A canonical problem in electromagnetic backscattering from buildings

In this paper, a geometric and electromagnetic model of a typical element of urban structure is presented, in order to analytically evaluate in closed form its electromagnetic return to an active microwave sensor. This model can be used to understand what information on geometric and dielectric properties of a building can be extracted from microwave remote sensing data. The geometrical model consists of a rectangular parallelepiped whose vertical walls form a generic angle with respect to the sensor line of flight. The parallelepiped is placed on a rough surface. The radar return from such a structure can be decomposed into single-scattering contributions from the (rough) ground, the building roof (a plane surface in our model), and vertical walls and multiple scattering contributions from dihedral structures formed by vertical walls and ground. In our model, single-scattering contributions are evaluated by using either physical optics (PO) or geometrical optics (GO), depending on surface roughness. In order to account for multiple scattering between buildings and terrain, we use GO to evaluate the field reflected by the smooth wall toward the ground (first bounce) or the sensor (second or third bounce) and GO or PO (according to ground surface roughness) to evaluate the field scattered by the ground toward the wall (first or second bounce) or the sensor (second bounce). Finally, the above model is used to analyze the field backscattered from a building as a function of the main scene parameters; in particular, the angle between vertical walls and sensor line of night and the dependence on the look angle are analyzed.