# Hybrid Dual-Polarization Synthetic Aperture Radar
## 4 Performance in Earth Applications
### Results from Appropriate Methodologies  
The correct approach is simple in principle [37]. _Start_ with HCP's \(2\times 2\) data matrix framework. _Stay_ with those data. Do _not_ expand that matrix. Do _not_ make assumptions. A variety of strategies are applicable to teasing out classifications from the \(2\times 2\) coherency (or covariance) matrix. The four Stokes parameters may be readily calculated from the \(2\times 2\) data. That is recommended as a starting point. Classifications based on the Stokes parameters enjoy a long and successful precedent, and consistently offer reliable results. One particular approach that seems towork well in a variety of situations is the _m-chi_ method [33; 39]. The example in Figure 2 illustrates that the color-coded classified images from the same scene seen through an HCP or a QP polarimetric radar look almost identical. Other variations or methods may be used for classification, depending on the application, and the investigator's preferences. No one technique should be expected to be the best for all situations, although all such approaches should be based on their \(2\times 2\) data matrix origin. Acceptable alternative approaches include the following:  
1. Circularly-polarized like- and cross-polarized radar brightness constituents derived from the HCP data are sufficient for certain applications [40], but only if evaluated in the circularly-polarized domain (see Appendix C.2), for example \(\sigma^{0}_{\text{RL}}\) and \(\sigma^{0}_{\text{RR}}\). 2. For decades, classical radar astronomy [41] has had success using the values of individual child parameters of the four-element Stokes vector, such as degree of polarization (\(m\)), circular-polarization ratio (\(CPR\)), degree of linear polarization (\(m_{L}\)), and sense of polarimetric rotation (see Appendix C.2) (opposite sense vs. same sense of rotation relative to that of the circularly transmitted EM field). These parameters as well as others may be useful in classification applications of Earth-oriented HCP radar data [42]. 3. The _m-chi_ method draws upon two of the three classical Poincare variables. The third, _psi_, indicates the orientation of the strongest linear polarization present in the backscattered field. This suggests that an _m-chi-psi_ decomposition as a three-parameter classification scheme (which could be helpful in response to a transmitted field that is not perfectly circularly polarized). 4. The _m-chi_ method weights ellipticity by (\(1\pm\sin 2\chi\)) factors [24], where \(-45^{\circ}\leq\chi\leq+45^{\circ}\). The _extrema_ represent L or R circular polarizations. An alternative has been suggested [43] that substitutes the linearized factor (\(1\pm 4\chi/\pi\)). If greater sensitivity to ellipticity variations in the neighborhood of perfect circularity is of interest, then this version may be preferable. 5. Although unsupervised classification techniques have been applied to polarimetric radar data for many years by several investigators, the approach seems neither to have attracted  
Figure 2: Example of classifications for a variety of agricultural fields as seen by (**a**) quad-pol and (**b**) hybrid dual-pol radars. Both images were derived from the same quad-pol data, using emulation to generate the corresponding HCP data (adapted from Figure 3 of [25]). much attention nor many adherents. The method deserves a second look. For example, multi-temporal agricultural crop studies using unsupervised classification of HCP-derived Stokes parameters achieved better results than quad-pol data classified through either entropy-alpha or Freeman-Durden decompositions [25]. To the surprise of many, classification accuracy by a hybrid compact-polarization architecture is proving to be very nearly as good as that from quadrature polarimetry. Studies using the appropriate methodology consistently yield very favorable HCP to QP comparisons.