## 2 Methods and Design
### Design of the Fundus Imaging System
#### 2.2.3 Imaging System Parameter  
In order to miniaturize the fundus optical system, the total length of the system was limited in 50 mm. The pupil of the human eye was used as the aperture diaphragm of the imaging system, and the pupil diameter of the human eye is about 4 mm [19], so the entrance pupil diameter of the imaging system was set at 4 mm. The field of view determined the size of the fundus imaging area, and the field of view of this system was 50\({}^{\circ}\), considering the fundus viewing range. The imaging optical path used the visible wavelength band of 486 nm-656 nm for imaging [14]. The CCD sensor was selected as the receiver of the imaging system. The design indicators of the fundus imaging system are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Pupil diameter & 4 mm \\ \hline Wavelength & 486 nm–656 nm \\ \hline Full field of view & 50\({}^{\circ}\) \\ \hline Object resolution & Distinguish the fundus 5 μm \\ \hline Total length & \textless{}50 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design indicators of fundus imaging system.  
As the pupil has the effect of limiting the amount of light entering the eye, it is usually used as the aperture diaphragm of the system in an optical system, and could be used as the aperture diaphragm of the imaging system in this system [16].  
The field of view of the fundus camera refers to the range of fundus imaging, and the conversion formula of the fundus field of view and field angle is as follows:  
\[h=f^{\prime}_{eye}\times tan\omega \tag{3}\]  
where \(h\) is the fundus half-field height, \(f^{\prime}_{eye}\) is the effective focal length of the human eye [15], and \(\omega\) is the half-field angle, as shown in Figure 4.The effective focal length of the eye mask type in this design was 9.6 mm, the half-field angle was 25\({}^{\circ}\), and the half-field height was 4.47 mm.  
Combined with the eye model, the imaging group used a combination of spherical lens and aspheric lens [20], which was matched to a CCD with a pixel size of 5 \(\upmu\)m \(\times\) 5 \(\upmu\)m and required a resolution of a 5 \(\upmu\)m retinal structure. From \(N=1000/2a\) (\(N\) is the limit resolution, \(\alpha\) is the pixel size), we can see that the ultimate resolution of the imaging system was 100 lp/mm. From \(\varphi=1.22\lambda/D\) (\(\varphi\) is the ratio of the pixel size \(d\) to the focal length \(f\) of the optical system, \(D\) is the diameter of the entrance pupil, and \(\lambda\) is the center wavelength), the diffraction-limiting aperture value was 4.8. The two-dimensional structure is shown in Figure 5. The imaging system uses four single lenses to complete the design, of which two were aspherical lenses. The structure was simple, the total length of the system was greatly shortened, and the total length was only 34.6 mm, so the compact design was realized. The imaging lens group was a combination of positive and negative lenses and aspheric lenses, which eliminated some of the eye differences and the main aberrations of the system. The distance between the sensor and the camera port was about 10 mm, and the back intercept of the imaging system was 18 mm, meeting the requirements. Lens data of imaging system are shown in Table 3.  
Figure 4: Imaging field of view.  
Figure 5: Design results of the imaging system in Zemax. (**a**) Two-dimensional structure of the imaging system. (**b**) Three-dimensional structure of the imaging system.