3-D Rotation Representation of Multiple Reflections and Parametric Model for Bistatic Scattering From Arbitrary Multiplate Structure

Based on geometrical optics (GO), this paper develops a representation theory of multiple specular reflections from perfect electric conducting target with an arbitrary patchwise smooth surface. In the course of rays' multiple reflections, the polarization of each ray is found to change in a manner consistent with the variations of its propagating direction, which can be described with an equivalent 3-D rotation transformation. This transformation provides a new representation of the polarization rotation effect induced by multiple reflections. More importantly, the parameters of this transformation characterize the target's GO field response, and their values can classify six classes of geometrical structures. Furthermore, we derive explicit formulas relating these parameters to target's geometrical attributes for double and triple reflections, by using a quaternion algebra method. In order to validate this representation theory, we construct a parametric model of bistatic scattering from an arbitrary multiplate structure, by combining the GO-physical optics (PO) method with this representation. Through two special cases, the representation theory is validated by comparing the RCSs calculated by the parametric model with those by a shooting and bouncing ray (SBR) algorithm. The representation and derived concise parametric model are useful for extracting geometrically relevant features from bistatic radar measurement.