Microlocal Analysis of Synthetic Aperture Radar Imaging

Abstract

We consider Synthetic Aperture Radar (SAR) in which backscattered waves are measured from locations along a single flight path of an aircraft. Emphasis is on the case where it is not possible to form a beam with the radar. The article uses a scalar linearized mathematical model 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 perturbation about a constant coefficient) to singularities in the scattered wave field. The goal of SAR is to recover a picture of the singular support of the coefficient, i.e., an a image of the underlying terrain. Traditionally, images are produced by “backprojecting the data.” This is done by applying the adjoint of the scattering operator to the data. This backprojected image is equivalent to that obtained by applying to the perturbed coefficient the composition of the scattering operator followed by 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.