## 3 Results and Analyses  
The ray tracing result of our designed CTLAS system by the ASAP software, shown in Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline  & \(c\) & \(k\) & \(A\) \\ \hline
**Lens1** & –46.65 & –2.3 & 0 \\ \hline
**Lens2** & –15.3 & –0.654 & –3.928 ×10\({}^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The \(c\), \(k\), and \(A\) values of the 2 nd surfaces of lens 1 and lens 2. Figure 7: The setup of the CTLAS system. It is composed of a two-lens confocal system. The optical efficiency, defined as the ratio of the luminous flux of the LEDs and the output luminous flux emerging from lens 2, is obtained by  
\[Optical\,Efficiency=\frac{F_{O}}{F_{L}}, \tag{3}\]  
where \(F_{L}\) and \(F_{O}\) are, respectively, the luminous flux of the LEDs and the output luminous flux emerging from lens 2. In Figure 9a, the light pattern on the specimen is a 27 mm diameter circular area that is 550 mm away from the bottom of the LEDs. Figure 9b shows the uniformity of the light patterns calculated by the illuminance values of 17 tested points. The red points show the testing positions. The uniformity of the light pattern is obtained by  
\[Uniformity=\frac{E_{ave}}{E_{min}}, \tag{4}\]  
where \(E_{ave}\) and \(E_{min}\) are the average and the minimum irradiation values of the light pattern on the specimen. After the calculation, the optical efficiency of this system is 72.7%. The uniformity of the light pattern is 1.14, and the central irradiation value of the light pattern is 62,950 lux. The result surpassed the requirement of the illumination value of our initial setting. In a commercial fluorescence microscope system, most LED light sources are just used to illuminate the specimen without any additional components to collect light. Some LED light sources are attached with a converging lens to enhance the illuminance. Therefore, we take three examples, a nine-LED  
Figure 8: The ray tracing result of the CTLAS system. Figure 9: (**a**) The circular light pattern on the specimen, (**b**) the uniformity of the light pattern calculated by the illuminance values of the 17 tested red points. array, a nine-LED array with a converging lens, and the CTLAS system, to compare the illuminance, as shown in Figure 10.  
In Figure 10b, a 150 mm diameter and 0.7 NA value converging lens are assembled at the center of the nine-LED array; the distance between the two is the focal length of the converging lens. The corresponding central illuminance and the uniformity of these three examples are shown in Table 2. The result shows that the CTLAS system obviously has the best uniformity and the greatest center illumination value, which is 46 times brighter than the nine-LED array and 40 times brighter than the nine-LED array with the converging lens. We successfully assembled the LED array and the CTLAS system. The system picture is shown in Figure 11.  
All the lenses in this system are made by mold injection. We used the CTLAS system to observe the fluorescent images of the vascular bundle organization modified with the Cy3 fluorescence molecules. \begin{table}
\begin{tabular}{c c c c} \hline  & **9-LED Array** & \begin{tabular}{c} **9-LED Array with** \\ **Converging Lens** \\ \end{tabular} & \begin{tabular}{c} **9-LED Array with the** \\ **CTLAS System** \\ \end{tabular} \\ \hline \
\begin{tabular}{c} **Central illuminance** \\ **value (Lux)** \\ \end{tabular} & 1377 & 1590 & 62,950 \\ \hline
\begin{tabular}{c} **Uniformity** \\ \end{tabular} & 2 & 1.81 & 1.14 \\ \hline \end{tabular}
\end{table} 
Table 2: The simulation results of the central illuminance values and the uniformity of the nine-LED array, the nine-LED array with the converging lens and the CTLAS system. Figure 11: The assembled CTLAS system. Figure 10: The three types of LED light sources, (**a**) the nine-LED array only, (**b**) the nine-LED array with the converging lens, and (**c**) the nine-LED array with the CTLAS system.