This paper considers synthetic aperture radar and other synthetic aperture imaging systems in which a backscattered wave is measured from a variety of locations.The paper begins with a (linearized) mathematical model, based on the wave equation, that includes the effects of limited bandwidth and the antenna beam pattern. The model includes antennas with poor directionality, such as are needed in the problem of foliage-penetrating radar, and can also accommodate other effects such as antenna motion and steering. For this mathematical model, we use the tools of microlocal analysis to develop and analyse a three-dimensional imaging algorithm that applies to measurements made on a two-dimensional surface. The analysis shows that simple backprojection should result in an image of the singularities in the scattering region. This image can be improved by following the backprojection with a spatially variable filter that includes not only the antenna beam pattern and source waveform but also a certain geometrical scaling factor called the Beylkin determinant. Moreover, we show how to combine the backprojection and filtering in one step. The resulting algorithm places singularities in the correct locations, with the correct orientations and strengths.The algorithm is analysed to determine which information about the scattering region is reconstructed and to determine the resolution. We introduce a notion of directional resolution to treat the reconstruction of walls and other directional elements. We also determine the fineness with which the data must be sampled in order for the theoretical analysis to apply. Finally, we relate the present analysis to previous work and discuss briefly implications for the case of a single flight track.

This paper considers synthetic aperture radar (SAR) and other synthetic aperture imaging systems in which a backscattered wave is measured from positions along an arbitrary (known) flight path. The received backscattered signals are used to produce an image of the terrain. We assume a single-scattering model for the radar data, and we assume that the ground topography is known but not necessarily flat. We focus on cases in which the antenna footprint is so large that the standard narrow-beam algorithms are not useful. We show that certain artifacts can be avoided if the antenna and antenna footprint avoid particular relationships with the ground topography. We give an explicit backprojection imaging algorithm that corrects for the ground topography, flight path, antenna beam pattern, source waveform, and other geometrical factors. For the case of a non-directional antenna, the image produced by the above algorithm contains artifacts. For this case, we analyze the strength of the artifacts relative to the strength of the true image. The analysis shows that the artifacts can be somewhat suppressed by increasing the frequency, integration time, and the curvature of the flight path.

No 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.

No abstract