# Design of Zoom Optical System from Visible to NIR-II for Vivo Fluorescence Imaging Device
## 3 Optical Design and Optimization
### Initial Structure Selection
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ELEM (S1–S2)** & **EFFL/mm** & **I/mm** & **I’/mm** & **Power/mm\({}^{-1}\)** \\ \hline (1–2) & \(-838.908988\) & \(856.928146\) & \(-830.307019\) & \(-0.001192\) \\ \hline (2–3) & \(509.499515\) & \(-501.816581\) & \(463.792934\) & \(0.001963\) \\ \hline (4–5) & \(649.766047\) & \(-661.913398\) & \(598.462667\) & \(0.001539\) \\ \hline (6–7) & \(-188.382558\) & \(193.390036\) & \(-187.898733\) & \(-0.005308\) \\ \hline (8–9) & \(-134.445631\) & \(136.704320\) & \(-136.088199\) & \(-0.007438\) \\ \hline (9–10) & \(203.022051\) & \(-203.075034\) & \(187.508803\) & \(0.004926\) \\ \hline (11–12) & \(-369.991328\) & \(368.785954\) & \(-375.935497\) & \(-0.002703\) \\ \hline (13–14) & \(517.164067\) & \(-497.424250\) & \(522.149309\) & \(0.001934\) \\ \hline (15–16) & \(611.601289\) & \(-605.083551\) & \(605.468528\) & \(0.001635\) \\ \hline (18–19) & \(340.996070\) & \(-340.135662\) & \(317.624498\) & \(0.002933\) \\ \hline (20–21) & \(1269.725526\) & \(-1277.621807\) & \(1248.774261\) & \(0.000788\) \\ \hline (22–23) & \(-479.887421\) & \(480.615973\) & \(-485.336322\) & \(-0.002084\) \\ \hline (24–25) & \(-219.869174\) & \(225.500765\) & \(-219.419265\) & \(-0.004548\) \\ \hline (26–27) & \(213.582213\) & \(-205.255629\) & \(207.937765\) & \(0.004682\) \\ \hline (28–29) & \(403.404418\) & \(-416.395251\) & \(379.400041\) & \(0.002479\) \\ \hline (30–31) & Infinity & \(0.000000\) & \(0.000000\) & \(0.000000\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of each lens in patent short focus state. group in the four groups of the zoom optical system are shown in Table 4. The distances of each group in the four groups at long and short focal lengths are shown in Table 5.  
According to Table 5, the theoretical configuration of the four-group zoom optical system is shown. The total length of the zoom optical system is flexible at over 200 mm, and the aperture diaphragm is located at 3.6 mm in front of group 4. During the zooming process, the aperture diaphragm and group 4 move at the same path, and the f-number of the optical system keeps changing continuously. When the focal length of the optical system gradually changes from 25 mm to 150 mm, group 2 and group 4 gradually move away from fixed group 1, and group 3 gradually moves closer to fixed group 1. So, all three zoom curves have no inflection point during the zooming process. Three structures are set up in ZEMAX with focal lengths of 25 mm, 100 mm, and 150 mm, corresponding to the short focal length, medium focal length, and long focal length, respectively. The operands are added in ZEMAX to control the image quality. The image quality weight is reduced in the design process to satisfy the prerequisite of the optical system, such as the parameters of the working spectrum, focal length, the field of view, etc. After satisfying the basic parameters of the optical system, the zoom curve of the system needs to be ensured so that it does not have an inflection point. The short focal length of each group is used as the basis; the need to ensure the change in each component during the zooming process is monotonic, and here, more multiple group states are set, with focal lengths of 50 mm, 75 mm, 110 mm, 120 mm, 130 mm, and 140 mm, respectively, to control each component monotonic. Because the change in the focal length curve is more drastic from a mid-focus to a long focus, it is necessary to set several more multiple groups.