The small-sized Micro-Channel Plate Photomultiplier Tube
(MCP-PMT), also called Fast-timing PMT (FPMT), has gained
significant attention across various fields due to its single-photon
detection capability and great time resolution. The after-pulses are
spurious pulses occurring after the main pulse and cannot be
distinguished from the true signals, which means the occurrence of
the after-pulses can contribute to the noise of the FPMT. In this
study, the waveforms of the FPMTs were recorded by a
high-sampling-rate oscilloscope, and we measured the after-pulse
characteristics of different types of FPMTs, including the time
distribution and the after-pulse rate. The causes of different
after-pulse groups are also analyzed. Additionally, we conducted a
comparative analysis of the distinct properties of after-pulses in
different types of FPMTs.