## 1 Introduction  
High-precision optical components, as the core components of optical systems, are widely used in consumer electronics, astronomy, national defence and military, the biomedical industry, industrial manufacturing and other fields [1]. The functional realisation of an optical imaging system relies on lens design, which requires the optical axis of each visual component or lens to coincide with the ideal axial direction. However, the centre deviation introduced during lens machining and assembly can destroy the coaxial and rotational symmetry of the system, leading to coma, dispersion, aberration, and other aberrations, which seriously affect the final imaging quality of the optical system. The centre deviation is shown in Figure 1. The Centre process is shown in Figure 2. Compared with the traditional manual assembly method, centring turning while machining has higher centring accuracy and machining efficiency [1], so it has attracted much attention. However, centring lathe components will be ageing during the machining process, so considering the time-varying nature of the equipment and accurately monitoring the status of key components, including tools, spindles, feed systems, etc., is the key to ensuring the machining quality and efficiency [2, 3]. As the key enabling technology of intelligent manufacturing, digital twin technology promotes significant changes in manufacturing technology systems and models [4; 5; 6; 7; 8]. In recent years, the related theoretical system has been improved, and the key technology of digital twins has been developed gradually [9; 10; 11]; digital twins have been successfully applied in the digital machining of complex equipment. [PERSON], [PERSON] et al. [12] elaborated on applying the digital twin concept in digital machining and investigated the digital representations of different objects involved in the machining process. [PERSON] et al. [13] proposed and developed a digital twin reference architecture and showed a significant relationship between digital twin service capabilities and large-scale personalisation, and these works laid the foundation for digital twin applications. [PERSON] et al. [14] proposed a framework for applying digital twin-based extended reality technology in the manufacturing environment, which consists of four layers, including a physical machine and its ROS-based ROS, with a digital twin. The application framework of extended reality technology is based on a digital twin with four layers, including a perception layer with physical machines and their ROS-based simulation models, a machine communication layer, a network layer containing three communication middleware, and a Unity-based service layer for creating XR-based digital applications, which improves the efficiency of extended reality application development and the usability of the HMI system. Combining digital twins with intelligent predictive algorithms for optimising machining processes is an important research idea nowadays. In the field of centring machining, [PERSON] et al. researched and developed a digital twin system for process optimisation through experiment-based genetic algorithm (DOE-GA) design, which reduced the process development time from 4 h to 1 h, reduced the entire inspection to 10% sampling inspection, and increased the yield by 20%. [PERSON] et al. proposed a hybrid deep learning model driven by digital twins, which combined the signals of motion displacement and speed during machining, accurately estimated the cutting force and predicted the  
Figure 1: The diagram of the centre deviation. Figure 2: The chart of the centre process. wear state of diamond tools. [PERSON], [PERSON] et al. [15] utilised Microsoft HoloLens to develop an AR application for the digital twinning of CNC milling machines. Through visual interaction and management of digital twinning data, they improved the efficiency of the machining process. [PERSON], [PERSON] et al.