# Hybrid Dual-Polarization Synthetic Aperture Radar
## 5 Conclusions  
The success of the HCP radars on two lunar missions is irrefutable, such that many proposals for imaging radars in response to opportunities for new missions to Venus or Mars have been based on the hybrid dual-polarimetric mode. India was the first to venture into Earth orbit with HCP, included in the suite of operating modes aboard RISAT-1. A decade ago Canada adopted HCP as its baseline architecture for all operational imaging modes aboard RCM, launched in June 2019. During its introductory years within the SAR community, compact polarimetry was challenged vigorously by many professionals as being a poor substitute for quadrature polarimetry, and therefore undeserving of serious consideration. Given the acknowledged and demonstrated capabilities of QP SAR, the need for, let alone the anticipated benefits of, a leap to compact polarimetry was not obvious at the time. Since then, that leap has enjoyed acceptance, largely due to users' interests. For users and operational applicational agencies, hybrid dual-polarity is emerging as the preferred form of SAR polarimetry because the alternatives are less attractive. Perhaps the most significant advantage for applications is that hybrid dual-polarimetric modes offer much wider coverage than the conventional quad-pol approach, at the same time supporting useful polarimetric classifications. For designers and system implementation and operations, an HCP mode implies technical demands on mission profile (including coverage, incidence, data burden, and power budget) that are less constraining than those for a QP system, thus enabling polarimetric SAR capabilities within realistic budget limitations as a routine operational mode. The heart of the HCP mode resides in the fundamental formulation by [PERSON] in 1852 that four real parameters are sufficient to completely characterize the polarimetric properties of any quasi-monochromatic partially polarized EM field. Microwave imaging radars satisfy the initial conditions required for a Stokes parameter representation to be applicable. The success of the hybrid dual-polarized form of compact polarimetry is a direct consequence. A dual-polarimetric radar's transmitted field's polarization must be the same, pulse to pulse, hence its polarization basis must be chosen thoughtfully. Circular polarization is the only option that gives rise to like- and cross-polarized backscatter constituents that are unbiased. Thanks to the Stokes parameter framework of the post-processing imagery, the polarization basis of the receiver can be selected based on hardware considerations. The optimum receiver basis for the receivers is orthogonal linearly polarizations when the transmitted field is circularly polarized. Results from the lunar-orbiting HCP pioneers have been well received by the radar astronomy community. For Earth-observing applications, user's acceptance of hybrid compact-polarimetry now is wide-spread. Studies aimed at quantitatively comparing the classification performance of emulated HCP SAR data to QP decompositions for Earth applications consistently yield encouraging results. The first Earth-orbiting SAR to incorporate HCP--RISAT--provided data that justify the early optimistic predictions about compact polarimetric performance. Evaluating the comparative performance of HCP vs. QP SARs is an ongoing enterprise. Such comparisons are to be encouraged, but they can be trusted only if the HCP radar's data are handled correctly. To do so requires that the \(2\times 2\) data array native to that architecture be the basis for classification methodologies. Expanding the HCP's \(2\times 2\) array into a \(3\times 3\) array induces classification errors. Reliance on image norms such as \(\sigma^{0}_{\text{RH}}\) can lead to errors, because the output image elements from the H channel of an HCP SAR is actually \(\sigma^{0}_{\text{(HH+HV)}}\), a form which makes obvious the fact that the cross-polarized power (HV) and the like-polarized constituent (HH) are bundled together, inseparable.