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The range Doppler algorithm (RDA) is based on Taylor series expansion for the transfer function (TF) phase component, resulting in increasing phase error as the range frequency or the squint angle increases. We introduce Legendre orthogonal polynomials into synthetic aperture radar data processing steps to replace Taylor series expansion used in approximating the TF phase. A novel range Doppler imaging approach based on Legendre expansion is addressed with an extended RDA as example, and the analytical expressions of the new phase multiplication factors are then derived. The simulation results show that the proposed method provides better focusing performance than the conventional RDA in the same squint case and is more suitable for the large squint mode while there is negligible increment of computation load.