## 1 Introduction  
The temperature field in the mesosphere and lower thermosphere (MLT) is an important parameter for the research of the terrestrial atmosphere. The temperature structure plays a significant role in studying the physical and chemical processes in the MLT region, the transport of energy and momentum between the MLT and its upper and lower layers, as well as the transport of atmospheric components. Currently, many measurements of temperature structure in MLT are troughing the passive remote sensing of airglow emission. Ground passive observation devices such as Michelson interferometer, Fabry-Perot interferometer, and grating spectrometer mainly retrieve the atmospheric temperature of the emission region by observing the airglow line width and the shape of the spectral band. However, ground observation devices, even rocket loads, cannot meet the requirements of space coverage and time resolution. The global temperature information can only be obtained through space-borne instruments. The O\({}_{2}\) visible band airglow \(A\) (0-0) band and the near-infrared band airglow 1.27 \(\upmu\)m (0-0) band emission layer exist in the MLT region [1]. At the same time, the emission intensity is related to the atmospheric temperature. Moreover, it has the advantage that the radiation lifetime is enough to be in local thermodynamic equilibrium with the background atmosphere, so it becomes a suitable tracer for temperature detection in MLT. Since the 1990s, several satellite programs for observing atmospheric parameters in MLT have been carried out mainly in the United States. In 1991, High Resolution Doppler Interferometer(HRDI) and Wind Imaging Interferometer (WINDII), carried on the UARS satellite, observed three rotational lines in O\({}_{2}\)_A_-band airglow (762 nm) and atomic oxygen green line airglow (OI577.7 nm) by limb observation. The atmospheric temperature in the range of 80-100 km was retrieved using the double-line ratio method and the Doppler broadening method, respectively. The best temperature measurement accuracy of HRDI is \(\pm\)7 K. The temperature measurement accuracy of WINDII is 20-75 K [2; 3]. In 2002, Optical Spectrograph and InfraRed Imaging System (OSIRIS) was carried on an Odin satellite. Additionally, the core component of the instrument was the grating spectrometer. The actual observed _A_-band spectrum was normalized and fitted to the normalized simulated spectrum. The sum of the square variance of the two spectra was calculated. The temperature when the sum of the square variance reached the minimum was taken as the temperature inversion result. The simulation results of the OSIRIS inversion algorithm show that the simulated accuracy of the temperature measurement of OSIRIS is about \(\pm\)2 K at 90 km and \(\pm\)6 K at 105 km [4]. Presently, domestic temperature detection in MLT through space-borne instruments is still in the initial stage of theoretical research. There are no actual observation data of the O\({}_{2}\)_A_-band night glow for our research group. Therefore, the corresponding temperature inversion algorithms are based on simulated observation data. In 2019, [PERSON] et al. studied the wind and temperature detection accuracy in near-space using O\({}_{2}\) 1.27 \(\upmu\)m near infrared airglow. [PERSON] from Wuhan University of Science and Technology proposed to carry out limb emission measurements, based on a wide-angle Michelson interferometer, to realize the simultaneous detection of the atmospheric wind field and temperature field in the stratosphere, mesosphere, and low thermosphere (40-80 km). Moreover, they studied the forward model and inversion algorithm. It is proposed to use the double-line ratio method to obtain temperature information, that is, the atmospheric temperature is determined by the ratio of absorptivity of two independent emission lines with different temperature sensitivity. The inversion accuracy of temperature is about 1.5-3 K [5]. In this paper, a spatial heterodyne spectrometer is adopted to observed the O\({}_{2}\)_A_-band night glow.