Imaging modeling and error analysis for a hybrid solid-state LiDAR system for the 3D terrain mapping and navigation of small celestial bodies

Abstract

Accurate imaging models and error analyses are critical for evaluating and calibrating LiDAR systems, particularly in high-precision 3D terrain mapping and navigation applications. This study focuses on a hybrid solid-state LiDAR system that integrates a 32 × 32 single-photon avalanche diode (SPAD) array, dual fast steering mirrors (FSMs), and a grating-based beam splitter to achieve high-speed, high-resolution imaging under dynamic asteroid conditions. This optical configuration, characterized by multi-stage beam deflection and array-based detection, presents significant challenges for accurate LiDAR modeling and systematic error analysis. To address these optical complexities, an imaging model was developed based on the system’s single-photon detection characteristics, scanning modes and multi-beam splitting. Specifically, a pixel-wise range estimation method was proposed based on histogram peak extraction, significantly enhancing measurement precision for single-photon detection under high frame-rate operation, thus enabling accurate 3D coordinate reconstruction from raw measurements under fast scanning conditions. Additionally, a Monte Carlo-based error analysis framework was established to quantify the impacts of eleven systematic error sources, including range deviations, FSM angular errors, and internal timing uncertainties. A pixel-wise consistency evaluation across all 1024 SPAD pixels was also conducted, providing detailed insights into error propagation and revealing critical pixel-level sensitivities. The simulated results indicate that arcminute-level angular errors lead to mean absolute position deviations exceeding 5  cm in lateral directions, while centimeter-level range errors typically result in position deviations below 2  cm. These findings are consistent with the system’s design specifications and highlight the dominant influence of angular uncertainties on 3D reconstruction accuracy. The proposed modeling and analysis framework provides an initial, model-based baseline for early design trade studies, sensitivity analysis, and calibration planning under static laboratory conditions. Optical simulations illustrate the scanning mode, and ground experiments under static laboratory conditions validate the ranging/TOF processing and static geometry. In addition, a coarse calibration method based on multi-position pixel measurements was implemented and validated, reducing range measurement errors to below 2  cm and further enhancing system accuracy for future deep-space exploration missions.