## 1 Introduction  
Ground-based telescopes play a crucial role in astronomical observations, and their resolution capability determines the extent of the observable universe. To achieve higher imaging resolution and detection sensitivity, the apertures of ground-based telescopes are progressively increasing. The manufacturing and installation of large ground-based telescopes are an intricate process, where errors can significantly impact the quality of observations. The fabrication of large-aperture ground-based telescopes requires high standards in high-precision measurement technology. Testing for aberrations in the optical system is a pivotal aspect of the manufacturing process. The traditional methods for the aberration measurement in optical systems mainly involve the interferometric method. In this method, an interferometer is placed at the focal point of the optical system. The beam emitted from the interferometer passes through the optical system and reflects by a standard flat mirror, then returns along the same path into the interferometer. Using the analysis of interference patterns, the information about the aberrations in the optical system can be obtained [1; 2]. It has the characteristics of simplicity, efficiency, and high accuracy. However, as the aperture of optical systems continues to increase, manufacturing the standard flat elements to match the aperture of the optical system becomes more difficult and expensive. The introduction of the sub-aperture stitching detection method addresses this issue by utilizing small-aperture flat elements to test the wavefront distribution of the sub-aperture of the system one by one. By using the wavefront consistency in the overlapping region of the sub-apertures as a constraint, the full-aperture aberrations of the optical system can be obtained. For example, the 3.5 m Herschel Space Telescope adopts the sub-aperture stitching method for system testing and achieves a final measurement accuracy of 400 nm [3; 4]. The LOTIS (Large Optical Test and Integration Site) system, which has an aperture of 6.5 m, is tested using the sub-aperture stitching method with a movable 1.8 m flat mirror in diameter [5; 6]. Researchers from the Xi'an Institute of Optics and Precision Mechanics, including [PERSON], proposed a joint testing solution for a large-aperture off-axis optical system. This solution integrates the sub-aperture stitching test method with computer-assisted alignment technology and successfully achieves the assembly and testing of the primary and secondary mirror systems of AIMS (The Infrared System for the Accurate Measurement of Solar Magnetic Fields), intermediate focal systems, and visible light focal system [7; 8]. The aberration testing of the primary mirror of the James Webb Space Telescope, with a diameter of 6.5 m, is conducted using an interferometer positioned at its center of curvature. During the integration testing of the system, the sub-aperture testing concept is applied by utilizing three flat mirrors with a size of 1.5 m each in diameter for full-aperture aberration testing [9; 10; 11; 12]. Additionally, the aberration testing of the primary mirror utilizes the Hartmann testing method, where the light emitted from a point source located at the center of curvature of the main mirror is divided into multiple beams by the Hartmann screen. A Hartmann plate located near the focal point of the main mirror receives the focused spot array of the reflected light, and the centroid coordinates of each spot can be used to calculate the wavefront slope corresponding to the sub-aperture of the tested wavefront; thus, the full-aperture wavefront is reconstructed [13]. [PERSON] et al. employed a multi-beam array scanning Hartmann method to detect the wavefront of a finished telescope [14; 15; 16]. The array integrated a 3 \(\times\) 3 small-aperture parallel beam array as a measurement tool.