# Design of Zoom Optical System from Visible to NIR-II for Vivo Fluorescence Imaging Device
## 3 Optical Design and Optimization  
### Initial Structure Selection  
The design specifications of the zoom optical system are shown in Table 2; the system uses a 1/2-inch InGaAs sensor, an image element size of 5 \(\upmu\)m \(\times\) 5 \(\upmu\)m, a light-sensitive size of 6.4 mm \(\times\) 5.12 mm, a diagonal length of 8.2 mm, working spectrum of 400-1700 nm, can be fast and provide comprehensive observation of fluorescence characteristics with the help of the filter; and the f-number is variable. However, the amount of incoming light should be as large as possible; distortion should be within 3%, and, by Nyquist sampling law, the system requires the modulation transfer function MTF \(\geq\) 0.3 at 100 lp/mm. There is a need for a macroscopic in vivo imaging device to determine the parameters of its supporting optical system. The primary parameter of a visible-NIR-II in vivo fluorescence imaging device is the wide-band optical system, which is required to observe different wavelengths without switching the lens system; we need to consider the working distance of the optical system, which needs to leave at least 35 cm of space with the lens for biologists to inject fluorescent dyes or apply anesthetic agents to live animals. The size of the mice and rabbits determines the field of view, and depending on the actual conditions, a square field view of 3 cm-20 cm is required. A simple calculation provides a field of view of 3-28\({}^{\circ}\). The adaptation of the optical system designed in this paper to the InGaAs detector is also reflected in these parameters. First, the image plane size (Type 1/2) and image element size (5 \(\upmu\)m \(\times\) 5 \(\upmu\)m), which determines the image plane size and image quality evaluation of the optical system at half 1/2 the size, means that the image plane size needs >4.1 mm, and there is a certain margin in the design with a 4.2 mm image plane size. Then, the optical system design index is determined by the image element size before the MTF (MTF indicates the modulation variation in an optical system imaging, and the MTF curve can be used to evaluate the imaging performance of an optical system more comprehensively) calculation shows that the corresponding design requirements need to be met at 100 lp/mm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Focal length & 25–150 mm \\ f-number & 5.0–6.0 \\ Working spectrum & 400–1700 nm \\ Full field of view & 3.1–18.6\({}^{\circ}\) \\ Distortion & \(\leq\)3\% \\ MTF(100 lp/mm) & \(\geq\)0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design specifications of the zoom optical system. Then, we need to meet the structural assembly requirements of this detector, which requires a back intercept of \(\geq\)17.526 mm; then, the detector band weights and the device observation band matching the following figure (Figure 3) is the quantum efficiency. It can be seen that in the visible band, there is a section of quantum efficiency that is low, but this is the observation band we need; in the design process, the weight of this band needs to be increased to ensure a more balanced imaging effect, and then combined with the nature of the organism to be observed. The absorption coefficient of water compared to visible light did not increase by much, but the water had absorption peaks at 900 nm and 1450 nm in the design of these two bands, which can be skipped without consideration. The initial layout of the optical system plays a crucial role in the subsequent design, and there are usually two methods for selecting the initial layout. One is the PW calculation method based on the primary aberration theory of the thin lens. However, it needs large and tedious calculations and is not effective for dealing with large aberrations in a wide band [11; 12; 13; 14; 15]. The second is the scaling method, so the second method was chosen in this paper. According to the required parameters, a four-group zoom system in the patent library was identified as the initial layout [16].