The Vorticity Concept

The concept presented in this section is actually not a decomposition but an approach to add to the existing decomposition approaches. As mentioned above in the Sphere/Diplane/Helix section, the helix type scattering is not orthogonal to the sphere and the diplane type scattering mechanisms. Yet the helix type scattering is rather interesting, and even though it is not orthogonal to sphere and diplane scattering mechanisms, it is still quite different in nature. While surfaces or diplanes reflect comparable energy regardless of the incident polarization, a helix or a thin dipoles virtually suppress backscatter for all incident polarizations but one. Therfore, the vorticity $\nu$ concept was proposed [Bebington], in order to contributes to the understanding of target structure in a way that is complementary to information in the coherent target vector. The vorticity is calculated as

$$\nu = \frac{span(S)-\det(S)}{span(S)+\det(S)}$$

$$\mathrm{where} det(S) = \left\vert (S_{HH} * S_{VV}) - (S_{HV} * S_{VH})\right\vert$$ (4.16)

$$\mathrm{and} span(S) = \left\vert S_{HH}\right\vert^2+\left\vert S_{HV}\right\vert^2+\left\vert S_{VH}\right\vert^2+\left\vert S_{VV}\right\vert^2$$

Targets can be highly vectorial in two essentially different ways. Those with low vorticity behave like ideal targets (e.g. surfaces or diplanes), which reflect comparable energy regardless of the incident polarization. By contrast, targets with high vorticity virtually suppress backscatter for all incident polarizations but one. Examples of ideals of this mechanism include the thin dipole and helix.