SAR with Two-Dimensional Aperture Synthesis

The omega-k algorithm follows from the Leith-Upatnieks hologram and the holography based SAR mathematical problem is solved using Fourier analysis. Holography stems from Huygens-Fresnel principle describing the scalar diffraction theory subservient to Maxwell´s equations of electromagnetic theory. It is the Huygens-Fresnel principle that renders SAR imaging phenomenon and Optical imaging phenomenon mathematically analogous. In this paper we have used SAR², the two dimensional variant of the contemporary one dimensional slant plane SAR. SAR² involves two dimensional rectangular aperture synthesis. Detailed simulations of SAR² are presented. Matched filtering in SAR² with incorrect altitude is demonstrated that bears striking resemblance to image plane that is ahead or behind the focal plane in Fourier optics. Optimum circular aperture shape is predicted from the knowledge of the mathematical condition encountered in the analytic formulation of SAR². Finally, Fourier optics model of Circular SAR (CSAR) algorithm is devised. Fourier optics analogy makes CSAR algorithm a predictable development in SAR imaging.