Determination of the Characteristic Polarization States of the Radar Target Scattering Matrix [S(AB)] for the Coherent, Monostatic and Reciprocal Propagation Space Using the Polarization Ratio ρ Transformation Formulation

Abstract

Listen

Translate article

A problem originating in radar polarimetry is considered for which the radar target is to be characterized by its coherent polarization state properties, given complete coherent backscattering scattering matrix data sets at one frequency and for one target aspect angle. First, the Jones vector formalism for the coherent monostatic case, together with Sinclair’s backscattering matrix [S(AB)] for the general polarization basis (AB) are introduced. Using the unitary change of polarization state transformation, the concept of the characteristic polarization states of a scatterer, first introduced by Kennaugh and Huynen, is presented. 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 co-polarization maximum state pairs, being identical and sharing one main circle with the co-polarization null and the orthogonal cross-polarization maximum state pairs, the latter being at right angles to the cross-polarized null pairs; and, a newly identified pair: the orthogonal cross-polarization saddle point extrema which 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 now possible to study the polarimetric radar target optimization problem more rigorously. Various examples are provided and interpreted by comparing the unique result with previous incomplete analyses. In conclusion, the relevance of these canonical results to optical polarimetry are highlighted and interpreted.