Poisson Three-Dimensional Inversion for Long-Range Single-Photon LiDAR from Motion–Acquisition-Decoupled Observations

Long-range single-photon LiDAR is limited by stop-and-go acquisition overhead and uncertain spatial attribution during scanner motion. We present a motion–acquisition-decoupled Poisson three-dimensional reconstruction framework in which scanning and time-correlated single-photon counting proceed concurrently under a common time base. Timestamp–trajectory reassociation recovers each acquisition window’s physical coordinate and intra-window motion, which are incorporated with spatial and temporal responses and background in a trajectory-aware Poisson model. Under matched field-of-view, sampling-density, and photon-acquisition conditions, the average acquisition time per effective spatial sample decreased from 1.380 s for conventional stop-and-go scanning to 0.997 s for the proposed motion–acquisition-decoupled continuous scanning, corresponding to a 27.8% reduction. Reassociation reduced edge misalignment, while 15 μrad overlapping sub-pixel sampling with Poisson inversion separated four stripe structures mixed in pixel-wise maximum-likelihood estimation. A controlled photon-thinning experiment over six levels (PPP = 5.90–0.60; 30 nested realizations per level) showed joint improvements in depth RMSE, valid reconstruction rate, and depth SSIM at PPP = 5.90 and 3.90; at PPP = 5.90, RMSE decreased from 1.680 m to 0.492 m and valid rate increased from 60.29% to 81.69%. In a separate approximately 3 km building experiment, local openings and façade details remained visually identifiable at PPP = 5.43 and SBR = 0.94. The framework improves acquisition efficiency while preserving trajectory-traceable observations for photon-limited three-dimensional imaging.