Analysis of Timing Errors in Time-of-Flight LiDAR Using APDs and SPADs Receivers

Abstract

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.