## 3 Simulation Experiments and Discussion  
An XS detector is selected with 40 anode strips in the X direction and 40 anode strips in the Y direction for the simulation experiment. Due to each anode spacing corresponding to 8 pixels, this detector can achieve a 320 \(\times\) 320 resolution. The quantum efficiency of the detector is 0.2. The time of each simulation experiment is T. The dead time of the detector \(\mathrm{t_{d}}\) is 200 ns. The position of the detected target is \((x_{a},y_{a})\). The diameter \(D_{r}\) of the optically dispersed spot in the detector is \(5P\), and \(\sigma_{r}=D_{r}/6\). The rate at which the detected target emits photons to the detector is \(s\). The diameter \(D_{e}\) of each electron cloud is \(5P\), and \(\sigma_{e}=D_{e}/6\). The software we used is MATLAB 2020b. The computer device for running the software is based on the Windows 10 operating system with 16 GB of RAM and an Intel(R) Core(TM) i7-10875H CPU (2.30 GHz). The steps of the simulation experiment are as follows:  
1. The position of the detected target \((x_{a},y_{a})\) is randomly selected, and after this position is determined, it does not change during the simulation experiment. 2. Randomly generate the arrival time of the photon. On average, one photon is received by the detector every \(1/(s\eta)\) nanosecond. The photons' arrival intervals obey an exponential distribution with parameter \(1/(s\eta)\). During the experimental time T, the arrival time of the photon is continuously generated, while the number of photons received by the detector is determined. 3. Randomly generate the arrival position of each photon according to the Gaussian distribution of Equation (2). 4. Obtain the charge distribution generated for the anode. As the number of collisions of electrons with the inner wall of the channel within the MCP and the number of electrons produced per collision varies, the total amount of electrons output will be different. The distribution of the charges generated at different voltages is studied in [33]. A curve with a voltage of 3150 V is chosen for the next simulation, and the curve is approximated using a Poisson distribution. \(Q_{total}\) is randomly generated for each photon according to this distribution. The charge distribution produced by each photon at the anode is obtained. 5. We determine whether the photons are aliased or not by checking the photon arrival time interval. If no photon arrives within 200 ns after the arrival of a certain photon,this photon is considered one non-aliased data point. Otherwise, all the photons within these 200 ns as a whole are considered one aliased data point. For the photons that do not undergo aliasing, we calculate their arrival positions according to Equation (7). 6. For the photons that have been aliased, the signals are superimposed onto a charge amplification circuit and onto the Gaussian shaping. Their peak positions are determined, and the reading of each anode strip is obtained. We perform the truncation during the signal processing. Specifically, for each aliased data point, we extract a waveform with a time width of 200 ns. We process each waveform separately and further obtain the peak of the waveform. We can further calculate the position of the aliased data. 7. Separately obtain the mean values of the data for the method of retaining the aliased photons and the method of removing the aliased photons. Calculate the residuals of the detection results. 8. In order to compare the differences between the two methods, for each T point, each s point and each \(D_{r}\) point, we repeated the procedure 1000 times. The accuracy of the results is evaluated by calculating the mean and standard deviation using the residuals obtained from the detection. Different detection times are selected for the simulation experiments, and the results are shown in Figure 4. The red line indicates the mean and standard deviation of the residuals of the detection results for 1000 simulation experiments with the method of removing the aliased data.