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The redundant calculation in Back-Projection Algorithm (BPA) is studied in Fast Factorized BPA (FFBPA). By dividing sub-apertures and accumulating signal coherently in polar format coordinate, image with high resolution is obtained. The progress of repeatedly searching every signal in full aperture for every pixel is avoided in FFBPA, thus the amount of computation is reduced. However, multi-stage interpolation operation increases the error accumulation. Combining with the original Polar Format Algorithm (PFA), a new multi-stage iteration Fast PFA is proposed, and it is modified to process data in curve orbit and multiple modes SAR. Analysis indicates that the proposed algorithm is more efficient than FFBPA in practice. Comparison of simulation results of spaceborne spotlight SAR with very high resolution (0.1 m) processed by the proposed algorithm and FFBPA verifies the superiority of the new algorithm over …