This paper focuses on the localization problem of lunar laser retroreflectors on the image plane of the faint target camera in a ground-based laser ranging system at different time epochs. Due to the variations in lunar phases, images of the lunar surface acquired by the ground-based laser ranging system exhibits significant differences in brightness and darkness, with noticeable shadow occlusion and illumination effects. Moreover, at different time instances, the relative positions and attitudes of the Sun, the Moon, and the ground-based camera result in perspective transformations in the captured images. These factors pose considerable challenges to the precise localization of lunar laser retroreflectors, making this research highly significant and necessary.

The research methodology of this paper involves constructing an imaging model for the lunar laser ranging camera. The development of this model consists of two main parts. The first part is the illumination model of the terrain around the lunar retroreflector. This study utilizes LOLA data, lunar albedo data, and the INPOP19a planetary ephemeris as foundational datasets. Using the INPOP19a ephemeris, the relative positions of the Earth, Moon, and Sun at any given UTC time, as well as lunar libration information, can be obtained. Under the constraint of the 1′ field of view of the faint target camera in the Tianqin laser ranging system, five templates of the terrain around the lunar retroreflector are generated. By integrating UTC time, LOLA data, and the illumination model, an illumination model of the surrounding terrain is established. Building on this foundation, the model further incorporates the earth-moon ranging model of the Tianqin laser ranging system, its optical system, and the camera imaging model, ultimately establishing a mapping relationship from the longitude and latitude coordinates of the lunar retroreflector to the pixel coordinates in the camera.

This paper establishes a versatile camera imaging model for lunar laser ranging systems, capable of simulating lunar surface images at arbitrary time epochs. The model is validated using the Tianqin laser ranging system, confirming its accuracy. Two typical scenarios are designed for simulation experiments: 1) imaging of terrain around five lunar retroreflectors without topographic obstruction, as shown in Fig. 11; 2) imaging of terrain around the Lunokhod 2 and Apollo 15 retroreflectors under topographic occlusion, as shown in Fig. 12. The results demonstrate strong consistency between the simulated and actual images in terms of visual characteristics, terrain representation, and shadowing effects. The model successfully reproduces the imaging features of lunar retroreflectors under varying illumination conditions and provides theoretical guidance for practical observations through coordinate annotation. It offers particular value for locating retroreflectors with less distinct image features, such as those of Apollo 11, Apollo 14, and Lunokhod 1.

To address the challenge of lunar laser retroreflectors being invisible or difficult to locate on the image plane of ground-based laser ranging system cameras, this paper proposes a camera imaging model capable of simulating the imaging results of the terrain surrounding lunar retroreflectors under arbitrary observation times. Comparative analysis between simulated images and actual captured images demonstrates strong visual consistency, validating the effectiveness of the proposed imaging model. The theoretical positions of retroreflectors derived from simulated images can guide their actual localization in lunar laser ranging operations, providing valuable support for the aiming and positioning of lunar retroreflectors.