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For different applications with different requirements, many synthetic aperture radar (SAR) modes have been developed in the literature, such as, Terrain Observation by Progressive Scans (TOPS) SAR and sliding spotlight SAR. In this paper, we call TOPS SAR, sliding spotlight SAR, and spotlight SAR as beam steering SAR (BS-SAR for short). Comparing with stripmap SAR, BS-SAR can obtain a wide diversity of resolutions by increasing or reducing the azimuth synthetic time. Traditional polar formation algorithm (PFA) is an efficient algorithm which is mainly developed for spotlight SAR. The PFA has been validated to obtain well-focused results of raw data. In this paper, we extend the traditional PFA to process sliding spotlight SAR and TOPS SAR data, and we call it generalized PFA (GPFA). Comparing with the traditional PFA, GPFA contains a different azimuth deramping function and an additional azimuth …