Abstrucr -Fast Polar Back-Projection (FPBP) is a variant of the Fast-Factored Back-Projection (FFBP) algorithm, originally developed for ultra-wideband airborne Synthetic Aperture Radar (SAR), but since applied with success to Synthetic Aperture Sonar (SAS). The paper outlines the FPBP and FFBP algorithms, comparing computation time and memory requirements for the two methods. Processing time comparisons with a standard FFT-based method are also given. Since FFBP and FPBP are both approximation methods, computation time also depends on the preset approximation error, which particutarly affects azimuth sidelobe level. The paper provides an opportunity to review speed and accuracy estimates made in previous literature. However reduction in computation time is not the decisive advantage of these timedomain methods. The difference from the FFT-based methods lies in the flexibility with which non-linear platform trajectories, wide swaths, wide bandwidths, and multi-element sonar arrays can be handled. It is also straightforward to obtain a set of intermediate physical aperture images for autopositioning purposes. I. INTRODUCTIONOver the last few years, there has been growing interest in iterative time-domain algorithms for SAS and SAR image reconstruction. These are more tolerant of non-linear platform trajectories and multi-channel antenna confgurations than the more familiar FFT-based algorithms (Chirp Scale, Range-Doppler etc. [1,2,3]), and have been claimed to achieve comparable execution times [4,5,6], The Fast Factored Back-Projection (FFBP) algorithm has been utilized for some years, but References 4-6 are actually predated by Houston's paper [7] on fast iterative beamformhg. Houston wrote his paper with large physical sonar antennas in mind, but the approach becomes even more interesting when applied to synthetic aperture sonar or radar imaging, where we christen it "Fast Polar Back Projection" (FPBP). In tbis paper we describe the differences between the FFBP and FPBP algorhhms, and present performance benchmarks, compared with each other and with the Chq-Scale Algorithm (CSA), which claims to be the fastest of the FFT methods. We will also discuss other advantages of the time-domain methods. II. OUTLINE OF METHODS A Phase-cenfresBoth FFBP and FPBP are easiest to describe in terms of "phase-centres", although it is unnecessary to use the phase-centre approximation in the actual algorithms [ 6 ] .

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