Fig. 1. （a）Shielding effect and （b）triggering effect caused by pulse pile up

Fig. 2. When the discrimination threshold is T=2.5 V and the current time interval Γ_i responds to 3 photon events，the piled up voltage waveforms of 3 （the first row）and 4 （the second row）photon events respond at the （a）Γ_i-1，（b）Γ_i-2，（c）Γ_i-3，（d）Γ_i-4 and （e）Γ_i-5 time interval （Γ_i=（t_i，t_i+τ），the time interval resolution is 200 ps）

Fig. 3. When the discrimination threshold is T=2.5 V，（I）the piled up voltage waveform while the current time interval Γ_i responds to one photon event and the （a）Γ_i-1，（b）Γ_i-2，（c）Γ_i-3，（d）Γ_i-4 and （e）Γ_i-5 time intervals respond to two photon events，（II）the piled up voltage waveform while the current time interval Γ_i responds to two photon events and the （a）Γ_i-1，（b）Γ_i-2，（c）Γ_i-3，（d）Γ_i-4 and （e）Γ_i-5 time intervals respond to one（ the second row）and two（ the third row）photon events （the time interval resolution is 200 ps）

Fig. 4. Photon counting Lidar system，（a）schematic （b）photograph

Fig. 5. Measured output waveform of SiPM under different conditions，（a）output waveform when responding to one photon event，（b）output waveform when responding to multiple photon events，（c）shielding effect caused by pulse pile up，（d）triggering effect caused by pulse pile up

Fig. 6. The theoretical and experimental comparisons of false alarm probability and detection probability with different discrimination thresholds

Fig. 7. Point cloud distribution under different discrimination thresholds when N_s =3 and f_n=15 MHz

Fig. 8. Comparison of the theoretical and experimental results of the recall，precision and F₁ coefficient of different discrimination thresholds，（a）N_s=0.35，f_n=7 MHz，（b）N_s=1.5，f_n=7 MHz，（c）N_s =3，f_n=5 MHz，（d）N_s =3，f_n=15 MHz

Fig. 9. The contour map of the theoretical F₁ coefficient under different average signal photon numbers N_s and discrimination thresholds R，（a）f_n=10 MHz，σ_p=2 ns，（b）f_n=30 MHz，σ_p=2 ns