# Hybrid Dual-Polarization Synthetic Aperture Radar
## 1 Introduction  
This paper provides an overview of compact polarimetry, an imaging mode of synthetic aperture radar (SAR) that is an alternative to quadrature polarimetry (Appendix A). Compact polarimetry has proven to be appealing to a wide variety of users because it provides quantitative polarimetric-based classifications of a scene observed by a space-based imaging radar without being encumbered by the coverage limitations and technical complexities inherent to quadrature polarimetry. This review is designed to be accessible and informative for interested non-experts, while providing theoretical background and technical perspectives pertinent to radar experts, data processing specialists, and operational agencies.  
Since its introduction to the SAR community nearly two decades ago, compact polarimetry has been a controversial subject. Partisan advocates defended quad-pol with a near-religious passion. They viewed those who promoted compact polarimetry--or \"partial polarimetry\" in their preferred jargon--as apostate, whose ideas were deemed to be sacrilegious, even dangerous. In the early days, loud voices of criticism often were raised in response to compact pol presentations at professionalconferences. One theme of those objections was that compact-pol could offer only an unacceptably poor alternative to quad-pol. In particular, it was argued that a compact-pol SAR would produce polarimetric classifications of vastly inferior accuracy, reliability, and repeatability relative to the high-quality classifications routinely achieved from airborne quad-pol systems.  
Times have changed. There now is extensive experience with operational systems, and a body of comparative performance evaluations. Compact-pol orbital systems have been flown, from which data and their associated classifications have been completed. The two lunar compact polarimetric imaging radars--aboard NASA's Lunar Reconnaissance Orbiter (LRO) [1] and India's Chandrayaan-1 [2]--gathered all data in the hybrid dual-pol (HCP) mode. India's Earth-observing SAR on RISAT-1 [3] included an operational HCP mode. Japan's ALOS-2 imaging radar [4] included an experimental compact polarimetry mode (which has had limited use due in part to calibration issues).  
Section 2 provides a summary of the compact-pol approach starting with the Stokes parameters which provide the theoretical foundations of compact polarimetry, and introduces the general idea and the early history of compact polarimetry for synthetic aperture radar imaging systems. Section 3 looks more deeply into a particular version of compact polarimetry, the hybrid dual-polarimetric mode. That sets the stage for commentary on the two orbital systems whose imaging radars first used that mode for polarimetric observations of the Moon. Section 4 focuses on Earth applications, with an emphasis on the question of performance quality, addressed through quantitative comparisons between compact-pol classifications and quad-pol decompositions for a variety of applications, and operational results from the RISAT-1 HCP mode. The answer is convincing: polarimetric classifications from hybrid dual-pol SAR data are comparable to those from a quad-pol SAR. The section also provides commentary on three groups of classification methods--two of which are error-prone, and a third which is recommended--for making such comparisons. The conclusions in Section 5 close the main body of the review.  
Four Appendices are included. Appendix A summarizes quad-pol SAR and its advantages and disadvantages. Appendix B offers reflections on the principal finding that hybrid dual-pol and quad-pol classifications achieve very similar results. That finding raises two issues: why should that be true, and what are its implications. Appendix C looks at several ancillary but relevant topics under the heading of terminology. Appendix D suggests a method for the in-flight polarimetric calibration of a hybrid dual-pol SAR