output of the laser interferometer. The mean values of the X-directional positions of the trigger points at P

_{1}and P

_{2}over the 5 sets of on-line qualification operations were 5.625 μm and 159.344 μm, respectively. Due to the thermal drift between the laser interferometer and the reflective mirror mounted on the X-PZT stage, the mean values at P

_{1}and P

_{2}were changed almost linearly due to the influence of thermal drifts. Figure 14c shows the value of L

_{12}calculated by taking the difference of the corresponding results of Figure 14a,b, in which the thermal drift error components were removed. The mean and the standard deviation of L

_{12}over the 5 sets of on-line qualification were 153.781 μm and 11.5 nm, respectively. Consequently, the effective diameter of the probe tip ball D

_{e}was estimated to be 53.781 μm.

_{3}, the probe was moved by the X-directional PZT stage toward the opposite surface of the micro-slit for the probing at P

_{4}. This operation was repeated 5 times. The results are shown in Figure 15. Figure 15a,b show the probing positions at P

_{3}and P

_{4}, which indicate the X-directional probe contact positions at the inner surface of the slot die. The mean values at P

_{3}and P

_{4}are −13.392 μm and 13.865 μm, respectively. Figure 15c shows the values of L

_{34}calculated based on the results in Figure 15a,b. The mean and the standard deviation of L

_{34}were estimated to be 27.243 μm and 14.8 nm, respectively. According to Equation (3), the gap width of the slot die micro-slit was estimated to be 80.962 μm.

_{ws}, which was the combined standard uncertainty of L

_{34}, is calculated based on Figure 11, Equations (11) and (14). The repeatability of probing was one of the main uncertainty sources for u

_{ws}. The total time for the gap width measurement was approximately 90 s, during which the temperature was measured to be 22.677 °C ± 0.011 °C. Consequently, u

_{ws}is estimated to be 10.5 nm, which corresponds to the combined standard uncertainty for the measurement of L

_{34}.

_{De}, which was the combined standard uncertainty of the on-line qualification of the effective diameter of the probe tip ball, was estimated based on Figure 10, Equations (10) and (14). As shown in Table 3, the cosine error caused by the misalignment of the gauge block and the probing axis was a relatively large uncertainty source because the X-directional servo stage was moved during the on-line qualification process. The total time for the on-line qualification of the effective diameter was approximately 250 s, during which the temperature was measured to be 22.677 °C ± 0.008 °C. As a result, u

_{De}was estimated to be 26.4 nm. u

_{wb}was the length tolerance of the calibrated gauge block. According to the calibration certification of the gauge block used in the micro-CMM, u

_{wb}was estimated to be 17.3 nm. u

_{∆s}was the uncertainty source introduced by the water layer on the measured surface. It was estimated to be 1.2 nm, based on Figure 4. Consequently, the expanded uncertainty U of the gap width measurement was estimated to be 66.6 nm (k = 2), which was smaller than the allowed maximum expanded uncertainty of 100 nm.

## 4. Conclusions

_{e}of the probe tip ball was evaluated to be 53.781 μm, and the expanded uncertainty in D

_{e}was estimated to be 52.8 nm (k = 2). After the qualification procedure, the gap width measurement of the slot die was carried out immediately. As a result, the expanded uncertainty of the gap width measurement was estimated to be 66.6 nm (k = 2), which can satisfy the required measurement accuracy. The use of an air-bearing linear slide with a stroke of 300 mm has made it possible for the micro-CMM to cover the entire length of the precision slot die. Furthermore, a micro-stylus with an effective working length of larger than 1 mm, which was composed of a capillary glass shaft and a micro-glass sphere, has been employed to measure the gap width from the inside of the micro-slit of the precision slot die.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Configuration of shear-mode micro-probe. (

**a**) Photograph of shear-mode micro-probe; (

**b**) Schematic diagram of shear-mode micro-probe.

**Figure 2.**Experimental configuration of the micro-CMM (micro-coordinate measurement machine) by using a shear-mode micro-probe.

**Figure 6.**Schematic for evaluation of the angular alignment errors: (

**a**) X-directional stages; (

**b**) Z-directional stage.

**Figure 7.**Tilt errors of the reflective mirror with respect to the optical axis of the laser interferometer.

**Figure 8.**Schematic of the cosine error between the laser interferometer and the X-directional moving axis.

**Figure 9.**Schematic of angular alignment errors evaluation of the reflective mirror of the laser interferometer.

**Figure 10.**Geometrical model of the alignment error of the probing points during the qualification procedure.

**Figure 11.**Geometrical model of the alignment error of the probing points during the gap width measurement.

**Figure 13.**Chamfered edge detection by using the micro-probe: (

**a**) Detection strategy of the chamfered edge; (

**b**) Measurement result of the slit position.

**Figure 14.**Experimental results of on-line qualification procedure: (

**a**) Probing results at P

_{2}; (

**b**) Probing results at P

_{1}; (

**c**) Measurement results of L

_{12}.

**Figure 15.**Experimental results of gap width measurement: (

**a**) Probing results at P

_{4}; (

**b**) Probing results at P

_{3}; (

**c**) Measurement results of L

_{34}.

θ_{y_X-PZT} | θ_{z_X-PZT} | θ_{y_X-Servo} | θ_{z_X-Servo} | θ_{x_Z-Servo} |

7.5 mrad | 2.8 mrad | 14.0 mrad | 3.6 mrad | 5.7 mrad |

θ_{y_Z-Servo} | θ_{Slotdie} | θ_{Gauge-block} | θ_{y_mirror} | θ_{z_mirror} |

14.1 mrad | 0.03 mrad | 0.07 mrad | 6.8 mrad | 0.34 mrad |

Stage | Axis | Stroke | Tilting Error |
---|---|---|---|

Y-linear slide | Rolling | 300 mm | 8.10 mrad |

Yawing | 12.31 mrad | ||

Z-servo motor | Rolling | 1 mm | 22.59 mrad |

Pitching | 73.40 mrad |

Uncertainty sources | Symbol | Value | Coverage Factor | Standard Uncertainty |
---|---|---|---|---|

Uncertainty in w_{S} | u_{ws} | - | - | 10.5 |

Cosine error by the alignment of the gauge block and the probing axis | u_{cos_slotdie} | 2.6 | $\sqrt{3}$ | 1.7 |

Cosine error by the alignment of the interferometer axis and the probing axis | u_{cos_laser} | 0.6 | $\sqrt{3}$ | 0.3 |

Abbe error of the X-PZT stage | u_{pzt_abbe} | 5.27 | $\sqrt{3}$ | 3.0 |

Resolution of the interferometer | u_{laser_resolution} | 0.79 | $\sqrt{3}$ | 0.5 |

Linearity error of the interferometer | u_{laser_linearity} | 5.0 | $\sqrt{3}$ | 2.9 |

Thermal drift by temperature change | u_{Thermal_drift} | 7.0 | $\sqrt{3}$ | 4.0 |

Repeatability of L_{34} | u_{rep_L34} | 14.8 | $\sqrt{3}$ | 8.5 |

Uncertainty in D_{e} | u_{De} | - | - | 26.4 |

Cosine error by the alignment of the gauge block and the probing axis | u_{cos_gauge} | 11.0 | $\sqrt{3}$ | 6.4 |

Cosine error by the alignment of the interferometer axis and the probing axis | u_{cos_laser} | 3.58 | $\sqrt{3}$ | 2.1 |

Abbe error of the X-PZT stage | u_{pzt_abbe} | 5.27 | $\sqrt{3}$ | 3.0 |

Abbe error of the X-servo stage | u_{servo_abbe} | 41.5 | $\sqrt{3}$ | 24.0 |

Resolution of the interferometer | u_{laser_resolution} | 0.79 | $\sqrt{3}$ | 0.5 |

Linearity error of the interferometer | u_{laser_linearity} | 5.0 | $\sqrt{3}$ | 2.9 |

Thermal drift by temperature change | u_{Thermal_drift} | 7.0 | $\sqrt{3}$ | 4.0 |

Repeatability of L_{12} | u_{rep_L12} | 11.5 | $\sqrt{3}$ | 6.6 |

Uncertainty in w_{b} | u_{wb} | - | - | 17.3 |

Length tolerance(Calibrated gauge block) | u_{tol_calibrate} | 20.0 | $\sqrt{3}$ | 17.3 |

Uncertainty in Ds | u_{s} | - | - | 1.2 |

Uncertainty due to water layer | u_{water} | 2.0 | $\sqrt{3}$ | 1.2 |

Expanded uncertainty (with a coverage factor k = 2) | U | - | - | 66.6 |

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## Share and Cite

**MDPI and ACS Style**

Ito, S.; Kikuchi, H.; Chen, Y.; Shimizu, Y.; Gao, W.; Takahashi, K.; Kanayama, T.; Arakawa, K.; Hayashi, A.
A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits. *Appl. Sci.* **2016**, *6*, 156.
https://doi.org/10.3390/app6050156

**AMA Style**

Ito S, Kikuchi H, Chen Y, Shimizu Y, Gao W, Takahashi K, Kanayama T, Arakawa K, Hayashi A.
A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits. *Applied Sciences*. 2016; 6(5):156.
https://doi.org/10.3390/app6050156

**Chicago/Turabian Style**

Ito, So, Hirotaka Kikuchi, Yuanliu Chen, Yuki Shimizu, Wei Gao, Kazuhiko Takahashi, Toshihiko Kanayama, Kunmei Arakawa, and Atsushi Hayashi.
2016. "A Micro-Coordinate Measurement Machine (CMM) for Large-Scale Dimensional Measurement of Micro-Slits" *Applied Sciences* 6, no. 5: 156.
https://doi.org/10.3390/app6050156