We introduce a general formulation for wavefront curvature correction in spotlight-mode SAR images formed using the polar-formatting algorithm (PFA). This correction is achieved through the use of an efficient, image domain space-variant filter which is applied as a post-processing step to the PFA. Wavefront curvature defocus effects occur in certain SAR collection modes that include imaging at close range, using a low center frequency, and/or imaging very large scenes. Our formulation is general in that it corrects for wavefront curvature in broadside as well as squinted collection modes, with no computational penalty for correcting squint-mode images. Algorithms such as the range migration technique (also known as seismic migration), and an enhancement known as frequency domain replication, FReD, have been developed to accommodate these wavefront curvature effects. However, they exhibit no clear computational advantage over space-variant post-filtering in conjunction with polar formatting (PF2). This paper presents the basic concepts of the formulation, and provides computer results demonstrating the capabilities of space-variant post-filtering.

A new 3D tomographic formulation of spotlight mode synthetic aperture radar (SAR) is developed. This extends the pioneering work of Munson et al. (1983), who first formally described SAR in terms of tomography but who made the simplifying assumption that the target scene was 2D. The present authors treat the more general and practical case in which the radar target reflectivities comprise a 3D function. The main goal is to demonstrate that the demodulated radar return data from a spotlight mode collection represent a certain set of samples of the 3D Fourier transform of the target reflectivity function and to do so using a tomographic paradigm instead of traditional range-Doppler analysis. They also show that the tomographic approach is useful in interpreting the reconstructed 2D SAR image corresponding to a 3D scene. Specifically, the well-known SAR phenomenon of layover is easily explained in terms of tomographic projections and is shown to be analogous to the projection effect in conventional optical imaging.