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 (<inline-formula> <tex-math notation= LaTeX >$> 10^{2}$ </tex-math></inline-formula>) number of detected photons <inline-formula> <tex-math notation= LaTeX >$\\text{N}_{\\text {ph}}$ </tex-math></inline-formula>. However, the systematic error can be cancelled by a separate measurement of <inline-formula> <tex-math notation= LaTeX >$\\text{N}_{\\text {ph}}$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation= LaTeX >$\\tau /\\surd N_{\\text {ph}}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation= LaTeX >$\\tau $ </tex-math></inline-formula> 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.