We analyze the ultimate timing error that can be achieved in the operation of a LiDAR based on the time-of-flight (ToF) measurement of distance using a pulsed light source and two possible detectors in the optic receiver: (i) an avalanche photodiode APD in linear mode, and (ii) a SPAD single photon detector. We analyze both the random and systematic contributions to the total error and find that the latter becomes dominant at large ( $> 10^{2}$ ) number of detected photons $\text{N}_{\text {ph}}$ . However, the systematic error can be cancelled by a separate measurement of $\text{N}_{\text {ph}}$ . As a conclusion, it is found that, aside from a multiplicative factor of the order of unity, all the schemes supply a timing error given by $\tau /\surd N_{\text {ph}}$ , where $\tau $ is the characteristic time describing the illumination waveform. The theory we have developed provides a theoretical framework for the evaluation of the precision of time-of-flight measurement, and the results are applicable as a benchmark of the timing performance obtained by practical instruments.

中文翻译：

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使用 APD 和 SPAD 接收器分析飞行时间 LiDAR 中的定时误差

我们使用脉冲光源和光接收器中的两个可能的检测器，基于飞行时间 (ToF) 距离测量，分析了 LiDAR 操作中可以实现的最终计时误差：(i) 雪崩光电二极管线性模式下的 APD，以及 (ii) SPAD 单光子探测器。我们分析了对总误差的随机和系统贡献，发现后者总体上占主导地位（ $> 10^{2}$ ) 检测到的光子数 $\text{N}_{\text {ph}}$ . 然而，系统误差可以通过单独的测量来抵消 $\text{N}_{\text {ph}}$ . 作为结论，发现除了单位阶乘法因子之外，所有方案都提供由下式给出的时序误差 $\tau /\surd N_{\text {ph}}$ ， 在哪里 $\tau $ 是描述照明波形的特征时间。我们开发的理论为评估飞行时间测量的精度提供了理论框架，其结果可用作实际仪器获得的计时性能的基准。