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The photon counting Lidar enhances the signal-to-noise ratio of the echo signal and reduces the number of photons required for signal analysis, thereby improving the detection range and measurement accuracy. At present, the photon counting Lidar is mainly used to detect stationary targets, and the mechanism of the influence of long-distance target motion characteristics on the photon echo probability distribution is still unclear. Therefore, it is urgent to study the photon ranging performance of long-distance moving targets.  In this paper, the probability distribution model of photon detection echo of moving targets is established, and a Monte Carlo model for photon detection of arbitrary targets is given. Through experimental comparison, the correctness of the Monte Carlo simulation model is verified. Furthermore, the probability distribution characteristics of the laser echo and photon echo of a small rectangular target in translation within a detection period are compared. And the variation law of the probability distribution of photon detection under different translational speeds is analyzed. In addition, the relationship between the photon ranging error and the translational speed of the target is discussed.  The results show that the photon echo probability distribution of the translational target is more forward and the width is narrower than the laser pulse echo probability distribution. Compared with the extended target, the detection probability of the translational small target is significantly reduced, and the maximum average echo photon number is   \begin{document}$ 1/10 $\end{document}times that of the extended target, as a result, the photon detection of the translational target requires higher laser pulse energy. When the length of target is 1m, the range walk error reaches a maximum value at a speed of   \begin{document}$25\;{\text{m/s}}$\end{document}, i.e.   \begin{document}$6.72\;{\text{ cm}}$\end{document}, which is   \begin{document}$ 1/2 $\end{document}times that of the extended target. With the increase of the translational speed, the range walk error first increases and then turns stable with the light spot acting as the boundary.  The method proposed in this paper can be further extended to photon detection and ranging of targets with other shapes, materials and attitudes. The research results provide a theoretical basis for the correction and performance improvement of the photon ranging of moving target. Furthermore, it lays the foundation for the detection of moving targets and accurate acquisition of information by photon counting Lidar.

Photon echo probability distribution characteristics and range walk error of small translational target for photon ranging