## 2 XS Detector Targeting for Passive Imaging Detection  
In passive imaging detection, detectors continuously receive the photons emitted by the target and further generate electron clouds on the anode. The center of mass of the electron cloud is calculated from the charge of the anode to obtain the arrival position of the photons. Moreover, the position of the detected target can be calculated from the photon arrival position data. In the XS detector, the readouts in the X direction and Y direction are completely independent of the arrival position of the photons, and the calculation methods are exactly the same for these two directions. In the following, we mainly analyze and discuss the computation for the X direction. Figure 2: Electron cloud produced by two photons at the XS anode. (**a**,**b**) shows two possibilities of photons arriving corresponding to the same charge distribution. We assume that the rate \(s\) (in Hz) at which the detected target emits photons to the detector is constant. Affected by the quantum efficiency \(\eta\) of the detector, some of the photons cannot realize photoelectric conversion. The effective number \(N\) follows a Poisson distribution [25; 26] for photons reaching the detector in time \(t\):  
\[N\sim Poisson(st\eta) \tag{1}\]  
We denote the position of the detected target in the pixel as \((x_{a}y_{a})\) and the standard deviation of the diffusion spot produced in the detector plane as \(\sigma_{r}\). Due to diffraction in the optical system with a finite aperture, the image of a point target at infinity can be characterized by a point spread function, referred to as a diffusion spot in this paper. Previous studies [27; 28; 29] have approximated this point spread function using a Gaussian distribution. We propose that the probability density of the photon arrival positions is directly proportional to the light intensity distribution of the diffusion spot. Consequently, each photon arrival position \((x_{j}y_{j})\) is approximated as following a Gaussian distribution. \[p(x_{j},y_{j})=\frac{1}{2\pi\sigma_{r}^{2}}\exp[-\frac{(x_{j}-x_{a})^{2}+(y_{j }-y_{a})^{2}}{2\sigma_{r}^{2}}] \tag{2}\]  
Its marginal distribution in the X direction is as follows:  
\[p(x_{j})=\frac{1}{\sqrt{2\pi}\sigma_{r}}\exp[-\frac{(x_{j}-x_{a})^{2}}{2\sigma _{r}^{2}}] \tag{3}\]  
When a photon is received by the detector, the photon generates an electron cloud on the anode, and each electron cloud covers a number of anode strips. The subsequent signal processing system processes the charges collected from the anode strips to obtain their center of gravity positions. In this paper, a center of gravity algorithm is used to obtain the photon position. In the case of no aliasing, the position of the center of mass of the electron cloud produced by the photon is denoted as \((x_{1}y_{1})\). The charge density of each electron cloud produced at the anode approximates a Gaussian distribution. The charge density of the electron cloud generated in the X direction is:  
\[\rho(x)=\frac{Q_{total}}{\sqrt{2\pi}\sigma_{e}}\exp[-\frac{(x-x_{1})^{2}}{2 \sigma_{e}^{2}}] \tag{4}\]  
where \(Q_{total}\) denotes the total charge generated by one photon at the anode, and \(\sigma_{e}\) denotes the size of the electron cloud. Since the width of the electrode is much smaller than the size of the electron cloud, the charge collected at the \(i\)-th electrode in the X direction can be approximated as:  
\[Q_{i}=\int\limits_{iP-\frac{d}{2}}^{iP+\frac{d}{2}}\rho(x)dx=\rho(\xi)d \tag{5}\]  
where \(d\) is the electrode width and \(iP-\frac{d}{2}\leq\xi\leq iP+\frac{d}{2}\). In this paper, we choose \(\xi=iP\) to obtain \(Q_{i}\)[19]. \[Q_{i}=\frac{Q_{total}}{\sqrt{2\pi}\sigma_{e}}\exp[-\frac{(iP-x_{1})^{2}}{2 \sigma_{e}^{2}}]d \tag{6}\]  
where \(P\) is the anode spacing corresponding to eight detector pixels.