Fast Synthetic Aperture Radar Imaging with a Streamlined 2-D Fractional Fourier Transform

The 2-D Fractional Fourier Transform (FRFT) has been shown to be applicable to the Synthetic Aperture Radar (SAR) imaging problem. Streamlined versions presented here makes the 2-D FRFT comparable with and slightly faster than the Range Doppler (RD) and Extended Chirp Scaling (ECS) methods. The 2-D FRFT is streamlined by eliminating redundancy due to the fact that the same fractional angle is applied to each pulse in the SAR phase history's range dimension while one other fractional angle is applied across each range-gate in the phase history's azimuth dimension. Eliminating the redundancy and approximating the 2-D Fractional Fourier Transform operation in each dimension produces several streamlined 2-D FRFT methods as well as a very fast approximate 2-D FRFT. The computational order of the fast approximate 2-D FRFT is less than that of other corrective SAR imaging techniques. Examples of SAR imaging with these streamlined and approximate FRFTs are given as well as a comparison of the computational speed and impulse response of the full, streamlined and approximate 2-D FRFT, and the RD and ECS methods of SAR imaging.