Fig. 1. Effect of pulse pile-up，in the figure，the green dashed line pulse represents the electron flow pulse of PMT responding to the output of a single photon，and the solid green line pulse represents the electron flow pulse after pile up：（a）dead time effect caused by pulse，（b）height increase effect caused by pulse pile-up

Fig. 2. The pulse height distribution of PMT anode output signal electron current

Fig. 3. PMT output pulse pile-up，dotted line is the part of pulse pile-up，solid line is the result of pulse pile-up

Fig. 4. Photon-events detection probability time distribution，in the figure，the solid orange line is the photon detection probability of the traditional single-photon model，the solid blue line is the detection probability of the simplified PMT model，and the yellow 'X' is the Monte Carlo simulation data point：（a）Ns=1，（b）Ns=2，（c）Ns=4，（d）Ns=8

Fig. 5. Comparison of ranging walking error and ranging accuracy between PMT photon detection model and traditional model，in the figure，the solid blue line represents the traditional photon detection model and the solid orange line represents the PMT photon detection model：（a）ranging walking error Ra，（b）ranging accuracy Rp

Fig. 6. The relationship between PMT detection probability，ranging walking error and photon event identification threshold，（a）the relationship between the detection probability and the threshold when the number of incident photons Ns=2，（b）the relationship between the ranging walking error and the number of incident photons under different threshold conditions

Fig. 7. Photon-counting radar system：（a）a block diagram of experimental system，（b）a photograph of thephoton counting LIDAR

Fig. 8. The relationship between photon detection probability and incident photon number：（a）GM-APD，（b）PMT

Fig. 9. Experimental results：（a）experimental results and theoretical curves of incident photon number and ranging walking error，the solid blue line in the figure is the theoretical curve of GM-APD ranging walking error changing with incident photon number，and the blue 'o' is the experimental data point of GM-APD，the solid orange line is the theoretical curve of PMT ranging walking error varying with the number of incident photons，and the orange 'x' is the experimental data point of PMT，（b）experimental results of the ranging accuracy of PMT and GM-APD varying with the number of incident photons

Fig. 10. Three pulse height distribution functions

Fig. 11. When the number of incident photons is 2，the relationship between the photon event detection probability and normalized dentification threshold of the three pulse height distribution functions：（a）T=0.3，（b）T=0.7，（c）T=1，（d）T=1.5

Fig. 12. When the threshold T=1，the relationship between the ranging walking error，ranging accuracy and incident photon number of the three pulse height distribution functions：（a）ranging walking error and（b）ranging accuracy

Fig. 13. The relationship between the signal-to-noise ratio of photon detection and the identification threshold of photon events：（a）T=1，（b）T=2，（c）T=3，（d）T=4

Fig. 14. The relationship between signal photon detection probability and threshold

Fig. 15. The shadowing effect of noise photons on signal photons：（a）the low identification threshold，（b）the high identification threshold

Fig. 16. The relationship between photon detection probability and normalized threshold at high noise rate

Fig. 17. The photon-events detection probability time distribution when the pulse width of echo pulse is 10 ns，in the figure，the solid orange line is the photon detection probability of the traditional single-photon model，the solid blue line is the detection probability of the simplified PMT model，and the yellow 'X' is the Monte Carlo simulation data point：（a）Ns=1，（b）Ns=2，（c）Ns=4，（d）Ns=8