Beamforming as a foundation for spotlight-mode SAR image formation by backprojection

In this paper we show that the technique for spotlight-mode SAR image formation generally known as "backprojection" or "time-domain" is most easily derived and described in terms of the well-known methods of phased-array beamforming. By contrast, backprojection has been typically developed via analogy to tomographic imaging, which restricts this technique to the case of planar wavefronts. We demonstrate how the very simple notion of delay-and-sum beamforming leads directly to the backprojection algorithm for SAR, including the case for curved wavefronts. We further explain why backprojection offers a certain elegant simplicity for SAR imaging, and allows direct one-step computation of several useful SAR products, including an orthographically correct image free of any geometric or defocus effects from wavefront curvature and also free of the effects of terrain-elevation-induced defocus. (This product requires as an input a pre-existing digital elevation map (DEM) of the scene to be imaged.) In addition, we'll demonstrate why beamforming yields a mode-independent SAR image formation algorithm, i.e. one that can just as easily accommodate strip-map or spotlight-mode phase histories collected on an arbitrary flight path.