Determination of the characteristic polarization states of the radar target scattering matrix [S(AB)] for the coherent monostatic and reciprocal propagation space by using the complex polarization ratio ρ transformation formulation

Abstract

We consider a problem originating in radar polarimetry for which the radar target is to be characterized by the properties of its coherent polarization state, given complete coherent backscattering matrix data sets at one frequency and for one target aspect angle. First, the Jones vector formalism for the coherent monostatic case and Sinclair’s backscattering matrix [S(AB)] for the general polarization basis (AB) are introduced. Using the unitary change of polarization state transformation, we present the concept of the characteristic polarization states of a scatterer, which was introduced by Kennaugh and Huynen. The generalized unitary transformation matrix formulation under the change-of-basis transformation, expressed in terms of the generalized polarization ratio ρ(AB), is developed for emphasizing the unique properties of the interrelation among the existing characteristic polarization states. For the monostatic reciprocal case (SAB = SBA) treated here, it is shown that there exist in total five pairs of characteristic polarization states: the orthogonal cross-polarization null and the copolarization maximum-state pairs, which are identical and share one main circle with the copolarization null and the orthogonal cross-polarization maximum-state pairs, the latter being at right angles to the cross-polarization null pairs; and a newly identified pair, the orthogonal cross-polarization saddle-point extrema that are normal to the plane (main circle) spanned by the other four pairs. With this complete and unique mathematical description of Huynen’s polarization fork concept, it is possible to study the problem of polarimetric radar target optimization more rigorously. Various examples are provided and interpreted by comparing the unique result with the results of previous incomplete analyses. In conclusion, the relevance of these canonical results to optical polarimetry are highlighted and interpreted.