## 1 Introduction  
The micro crystal resonator (MCR) is an electronic device used to provide clock frequency for electronic products. It has the advantages of high frequency, small package size, high stability and low power consumption [1]. The commonly used MCR can be divided into tuning fork type and circular slice type. The frequency of the tuning fork type crystal resonator is 32.768 kHz [2]. In the basic manufacturing process of the MCR, firstly, a quartz wafer is processed according to the required target frequency [3]. Secondly, the tuning fork electrode and circuit part of the MCR are produced. Thirdly, the frequency of the MCR is adjusted to near target frequency by changing the mass of the electrode. Finally, the frequency of the MCR is further adjusted to make its natural frequency reach the target value. The main part of the MCR is a quartz wafer with silver coatings on the upper and lower sides as electrodes. The two electrodes are connected with the circuit through the lead. With both ends of the electrode having alternating electric fields, the wafer will be mechanically deformed and vibrated. When the voltage frequency is equal to the natural frequency of the MCR, piezoelectric resonance will occur to realize the conversion of electrical energy and mechanical energy. According to the physical characteristics of the MCR, the surface silver layer on the MCR can be removed by laser so that the natural frequency of the MCR can be adjusted to achieve the desired target value. In the production process of the MCR, electrode area, density and shear elastic modulus are the inherent properties of quartz crystal. The original resonant frequency of the MCR is the original frequency of the MCR before frequency adjustment, and it is also a fixed value. Therefore, the frequency of the MCR can be changed by changing the mass of the MCR. When the mass of the silver layer is increased, the resonant frequency of the MCR decreases. When the mass of the silver layer is reduced, the resonant frequency of the MCR increases [4]. The laser processing system for MCR frequency modulation mainly includes the MCR carrier module, the frequency detection module and the laser processing module. In the process of laser frequency modulation, the wafer is transported to the processing position by the MCR carrier module. The frequency of the MCR is measured by the frequency detection module. According to the difference between the actual frequency and the target frequency of the MCR, the frequency of the MCR is adjusted by the laser processing module. A laser with a wavelength of 532 nm is used to thin the electrodes of the MCR with a fundamental frequency of 10 MHz [4]. Laser irradiates the surface of the MCR to vaporize the silver layer. The thickness of the wafer is 0.8 mm. The processing object is the 3225 MCR (3.2 \(\times\) 2.5 \(\times\) 0.8 mm) produced by TKD Science and Technology Co., Ltd in Suzhou, China. In terms of frequency modulation technology, [PERSON] et al. [5] designed the laser etching frequency adjustment and ion beam etching fine tuning technology to achieve the fine tuning of MCR frequency. [PERSON] [6] developed ion etching equipment and designed an ion etching frequency modulation experiment in an inert gas environment. The frequency offset pattern after etching was obtained to optimize the ion etching process. [PERSON] [7] proposed and realized two laser etching methods, laser thinning and laser etching pattern, to finely tune the frequency of quartz crystal resonant devices. [PERSON] [8] used the laser marking machine and the corresponding electrical performance testing instrument to measure the frequency shifts of the crystal oscillator at different working currents and Q pulse widths under frequency modulation and analyzed the change of the electrical performance parameters of the crystal oscillator after frequency modulation. In terms of the motion control method, [PERSON] et al.