# Effect of Fiber Optic Plate on Centroid Locating Accuracy of Monocentric Imager
## 3 Materials and Methods  
### Evaluation Standard of Centroid Locating Accuracy  
Moreover, in the aerospace field, image processing is more complicated, and star image processing can only be done with traditional methods. We use centroid method to solve the centroid location of the spatial target. The centroid method is a centroid location algorithm with the pixel intensity value as the weight [9; 10]. Assuming that only one target is imaged on the sensor (see Figure 1), the intensity value of any pixel whose coordinate is  
Figure 2: Whether in \(x^{\prime\prime}\) or \(y^{\prime\prime}\) direction, the centroid position of the imaging spot is the same as the centroid position of the imaging spot after being translated by one image sensor pixel. \(S_{1}\) is the initial imaging spot, \(S_{2}\) is the imaging spot over one periodic translation and T is the translation period of the imaging spot.  
\((x^{\prime\prime},y^{\prime\prime})\) on the image sensor is \(l^{\prime\prime}(x^{\prime\prime},y^{\prime\prime})\). The centroid coordinate \((x^{\prime\prime}_{0},y^{\prime\prime}_{0})\) of the imaging spot calculated by centroid method can be obtained from:  
\[x^{\prime\prime}_{0}=\frac{\sum{l^{\prime\prime}(x^{\prime\prime},y^{\prime \prime})x^{\prime\prime}}}{l^{\prime\prime}(x^{\prime\prime},y^{\prime\prime})},y^{\prime\prime}_{0}=\frac{\sum{l^{\prime\prime}(x^{\prime\prime},y^{\prime \prime})y^{\prime\prime}}}{l^{\prime\prime}(x^{\prime\prime},y^{\prime\prime})} \tag{1}\]  
We set the ideal coordinate of the space target to \((x_{0},y_{0})\) and set the distance difference between the ideal position of the space target and the centroid position of the imaging spot to the centroid locating error (CLE) which can be expressed by:  
\[CLE=\sqrt{\left(x^{\prime\prime}_{0}-x_{0}\right)^{2}+\left(y^{\prime\prime}_ {0}-y_{0}\right)^{2}}, \tag{2}\]  
We use centroid locating error standard deviation (CLESD) to quantitatively describe the CLA of a space target. CLESD is defined as:  
\[\mu=\frac{1}{MN}\sum_{i=1}^{M}\sum_{j=1}^{N}CLE_{ij}, \tag{3}\]  
\[CLESD=\sqrt{\frac{1}{MN-1}\sum_{i=1}^{M}\sum_{j=1}^{N}\left(CLE_{ij}-\mu \right)^{2}}, \tag{4}\]  
where \(CLE_{ij}\) is the CLE when the imaging spot is translated \(i\) times in the \(x\) direction and \(j\) times in the \(y\) direction. \(\mu\) is the average value of CLE. \(M\) is the total number of imaging spot translations in the \(x\) direction and \(N\) is the total number of imaging spot translations in the \(y\) direction. CLESD is comprehensive and objective. It is not an evaluation standard for the instantaneous imaging of a certain space target, but an evaluation standard based on comprehensive consideration of dynamic imaging of multiple space targets that can be detected by the monocentric imager.  
When \(M=N\) and \(L_{M}=L_{N}=1\) pixel, CLESD can be used to quantitatively evaluate the CLA of the PTOIS process, where \(L_{M}\) is the distance when the imaging spot is translated \(M\) times in \(x\) direction and \(L_{N}\) is the distance when the imaging spot is translated \(N\) times in \(y\) direction. The lower the CLESD, the higher the CLA.