An analytical expression for the three-dimensional response of a point scatterer for circular synthetic aperture radar

Three-dimensional (3-D) spotlight-mode synthetic aperture radar (SAR) images of point scatterers provide insight into the achievable effectiveness of exploitation algorithms given a variety of operating parameters such as elevation angle, azimuth or synthetic aperture extent, and frequency bandwidth. Circular SAR, using 360 degrees of azimuth, offers the benefit of persistent surveillance and the potential for 3-D image reconstruction improvement compared with limited aperture SAR due in part to the increase in favorable viewing angles of unknown objects. The response of a point scatter at the origin, or center of the imaging scene, is known and has been quantified for circular SAR in prior literature by a closed-form solution. The behavior of a point scatterer radially displaced from the origin has been previously characterized for circular SAR through implementation of backprojection image reconstructions. Here, we derive a closed-form expression for the response of an arbitrarily located point scatterer given a circular flight path. In addition, the behavior of the response of an off-center point target is compared to that of a point scatterer at the origin. Symmetries within the 3-D point spread functions (PSFs), or impulse response functions (IPRs), are also noted to provide knowledge of the minimum subset of SAR images required to fully characterize the response of a particular point scatterer. Understanding of simple scattering behavior can provide insight into the response of more complex targets, given that complicated targets may sometimes be modeled as an arrangement of geometrically simple scattering objects.