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This paper presents an efficient phase preserving processor for the focusing of data acquired in sliding spotlight and Terrain Observation by Progressive Scans (TOPS) imaging modes. They share in common a linear variation of the Doppler centroid along the azimuth dimension, which is due to a steering of the antenna (either mechanically or electronically) throughout the data take. Existing approaches for the azimuth processing can become inefficient due to the additional processing to overcome the folding in the focused domain. In this paper, a new azimuth scaling approach is presented to perform the azimuth processing, whose kernel is exactly the same for sliding spotlight and TOPS modes. The possibility to use the proposed approach to process data acquired in the ScanSAR mode, as well as a discussion concerning staring spotlight, is also included. Simulations with point targets and real data acquired by TerraSAR-X in sliding spotlight and TOPS modes are used to validate the developed algorithm.