Principles of Modern Radar - Volume 2 1891121537

220 CHAPTER 6 Spotlight Synthetic Aperture Radarentire scene at once. Later we will see that it allows us to easily describe the samplingrequirements, resolution, and area coverage of an image.6.2.4 Fundamental Assumptions of SAR ImagingMost of SAR processing is based on the following key assumptions:1. The world can be modeled as a continuum of infinitesimally small point scattererswhose reflections do not affect one another. In other words, we assume that the thereis no multiple scattering and that the principle of superposition applies to the reflectedsignals. The linearity of the signals is one reason we can reconstruct imagery withoutprior knowledge of the scene content.2. The incident radiation does not penetrate the reflecting surface. Consequently, the scenecan be modeled as a sheet which is not necessary flat, but is infinitesimally thin. It is thismodel that gives meaning to the interferometric applications of SAR used for derivingtopographic information from image pairs. When the scene deviates vertically from aplane, the resulting three-dimensional spectrum has a component whose phase can beused to infer the terrain height. (See Chapter 8 for more information.)3. The medium is assumed to be infinite in extent, so there are no boundaries to consider.The presence of boundaries can give rise to multipath effects resulting in multiplereflections, or ghosts, in imagery.4. The scene content does not move during the collection interval of the SAR data. Therelative motion between sensor and scene is used to resolve and place targets in crossrange.An object moving against the static background may not appear in the imageryin the correct location. A classic example often cited is the phenomenon of imaginga moving train. If the train’s velocity vector has any component along the radar’sline of sight, the cars will appear displaced in cross-range. It is possible to get ratherdisconcerting imagery showing a well-focused train that appears to be riding off itstrack.These assumptions are somewhat predictable, representing a commonsense approach tomodeling the radar’s environment. They also have deeper mathematical meaning, enablingus to obtain simple solutions to the wave equation governing the propagation of electromagneticwaves. In particular, restrictions 1 and 3 give rise to the term e − jkR /R, whichis ubiquitous in the radar discipline. It is the Green’s function representing the solution tothe free space wave equation [13].Sometimes additional simplifications are made in order to derive efficient algorithms.A common approximation is that the transmitted spherical wavefronts are effectivelyplanar over the scene to be imaged; this assumption is key to the polar format algorithm.Other methods, such as backprojection and the ω-k algorithm recognize the sphericalnature of the wavefronts.6.3 SPOTLIGHT SAR NOMENCLATURESynthetic aperture radars are flexible instruments that are used under a variety of conditions.This section establishes the vocabulary necessary to describe the features of a SARcollection. We will also mention how the collection geometry influences the imagery.Much of this discussion applies to stripmap SAR as well as spotlight.