## 5 Conclusions  
To study the characteristics of an exoplanetary atmosphere, a novel optical system based on transit spectroscopy was designed. The optical-system indices were systematically analyzed on the basis of the principles of astronomy and optics, of which the transit SNR was introduced into the determination of telescope aperture and throughput. Furthermore, a modular design of optical system within index requirements is newly presented.  
In order to detect transit spectrum, the parameter requirements of optical system are derived. Wavelength coverage is selected via the target characteristic, and the F number is determined according to the relationship between PSF and pixel size under given wavelength distribution. Spectral resolution and SNR are limited according to existing retrieval codes. Telescope aperture and overall throughput were discussed according to the potential for the realization of the goal SNR during missions. Combined with pointing accuracy, Airy spot, and assembly tolerance, telescope and payload FOV assignments are listed. The operating environment of the instrument, including temperature and orbit, was also considered. Optical indices of instrument are listed.  
Furthermore, a feasible optical system was proposed, and performance was evaluated to verify the validity of the indices. The simulation showed that the design and performance met the requirements. The off-axis dual-paraboloid mirror telescope, designed with a 2.1 m aperture to reach the goal SNR, was matched with a dichroic system to provide diffraction-limited input beams for payloads. The spectral resolutions of the dual-channel spectrometer were 111-200 and 43-94. The image points in each wavelength were smaller than the Airy spot within slit FOV, and the PSF FWHM at \(\lambda_{min}\) was 36 \(\upmu\)m providing 2 pixels of 18 \(\upmu\)m sampling. The overall optical system achieved good performance and met the index requirements, which could achieve the scientific goal of studying the atmospheric characteristics of exoplanets.  
In order to obtain a larger collection area and sufficient SNR, a primary mirror of the telescope with a larger aperture was designed in this simulation study. However, larger-aperture mirrors have higher requirements for the carrying capacity of aircraft, and the corresponding manufacturing technology of mirrors still needs to be improved. Therefore, in a future study, methods to improve SNR should be deeply discussed to reduce the requirements of telescope apertures, and the improvement of mirror-manufacturing technology should be paid more attention.  
Conceptualization, F.W.; methodology, F.W.; software, X.D.; validation, Y.P.; formal analysis, X.F.; investigation, F.W.; resources, H.W.; data curation, X.L.; writing--original-draft preparation, F.W.; writing--review and editing, Y.S.; visualization, X.D.; supervision, H.W.; project administration, X.F.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
Figure 12: PSF curves for (**a**) CH1 and (**b**) CH2 in \(\lambda_{min}\). Optical system of two channels was designed to achieve 2-pixel full width at half-maximum (FWHM) sampling when pixel size is 18 \(\upmu\)m.  
**Funding:** This research was funded by National Natural Science Foundation of China (NSFC) grant number 11803075.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.