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 [1], 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.