Asteroids are inextricably linked to the fate of humanity: their structure and composition provide crucial insights into the evolution of the solar system, and the mineral resources they harbor hold the potential to alleviate Earth's energy crisis. However, the risk of asteroid impacts on Earth is equally significant and cannot be overlooked. Conducting imaging and exploration of asteroids can significantly enhance our understanding of these celestial bodies. In practical asteroid exploration missions, the functions of detection and imaging are typically achieved through either a single camera with multiple optical paths or multiple cameras. To reduce system complexity and manufacturing challenges, this paper proposes an optical system design that integrates both detection and imaging functionalities within a single optical path. Initially, based on the requirements of the asteroid detection mission, the limiting magnitude for detection was determined to be 14th magnitude. This allowed for the calculation of the irradiance at the entrance pupil of the optical system corresponding to this magnitude. Subsequently, by considering the specifications of the selected detector and the signal-to-noise ratio threshold requirements, the necessary entrance pupil diameter was calculated to be 280 mm, with a focal length of 1 472 mm and a full field of view angle of 0.895°. In terms of optical system configuration, the need for a long focal length and large aperture to detect faint stars was taken into consideration. A fully transmissive system would inevitably result in an excessively long overall size, making it susceptible to temperature variations. Additionally, correcting chromatic aberration would require a combination of lenses made from different materials, complicating the achievement of a lightweight design. On the other hand, a fully reflective system could achieve a large field of view and long focal length design without chromatic aberration, but compared to coaxial systems, it might face challenges in overall assembly and alignment. Therefore, this paper combines the advantages of both transmissive and reflective systems by adopting a Ritchey-Chrétien configuration with corrective lenses: the front group eliminates spherical aberration and coma, compressing the axial distance of the system, while the rear group incorporates corrective lenses to address other types of aberrations and simultaneously expand the system's overall field of view. Building upon the calculated initial R-C structure, corrective lenses were incorporated and optimized, resulting in a relatively simple catadioptric optical system with excellent imaging quality. When operating in detection mode, the detector employs 2×2 pixel binning to increase the received light flux, while the focal plane is positioned 0.04 mm outside the ideal focal plane to ensure that 80% of the encircled energy diameter is approximately equal to one binned pixel. In imaging mode, through appropriate focusing adjustments, the system can achieve clear imaging of targets at distances ranging from 10 to 150 km. Tolerance analysis indicates that under reasonable manufacturing and assembly conditions, the modulation transfer function at the edge of the field of view decreases by a maximum of 0.036 compared to the design phase, and the maximum dispersion range of the encircled energy is 5.7 μm. Both values remain within acceptable limits and do not affect the system's normal operation. In terms of stray light suppression, an approximate calculation method was employed to allocate the roughness of each optical surface, resulting in a final backscattered light flux reaching the imaging plane of 3.52×10^-16 W. This value is one order of magnitude lower than the target light flux, ensuring that it does not interfere with the system's normal operation. For out-of-field stray light, the suppression requirements for stray light Point Source Transmittance (PST) were calculated using parameters such as the solar constant. To mitigate out-of-field stray light, an external baffle with gradient vertical vanes and internal baffles for the primary and secondary mirrors were designed specifically for this optical system. The optomechanical system, configured with optical surfaces of varying roughness, was then simulated in Tracepro. The results demonstrate that the PST value can reach the order of 10^-4 at a 30° off-axis angle, indicating that the overall system meets the operational requirements.