| Affiliation: | (1) Department of Mathematics and Statistics, University of Limerick, Plassey Technology Park Limerick, Rep. of Ireland;(2) Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA |
| Abstract: | We consider Synthetic Aperture Radar (SAR) in which backscattered waves aremeasured from locations along a single flight path of an aircraft. Emphasis is on the case where itis not possible to form a beam with the radar. The article uses a scalar linearized mathematicalmodel of scattering, based on the wave equation. This leads to a forward (scattering) operator,which maps singularities in the coefficient of the wave equation (viewed as a singular perturbationabout a constant coefficient) to singularities in the scattered wave field. The goal of SAR is torecover a picture of the singular support of the coefficient, i.e., an a image of the underlyingterrain.Traditionally, images are produced by  backprojecting the data. This is done by applyingthe adjoint of the scattering operator to the data. This backprojected image is equivalent to thatobtained by applying to the perturbed coefficient the composition of the scattering operator followedby its adjoint. We analyze this composite operator, and show that it is a paired Lagrangian operator.The properties of such operators explain the origin of certain artifacts in the backprojected image. |
