Objective  With the proposal of digital equipment construction, it is imperative to build space-based digital equipment that can simulate situational awareness capabilities. As one of the core equipment for space-based situational information acquisition, the optical imaging system is inevitably an integral part of the construction of space-based digital equipment systems. Establishing a scientifically and reasonably accurate model of space target imaging link is crucial for constructing a space-based digital imaging system. Additionally, due to the involvement of various scientific and technological fields, the construction of a space target imaging system is characterized by a large-scale system and a long development cycle. Traditional research methods are unable to meet the needs of key technology verification for space-based systems. Therefore, it is also necessary to construct this digital model. By using simulation and comprehensive integration, critical technologies of imaging systems can be validated. Additionally, it provides a demonstration environment for research on space target imaging technology and serves as an auxiliary tool for the design of space-based observation platforms.

  Methods  Based on Kepler's three laws and visibility analysis (Tab.2), this paper constructs a visible model for camera and target optical observations. Based on the uniform smoothing algorithm and advanced wavefront algorithm, the triangulated mesh division technique and the five-parameter bidirectional reflectance distribution function (BRDF) (Tab.3) are used to construct the geometric and optical characteristic model of the target. By employing path tracing and importance sampling of light rays, a global illumination algorithm (Fig.5) is used to construct the imaging radiative transfer model. Finally, the target radiance image undergoes optical-electric energy conversion and imaging modulation (Fig.7) to become the final output image of the sensor. This paper simulates target images satisfying visibility conditions using the Hubble Space Telescope as the imaging object, based on the given orbital parameters of imaging platform and space target.

  Results and Discussions   By comparing the visibility simulation results within 15 days of the two-body orbit model in Satellite Tool Kit (STK) (Fig.9), the correctness of the imaging visible model proposed in this paper is validated. The close-range imaging results of the target (Fig.11) demonstrate the accuracy of the global illumination algorithm in a multi-light source space-based imaging scenario. The quality degradation simulation results (Fig.14) indicate that the convolution of the frequency domain transfer function and the accumulation of temporal noise can simulate different levels of image quality degradation in on-orbit imaging. Under the conditions of a time interval of 3 seconds and a distance range of 70 to 200 km, imaging simulations were performed on the target with a Earth-oriented attitude. The imaging results (Fig.10) demonstrate that the imaging chain model can effectively generate target sequence images that satisfy the requirements of orbit monitoring conditions.

  Conclusions  This paper starts from the camera and target's orbital parameters and calculates the observable time periods of the target under the condition of orbital flight using the camera and target visible model. Using the target geometry and optical characteristic model, the reflection of light source energy by targets with different materials and geometric shapes is described. The target radiance image is obtained by performing a rapid calculation of the visible parts of the target using the imaging radiative transfer model. Finally, the final sensor output image is generated through the process of photoelectric energy conversion and imaging modulation model. The imaging chain mathematical model constructed in this paper allows for the research of digital imaging technology in specific imaging scenarios without relying on other orbit and imaging software such as STK and OpenGL. It provides references and foundations for the design of physical cameras, detector selection, and the construction of core modules in the digital twin system for space-based imaging.