# Improved Design of Imaging System for Online Detection of Large-Sized Step-Shaft Runout Errors
## 1 Introduction  
A large-sized step shaft is a piece of modern, large-scale precision equipment that is important in transmission machinery parts, the transfer of movement, torque, and other important aspects. However, step shafts are affected by processing equipment and environmental factors, and in the case of rotary radial runout error and end-face runout error in rotary processes, runout error directly affects the transmission accuracy of the shaft parts, which leads to friction, vibration, and noise phenomena, reducing the service life of the stepped shaft [1; 2; 3]. In stepped-shaft runout error detection, the non-contact online measurement method is used to obtain measurement values for runout errors via imaging analysis of the stepped-shaft rotary process. However, in actual measurements in factories, it has been found that the stepped-shaft extraction and installation process causes the installation of different axes, center-position offset, and other impacts on imaging results, resulting in a reduction in measurement accuracy [4; 5; 6]. Therefore, for the non-contact online measurement of runout errors in large-sized step shafts, it is very important to reduce the influence of coaxiality errors and center-position errors on imaging during the extraction and installation process so as to improve the accuracy of the detection of runout error in large-sized step shafts.  
In recent years, researchers and scholars at home and abroad have proposed a variety of methods for developing non-contact online inspection imaging systems to assess runout error. For instance, [PERSON] et al. designed a long-distance imaging system for the non-contact measurement of radial runout errors in lathe spindles, where the ratio of the object image was close to 1, and the system was combined with a sub-pixel positioning algorithm toimprove the edge of the actual positioning accuracy. The measurement accuracy for radial runout error reached the sub-micrometer level, but the system could only be applied at low speeds, as it was only applicable to the spindles of machine tools with low rotational speeds [7]. [PERSON] et al. proposed a structured, light-based runout error measurement method that used a fisheye lens and divided the field of view into multiple regions for correction, and the experimental results showed that the measurement accuracy for a 30 mm axis was 20 \(\upmu\)m [8]. [PERSON] et al. proposed a method of coaxiality error measurement based on the principle of laser ranging for large-sized parts, and the Kalman filtering method was used to measure the data. The Kalman filtering method is used to process the data, and coaxiality error measurement can be achieved for large parts less than 0.5 mm in size [9]; however, the system is affected by ambient light. These methods are based on the algorithmic processing of measurement data, and it is difficult to realize the correction of coaxiality errors when large-sized stepped-shaft runout error detection uses these data, such that these techniques cannot guarantee real-time, accurate online measurement. Therefore, in view of the shortcomings of the above methods, such as their low measurement accuracy and the great influence of ambient light, this paper proposes an improved design for an imaging system in order to meet the needs for the accurate online detection of large-sized, stepped-shaft runout errors based on a plane mirror set with a diameter range of 500-700 mm.