标题： 基于SPAD的dToF LiDAR的距离精度性能界限 显示英文标题

标题： Performance Bounds of Ranging Precision in SPAD-Based dToF LiDAR

摘要： 基于单光子雪崩二极管探测器（SPAD）的直接飞行时间（dToF）激光雷达已在各种应用中得到广泛采用。 然而，对其基本测距性能极限的全面理论理解——特别是由于系统死时间和光子数分辨架构的潜在优势所导致的退化——仍然不完整。 在本工作中，理论推导了考虑死时间效应的dToF系统的Cramer-Rao下界（CRLB），并将其推广到具有光子数分辨能力的SPAD探测器，进一步通过蒙特卡洛模拟和最大似然估计进行验证。 我们的结果表明，堆积效应不仅减少了单个飞行时间中的信息量，还引入了距离和光子通量率之间的统计耦合，从而进一步降低了测距精度。 所推导的CRLB用于确定产生最佳可实现测距精度的最优光学光子通量、激光脉冲宽度和飞行时间量化分辨率。 分析进一步量化了增加光子数分辨能力所带来的有限性能提升，该提升表现出迅速递减的回报。 这些发现为dToF系统的设计及其最佳工作点的选择提供了理论指导。 显示英文摘要

摘要： Lidar with direct time-of-flight (dToF) technology based on single-photon avalanche diode detectors (SPAD) has been widely adopted in various applications. However, a comprehensive theoretical understanding of its fundamental ranging performance limits--particularly the degradation caused by pile-up effects due to system dead time and the potential benefits of photon-number-resolving architectures--remains incomplete. In this work, the Cramer-Rao lower bound (CRLB) for dToF systems is theoretically derived accounting for dead time effects, generalized to SPAD detectors with photon-number-resolving capabilities, and are further validated through Monte Carlo simulations and maximum likelihood estimation. Our results reveal that pile-up not only reduces the information contained within individual ToF but also introduces statistical coupling between distance and photon flux rate, further degrading ranging precision. The derived CRLB is used to determine the optimal optical photon flux, laser pulse width, and ToF quantization resolution that yield the best achievable ranging precision. The analysis further quantifies the limited performance improvement enabled by increased photon-number resolution, which exhibits rapidly diminishing returns. These findings provide theoretical guidance for the design of dToF systems and the selection of their optimal operating points.