Analysis of circular aperture SAR image formation

Remote surveillance using a synthetic aperture radar (SAR) flying a circular aperture offers several operational advantages over more traditional linear aperture SAR. Over the years, different SAR image formation algorithms have been proposed and analyzed. Almost exclusively, the analysis is based on straight line trajectory or linear aperture SAR. In this paper, we provide a theoretical analysis of circular aperture SAR image formation using backprojection. In particular, we show the standard backprojection formula results in a distorted image when applied to circular aperture data. We develop a modification to the standard backprojection formula that results in a distortion free SAR image. To highlight one of the main benefits of circular versus linear aperture SAR, we discuss the impact of a scatterer out of the 2-D image plane and the reconstruction of the 3-D scene reflectivity. In contrast to the linear aperture case, an out of plane scatterer is blurred in the SAR image and the amount of blurring is proportional to the height of the scatterer above the image plane. Closed form expression for the blurring are developed. Examples using simulated data are used to illustrate the applicability of the theoretical results.