Imaging Modeling and Calibration Framework of a Hybrid Solid-State LiDAR for Small Celestial Body Exploration

High-precision 3D terrain mapping and navigation are critical for missions exploring small, fast-rotating asteroids, such as the Tianwen-2 mission to 2016 HO3. This study analyzes a hybrid solid-state LiDAR system developed for such missions, which integrates a 32×32 single-photon avalanche diode (SPAD) array, dual fast-steering mirrors (FSMs), and a Dammann grating beam splitter. While this multi-stage architecture enables high-resolution scanning, it introduces complex geometric errors and pixel-dependent non-uniformities, particularly under the photon-limited conditions typical of deep-space exploration.

We established a rigorous imaging model that explicitly characterizes the multi-stage optical deflection and the single-photon timing mechanism. A Monte Carlo error propagation analysis was performed to quantify the impact of eleven systematic error sources, identifying FSM angular misalignments and internal timing jitter as the dominant contributors to 3D reconstruction uncertainty. To address the challenges of array non-uniformity and signal-dependent range biases, we propose a robust two-stage calibration framework. Unlike traditional geometric calibration methods, this approach incorporates a photon-count-sensitive range correction strategy. By utilizing photon-count statistics as intermediate variables to model the dependence of range bias on acquisition settings (such as varying emission powers and target reflectance), we implemented a per-pixel correction that mitigates range errors. Building on this range-calibrated data, residual angular errors are then corrected via a Jacobian-based least-squares optimization.

The proposed framework was validated through systematic ground experiments at the Deep Space Integrated Test Site, Tongji University. For pixel-wise range calibration, experiments using planar targets demonstrated that the photon-count-indexed correction significantly suppresses signal-strength-dependent trends, reducing ranging dispersion (3σ) from 2.43 cm to 0.82 cm. For system-level evaluation under asteroid-analogue conditions, we constructed a 12 m × 12 m outdoor terrain model simulating the topographic features of asteroid 2016 HO3. Ground truth was provided by a RIEGL VZ-2000i scanner and a Leica TS30 total station. The validation results demonstrate that the calibrated system achieves a ranging accuracy of approximately 2.86 cm (3σ) in global mapping mode (MODE-A) and maintains stable performance (~3.10 cm, 3σ) in step-scanning navigation mode (MODE-B) over ranges of 34–83 m. This study validates the effectiveness of the proposed modeling and photon-driven calibration methods, providing a reliable workflow for enhancing the performance of array-based single-photon LiDARs in complex deep-space environments.