A new imaging algorithm is presented for Synthetic Aperture Radar (SAR) that is exact in the sense that it is capable of producing a complex image with excellent geometrical, radiometrical and phase fidelity. No interpolations or significant approximations are required, yet the method accomplishes range curvature correction over the complete range swath. The key to the approach is a quadratic phase perturbation of the range linearly frequency modulated signals while in the range signal, azimuth frequency transform (Doppler) domain. Range curvature correction is completed by a phase multiply in the two-dimensional frequency domain. Other operations required are relatively conventional. The method is generalizable to imaging geometries encountered in squint and spotlight SAR, inverse SAR, seismics, sonar, and tomography.