# Effect of Fiber Optic Plate on Centroid Locating Accuracy of Monocentric Imager
## 4 Simulation Analysis and Results  
### FOP Parameters: Fill Factor and Fiber Diameter  
The fill factor is an important parameter of a FOP, which is determined by the ratio of the light passing area of the FOP to the total area and can be expressed as  
\[K=0.907\times\frac{d_{c}^{2}}{d_{f}^{2}} \tag{8}\]  
where \(K\) is the fill factor, 0.907 is the fill coefficient of the FOP arranged in a hexagonal shape, \(d_{c}\) is the fiber core diameter and \(d_{f}\) is the fiber diameter. We note that the fill factor is determined by the fiber diameter and the fiber core diameter. If the filling factor increases, and the fiber diameter decreases, the luminous flux of FOP also increases. The image transmitted by the FOP is closer to the image received by the image sensor which is directly coupled to the imaging focal plane. The FOP image transmission performance is greatly enhanced [6; 13]. At the same time, the fiber cladding thickness become thinner. If the fiber cladding thickness is too thin, it is very easy to cause mutual interference of the transmitted signals between the fibers, and the fiber cladding no longer plays a mechanical protection role. During the entire FOP preparation process, it is extremely easy to produce the fiber deformation resulting in the large-area dark filaments, the broken filaments and other phenomena that damage the image transmission quality of the FOP. Therefore, the optical fiber cladding cannot be too thin--that is, the fiber diameter cannot be too small--and the fill factor cannot be too large. However, if the filling factor is too small, the luminous flux of the FOP must be reduced, and the overall image transmission performance of the FOP is greatly reduced. The signal strength that the image sensor can receive is also very weak, which is bound to increase the difficulty of space target identification. Therefore,considering the high stability and the high luminous flux of FOP image transmission, it is more reasonable to choose a FOP type with a larger fiber diameter and a larger fill factor. We set the image sensor pixel spacing to 10 \(\upmu\)m. We note that the fill factor should be less than 0.907. The fiber cladding should not be too thin, so the fill factor cannot be too close to 0.907. We set the fill factor to increase from 0.5 to 0.8 with a single step size of 0.1. The FOP is made by secondary drawing, so the fiber optic diameter should not be too large. We set the fiber diameter to increase from 3 \(\upmu\)m to 10 \(\upmu\)m with a single step size of 1 \(\upmu\)m. Once the fill factor and the fiber diameter are determined, the fiber core diameter is determined. We set relative initial position where a certain fiber center coincides with a certain image sensor pixel center. We made a PTOIS simulation in MATLAB and established the relationship among the fill factor, the fiber diameter and CLESD. Figure 5 intuitively shows the simulation result that after adding FOPs as relay image transmission elements, the CLA will be more or less reduced. Under the conditions that the fiber diameter remains unchanged and the fill factor becomes smaller, the CLA tends to enhance as a whole. Under the conditions that the filling factor remains unchanged and the fiber diameter becomes larger, the CLA tends to decrease as a whole. The case of an FOP with a smaller fiber diameter and a smaller fill factor has a higher CLA. In a word, in order to make the monocentric imager with the FOPRIT scheme have a higher CLA, we choose the FOP case with a smaller fill factor and a smaller fiber diameter. Then, as mentioned above, in order to prevent the fiber cladding from becoming too thin and increase the luminous flux of FOP, a FOP with a larger fiber diameter and a larger fiber diameter should be selected. In summary of the above two conclusions, observing Figure 5, we note that when the fiber diameter value of 4 \(\upmu\)m or 6 \(\upmu\)m, the fill factor has a weak effect on CLA. When fill factor values are 0.5, 0.6 and 0.7, CLAs are almost uniform.