Ground-Based Airglow Imaging Interferometer (GBAII) is a ground-based wind field detection prototype developed by our research group that integrates the principles of "rotational spectral line temperature measurement" and "four-intensity method". The imaging interferogram of airglow 90~100 km above the earth can be obtained by taking long time exposure of 200 s. Then the information of atmospheric wind speed, temperature and volume emissivity over the Earth can be obtained from the imaging interference fringe. Modulation Transfer Function (MTF) is a very important index in the design, development and testing of ground-based airglow imaging interferometer GBAII, which can characterize the imaging quality of GBAII. In this paper, the modulation transfer function of ground-based airglow imaging interferometer is studied. By using He-Ne laser wavelength of 632.8 nm, O2(0-1) 867.7 nm and O(1S) 557.7 nm as light sources, the MTF values of the optimized design, theoretical calculation and actual images are given. Firstly, the optical imaging structure of GBAII consists of five parts: a tapered mirror light receiving system, a wide-angle MI phase modulation system, a narrowband interference filter, a CCD and three lenses. The optical structure of GBAII is optimized by Code V, and the point sequence diagram of GBAII was obtained. 4×4 was used as a bin, and the diameter of dispersion spot was about 60 μm at 0° field of view, and 80~90 μm at 2°~9.5° field of view, and the limit resolution was 6.25 lp/mm. For the three airglow lines with wavelength 557.7 nm, 630.0 nm and 867.7 nm, all the MTF values are above 0.3, and some of the MTF values are higher than 0.6. However, it can also be seen that the MTF meridional branch and sagittal branch differ greatly in the full field of view, mainly caused by astigmatism. Secondly, according to Fourier optical theory, the MTF expression of GBAII optical system is obtained by calculating the MTF of wide-angle Michelson interferometer, interference filter and CCD. The MTF curve of GBAII is given by substituting the MTF expression of GBAII into the relevant structure and size of GBAII optimized by ultra-wide Angle, thermal compensation and achromatic conditions. For airglow wavelengths at 557.7 nm and 867.7 nm, the MTF value is 0.508 and 0.510, corresponding to Nyquist frequencies of 20 lp/mm and 16 lp/mm, respectively. For the GBAII developed by our researcher group, the MTF value is greater than 0.51 at low frequency, which is greater than 0.35 MTF of international famous wind imaging interferometer WINDII. Thirdly, in order to obtain the experimental MTF value of GBAII, it is necessary to take imaging interferogram through GBAII first, and use software to read gray value of image point by point to calculate contrast of interference fringes. The MTF of GBAII imaging system is equal to the contrast of the image divided by the contrast of the object, where, the contrast of the subject is not equal to but less than 1. He-Ne laser spectrum line of 632.8 nm, O2(0-1) 867.7 nm and O(1S) 557.7 nm were used as light sources respectively to obtain the indoor and outdoor imaging interferogram of GBAII. The experimental MTF of different wavelengths was obtained according to contrast of imaging interferogram. The MTF value of GBAII is greater than 0.8, 0.58 and 0.24 at the wavelength of 632.8 nm laser, O2(0-1) 867.7 nm and O(1S) 557.7 nm airglow, respectively. Based on the MTF value of GBAII studied in this paper, the experimental MTF values show that GBAII has better imaging effect on the vibration spectra of diatomic O2 molecules than that of single atomic O airglow. Since the intensity of O(1S) 557.7 nm and O2(0-1) 867.7 nm airglow is very low, the imaging interference fringes of GBAII airglow need to be obtained by long time exposure on the ground. In terms of the results, the MTF results of the two airglow spectra obtained by GBAII outdoor experiment have a certain gap with that of the laboratory 632.8 nm He-Ne laser, which can be improved by further optimization of GBAII later. It can be seen from the above results that the MTF value of GBAII optimized design, theoretical calculation and actual image has a certain deviation. When laser is used as the light source, the experimental MTF value of GBAII is the largest, and the experimental MTF value of 557.7 nm airglow spectrum line is slightly smaller, and the MTF value of software optimization is in the middle. Overall, the MTF result of GBAII theory and experiment is better than 0.35 MTF of WINDII. The study of MTF of GBAII can provide technical basis for GBAII to successfully detect atmospheric wind field parameters. The research results can provide accurate technical basis for GBAII to successfully detect physical quantities such as wind speed, temperature and volume emissivity in the upper atmosphere, and also lay a theoretical and experimental foundation for the development of similar instruments in China.
判断成像系统的像质优劣可用瑞利判据、中心点亮度、分辨率、点列图和光学传递函数 （Modulation Transfer Function，MTF）等方式，而MTF是判断像质优劣的定量指标［18-20］。MTF是成像系统所成的像对被摄原物的还原比例，其值在0~1之间。因为GBAII是针对强度很弱的气辉既要成像还要发生干涉，其MTF就成为GBAII设计、研制和测试过程中一个非常重要的指标，本文针对GBAII的MTF开展研究。
Fig. 6. Imaging interference fringes and gray level distribution of GBAII. The light sources used in the interferogram are 632.8 nm laser，O2（0-1）867.7 nm airglow and O（1S）557.7 nm airglow respectively
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