# Hybrid Dual-Polarization Synthetic Aperture Radar
## 3 Hybrid Dual-Polarization
### Rationale  
From a user's perspective, why should circular polarization be a candidate for transmission? The answer follows from the higher-level objective, which is to generate an unbiased polarimetric characterization of an observed scene [23]. Transmission of any field that is dominated by a linearly-polarized component introduces rotational selectivity into the observation. This is true regardless of the degree of linearity, be it elliptical or purely linear, or its orientation, be it H or V or somewhere in between. When illuminated by linearly-polarized radiation, the backscattered polarization from a dihedral, for example, will depend to first order on the relative alignment of the axis of the dihedral with respect to the incoming field. In short, transmission of any field that has a dominant linearly-polarized component will lead to errors or omissions when attempting to classify double-bounce backscatters [7]. The only globally valid option is to transmit circular polarization. A circularly-polarized transmitted field leads to rotationally invariant backscatter, since there is no favored linear alignment between the illumination and the scene's geometrical structure.  
A CP radar by definition is constrained to only one transmitted polarization. Since transmitting only one linear polarization is not acceptable, a reasonable challenge by the user would be to ask that the radar transmit H and V simultaneously, which if it could be done would assure equal opportunity for H and V like- and cross-polarized backscatter constituents to be observed. If H and V were transmitted simultaneously having zero relative phase, the result would the slant (\(\pi\)/4) mode, hence linearly-polarized, still not acceptable. An innovative alternative is to transmit H and V simultaneously at 90\({}^{\circ}\) out of phase with respect to each other. This generates a circularly polarized field, but if and only if the H and V constituents have the same amplitude and waveform as well as being orthogonal in phase. (From a science point of view, it does not matter which sense of circular polarization, L or R, is transmitted. That choice is best made during pre-launch testing of the radar by the instrument technicians, who should then select the one which shows the higher quality of transmitted polarization circularity.)  
Circular transmit polarization enjoys a long and strong heritage in radar astronomy, where in that discipline selection of circular polarization originally was driven in part by the need to overcome Faraday polarimetric rotation of EM waves as they propagate through the ionosphere. That choice also was consistent with well-established traditions in radio astronomy [19].  
If the transmitted field is circularly polarized, does the receiver also have to be? The answer to this question was anticipated by [PERSON] in 1852 [5; 9; 19]. Any pair of orthogonally polarized receiver channels would be acceptable, since the objective data product--the four Stokes parameters--have values that do not depend on the polarization basis in which the data are observed.  
It turns out that a radar that transmits circular polarization is simpler to realize, its performance more reliable, and its calibration more robust, if the basis of the receiver channel pair is chosen to be orthogonal linear polarizations, such as H and V [23]. The principal reason is that neither receive channel has a like- or cross-polarized relationship with respect to the circularly-polarized transmissions. That choice has helpful hardware consequences, as it simplifies antenna and receiver implementations. Further, the mean signal levels in the two channels are always comparable, since neither receive channel is cross-polarized with respect to the transmitted polarization. That simple but essential fact is helpful because, in the usual end-to-end H and V quad-pol configuration [26], the mean signal levels through the two channels differ by 6-10 dB, which imposes additional requirements and tighter constraints on system design and calibration.