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When observing the Earth’s radiation signal with a geostationary orbiting (GEO) mechanically scanned microwave radiometer, it is necessary to correct the antenna beam pointing (ABP) in real time for the deviation caused by thermal distortions of antenna reflectors with the help of the on-board Image Navigation and Registration (INR) system during scanning of the Earth. The traditional ABP determination and beam-pointing error (BPE) analysis method is based on the electromechanical coupling principle, which usurps time and computing resources and thus cannot meet the requirement for frequent real-time on-board INR operations needed by the GEO microwave radiometer. For this reason, matrix optics (MO), which is widely used in characterizing the optical path of the visible/infrared sensor, is extended to this study so that it can be applied to model the equivalent optical path of the microwave antenna with a much more complicated configuration. Based on the extended MO method, the ideal ABP determination model and the model for determining the actual ABP affected by reflector thermal distortions are deduced for China’s future GEO radiometer, and an MO-based BPE computing method, which establishes a direct connection between the reflector thermal distortion errors (TDEs) and the thermally induced BPE, is defined. To verify the overall performance of the extended MO method for rapid ABP determination, the outputs from the ideal ABP determination model were compared to calculations from GRASP 10.3 software. The experimental results show that the MO-based ABP determination model can achieve the same results as GRASP software with a significant advantage in computational efficiency (e.g., at the lowest frequency band of 54 GHz, our MO-based model yielded a 4,730,000 times faster computation time than the GRASP software). After validating the correctness of the extended MO method, the impacts of the reflector TDEs on the BPE were quantified on a case-by-case basis with the help of the defined BPE computing method, and those TDEs that had a significant impact on the BPE were therefore identified. The methods and results presented in this study are expected to set the basis for the further development of on-board INR systems to be used in China’s future GEO microwave radiometer and benefit the ABP determination and BEP analysis of other antenna configurations to a certain extent.

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