## 2 Proposed Metrology System
### System Design  
Figure 1 shows the schematic of the automatic optical measurement system. Figure 1a shows the direction in which the sample is loaded on the rotary table in the top view. Figure 1b shows the equipment; the equipment includes CCD components (IDS 500 million CCD/UI-3580 CP-C-HQ_REV 2), a Computer 2/3\" 8 mm f1.4 locking iris and focus (M0814-MP2) lens, an LS-7030 CCD micrometer (LS-7001 micrometer display), a programmable logic controller (PLC) of KV-7500, a rotary table, an XY linear micrometer manual stage (TSD XY-TS100 AR), a harmonic reducer (GTC 1:80), a servo motor (SME-L04030 SAB, AC400W) and servo motor driver, and a control box. In the rapid measurement system, an I/O Special Unit (KV-SIR32 XT) was added; this unit uses the Ethernet/IP interface to communicate with a PC, to facilitate high-speed data transfer. The upper CCD is used to determine the rotation center of the machine rotating platform. The measurement sample is directly placed on the platform, using the outer diameter of the platform for alignment/fixation. There are two diameters within the inner diameter, as shown in the cross-section A-A of Figure 1a: a large diameter and a small diameter. The large diameter is the outer diameter of the platform and is used for alignment and fixation, and the small diameter is used to stop the sample on the platform. Thus, the workpieces to be measured can be simply and stably placed on the platform; however, a gap typically exists between the platform and the workpiece, resulting in a slight eccentricity error on the workpiece. The rotary table consists of a harmonic reducer (1:80) and an AC servo motor. In addition, there is a pointer for positioning the machine to the 0\({}^{\circ}\) position. An inductive limit switch is used to return the machine to the 0\({}^{\circ}\) position. This study used the KEYENCE line-scanning optical measurement system LS-7030, which is an all-in-one optical measurement instrument; the measurement range is 0.3 to 30 mm, the accuracy is \(\pm\)2 \(\upmu\)m, and the repeatability is \(\pm\)0.15 \(\upmu\)m. The LS-7030 consists of an integrated parallel beam system and an imaging system (high-brightness GaN light-emitting diode (LED), telecentric lens, and HL-CCD. The HL-CCD facilitates continuous exposure measurement (reaching 2400 times/s), so it can be used for high-speed continuous detection. The following are the advantages of a harmonic reducer: (1) Compared with other reducers, the harmonic reducer has a smaller volume and simpler structure, and it generally consists of three basic components (wave generator, flexible wheel, and rigid wheel) [20]. (2) The harmonic reducer can be used with large loads. Because a large number of teeth mesh when the harmonic gear rotates and the flexible wheel meshes with the rigid wheel after elastic deformation, the teeth are in surface contact  
Figure 1: Schematic of the automatic optical measurement system. (**a**) Top view. (**b**) Front view and equipment. with other teeth. Therefore, the backlash is small, and meshing is possible even without side backlash, which is suitable for reverse rotation during movement and maintaining output accuracy. Other control buttons are on the outer cover of the control box, such as the start button, which triggers the rotating table to rotate once, the home position return button, which triggers the rotating table to return to the zero point position of the system, and the emergency stop button, which is required in case the measurement needs to be stopped. In the prototype system, the rotation speed was only 0.25 rpm, and the measurement time was approximately 4 min. To achieve a measurement time of within 1 min, the rotation speed must be increased. According to Reference [21], the harmonic reducer has different vibration values for different rotation speeds.