# Hybrid Dual-Polarization Synthetic Aperture Radar
## Appendix D Calibration of an HCP Radar  
The polarimetric calibration of an HCP radar is straight-forward, at least in principle. In brief, start with the receiver, and then work on the transmitter. The objective for a well-calibrated receiver is to assure that the data at the outputs of the two polarimetric channels have the same phase and amplitude relationship as the incoming signals that appear at the antenna. In the following summary description, the terminology \"channel\" is meant to include the antenna, receiver, and all other aspects of the signal paths, including waveguides, cables and connectors. After calibration corrections are applied, the two channels should be matched, in the sense that end-to-end the differential phase shift is zero, and their respective gains are equal. The result expected from amplitude and phase calibrations of the HCP radar's receive channels is to have an instrument, after calibration, that preserves the polarimetric properties of the signals incident on the antenna so that the data products convey information about the observed scene, free from biases or distortions imposed by the instrument. Note that reliance on an external source of circularly-polarized illumination of the radar's receiving antennas is essential. The radar's own transmitted signal, either reflected by a corner reflector or replicated by a calibration transponder, cannot suffice because its imperfections will obscure measurement of the receive channel's gain and phase characteristics. Before calibration, the relative gains of the two channels may not be equal. Likewise, before calibration, there is likely to be a differential phase shift between the two channels. The task is to measure the differential gain and phase shift between channels, and then to apply corrections during the post-reception processing such that the two channels after applying calibration corrections are matched. The recommended method is to rely on an external reference. In the field of radio astronomy, for example, calibration strategies use a \"candle\", jargon for the radiation from a distant stable source [66] such as a quasar. The same approach is applicable to an HCP radar, for which an active radar calibrator (ARC) should illuminate the HCP radar's antenna with a near-perfect circularly-polarized field. A calibration dataset is generated each time the antenna pattern sweeps past the ARC. The lunar Mini-RF HCP radar was calibrated by this method using illumination from the Arecibo Observatory [27]. The antenna may have unwanted phase and amplitude variations in elevation and azimuth relative to its properties at boresight. In the azimuth coordinate, signal gain and phase off boresight can be observed directly in the Doppler domain of the image processor. Hence, if calibrations are needed to account for corrections that are a function of antenna azimuth angle, said variations can be directly measured, from which a calibration factor may be derived that includes Doppler-dependent corrections. Channel gain and phase characteristics also may be a function of the antenna's elevation pattern variations. In the normal side-looking attitude, the radar antenna's elevation angles correspond (on average) to radar range. Hence, range-dependent variations in antenna characteristics may be estimated by repeated passes over the ARC, for each one of which the spacecraft has a small known roll angle. Once the receiver is calibrated, then it can be used to characterize the transmitted field. The recommended method is to rely on the backscatter from a known point target, such as a corner reflector (or transponder). The transmitted field is not likely to be perfectly polarized. Following a skilled design and build, its properties near boresight should be good. Beyond that, there may be departures from pure circularity in azimuth and in elevation. When the receive channels already have been calibrated to be nearly perfect, the transmitted field can be characterized.