The side‐looking radar image of time‐variant scenes

The image formed by a side-looking radar system of a scene characterized by a temporally and spatially varying reflectivity density effectively distributed over a plane is given. The implied spectral density transformation, with its intrinsic distortion of the scene's wave number spectral density, is noted. In the remainder it is assumed that the temporal and spatial behaviors are connected via a dispersion relation. It is shown that the image is a linear, space-variant transformation of the scene at, say, t = 0, which can be described as the concantenation of three linear transformations: the first two are space-invariant, one being the system transformation for a time-invariant scene, and the third is space-variant and gives a geometric distortion, most simply a scaling and skewing, which is present in any system using a side-looking scan. Sufficient conditions are given for faithful imaging and spectral density mapping; those for the latter are more easily met.