## 4 Results of Optical-System Design and Simulation
### Infrared Spectrometer  
Due to the particularity of observed targets, the design requirements of infrared spectrometer have the characteristics of lower spectral resolution demand, higher system stability and throughput, no angular resolution. Therefore, a prism-dispersing spectrometer is selected as the design proposal, which has higher optical efficiency at required resolution than that of others, increasing the photoelectron count in spectral resolution elements and decreasing influence of the dark current and readout noise to signal. Additionally, prism can reduce the stray light caused by manufacture tolerance as well. The spectrometer module is connected to the dichroic system. The focused beam from dichroic enters two independent channels (CH1 and CH2) of the infrared spectrometer through slit. Then it is shaped into parallel beam by collimator and dispersed to spectrum by prisms. Finally, the spectrum is focused on the detector by lenses of camera. Compared with the double lens scheme, the off-axis parabolic mirror scheme is adopted as the collimator to improve the throughput and reduce the influence of chromatic aberration. The optical parameters of infrared spectrometer are summarized in Table 7. The layouts of two spectrometer channels are shown in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **CH1 (2–4 μm)** & **CH2 (4–8 μm)** \\ \hline Input F/\# & f/10.8 & f/10.8 \\ Slit size & 0.33 mm \(\times\) 2.2 mm & 0.43 mm \(\times\) 2.2 mm \\ Prism material & CaF\({}_{2}\) & CaF\({}_{2}\) \\ Prism apex and incidence angle & 29.4\({}^{\circ}\) and 39.6\({}^{\circ}\) & 8.9\({}^{\circ}\) and 9.1\({}^{\circ}\) \\ Camera material & Silicon and germanium & CaF\({}_{2}\) and ZnS \\ Airy radius in \(\lambda_{min}\) & 36 μm & 36 μm \\ PSF sampling \(\lambda_{min}\) and \(\lambda_{max}\) & 2 and 4 pix & 2 and 4 pix \\ Pixel scale & 0.12′′/pixel & 0.24′′/pixel \\ Pixel size & 18 μm & 18 μm \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of optical parameters of infrared spectrometer. Figure 8: Matrix spot diagrams at exit of dichroic system (slit surface) for (**a**) CH1 and (**b**) CH2. Different boxes show image spots and Airy spots at different FOVs and wavelengths. (**a**) Spot diagram of CH1. Boxes in different rows correspond to different FOVs. Second, third, and fourth columns show imaging results at the exit of dichroic system at wavelengths of 2, 3, and 4 μm, respectively. The overall design of optical system is shown in Figure 10, including the telescope, dichroic system, and spectrometer. Combined with the proposed optical system, the optical performance of the spectrometer is evaluated. Spot diagrams and PSF curves of two channels at the maximal and minimal wavelengths are shown in Figure 11. For example, in (a) left, there are 5 boxes in the spot diagram that correspond to imaging spots at different FOVs. Blue and green spots represent imaging spots with wavelengths of 2 and 2.018 \(\upmu\)m, respectively. Black circles denote Airy rings. The image spots of each wavelength were diffraction-limited in the required FOV; (a) right shows the PSF curve distributed along the Y axis in the central FOV. Two peaks of the curve correspond to image spots with wavelengths of 2 and 2.018 \(\upmu\)m. At the minimal wavelength of CH1, spots could be distinguished when \(\Delta\lambda\) = 0.018 \(\upmu\)m. Moreover, the resolution for CH1 was estimated to be 111-200, and for CH2 is 43-94. Figure 12 shows the PSF curve distributed along the Y axis at minimal wavelength (\(\lambda_{min}\)) in each channel.The first dark rings of PSF were located at 36 \(\upmu\)m for both CH1 and CH2, which means that the FWHM at all wavelengths was no less than 36 \(\upmu\)m. Thus, at least 2-pixel FWHM sampling can be provided when the detector pixel size is 18 \(\upmu\)m.  
Figure 10: (a) Overall structure of optical system, including telescope, dichroic system, and spectrometers. FGS, CH1, and CH2 channels represented by blue, green, and red, respectively.