## 5 Conclusions  
The radiation of O\({}_{2}\)\(A\)-band airglow is distributed in the altitude range of 80-120 km, and the rotational spectra can be used to measure the atmospheric temperature structure within the corresponding altitude range. Based on the parameters of the spatial heterodyne spectrometer as the instrument model, this paper adopts the limb mode and simulates the detection of O\({}_{2}\)\(A\)-band night glow. In the full spectrum of O\({}_{2}\)\(A\)-band night glow, based on the sensitivity of emission line intensity on temperature, the most reasonable band for retrieval of temperature is selected, which can take into account the narrower band design of spectrometer, higher inversion efficiency, and higher inversion accuracy. It has been verified that the band selected in this paper can obtain an accuracy of about 3.4 K for the retrieval of temperature, slightly higher than 0.2 K by other sampled bands.  
According to the observed spectral radiance of the selected band, several temperature inversion algorithms commonly used in O\({}_{2}\) airglow are used to obtain the temperature profile in MLT. An optimal estimation algorithm for the temperature structure, which is most suitable for limb observation, is matched. When a priori temperature profile is extracted directly from the MSISE-00 atmospheric model database, the retrieved accuracy is 3.4 K, which is much better than 6.5 K through the least squares method, and 16.7 K through the peak relative intensity ratio method. At the same time, optimization is carried out based on the traditional optimal estimation method, which is characterized by the selection of the Gauss-Newton iterative method, and the combination of Tikhonov regularization constraints. The results show that the mean absolute bias in all the tangent heights can be reduced by about 0.4 K by constructing an a priori covariance matrix with regularization constraints.  
In this paper, the influence of a priori constraints on the accuracy of retrieved temperature is further studied. The results show that the accuracy of atmospheric temperature can be significantly improved by improving the accuracy of a priori. When a priori accuracy temperature is controlled within \(\pm\)5 K, the average absolute bias of temperature is 0.58 K within the range of 95-110 km, and the average accuracy of temperature in all the vertical fields of view can reach 1.35 K, which is better than the accuracy of OSIRIS on Odin at 90-105 km, as described in the introduction. In the later work, many independent profile data can be obtained from the atmospheric database or the detection data of other satellites or radiosondes. Statistical training can be used to construct the optimal a priori information so as to continue to improve the accuracy of a priori. It can further improve the accuracy of retrieved atmospheric temperature in MLT.  
Conceptualization, W.W., H.L., Z.L. and W.X.; methodology, W.W., H.L., Z.L. and W.X.; software, W.W.; validation, W.W., H.L., Z.L. and W.X.; formal analysis, W.W.; investigation, W.W., H.L., Z.L. and W.X.; resources, W.W., H.L., Z.L. and W.X.; writing--original draft preparation, W.W.; writing--review and editing, W.W., H.L., Z.L. and W.X.; visualization, W.W.; supervision, H.L., Z.L. and W.X.; project administration, H.L., Z.L. and W.X.; funding acquisition, H.L., Z.L. and W.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Program of China (No. 2022 YFB3901800, No.2022 YFB3901803, No. 2021 YFB3901000, No.2021 YFB3901004, No.2022 YFB3904805). National Natural Science Foundation of China (41975033, 61975212). Key Research Program of the Chinese Academy of Sciences (Grant No. JCPYJJ)-22010). HFIPS Director's Fund (Grant No. YZJ)202210-TS).  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.