An application of the monopulse principle to determining elevation angles in SAR images

In mapping nonflat regions of the Earth using airborne synthetic aperture radar, (SAR), terrain height variations cause two problems in radiometric calibration: the first being that the local incidence angle for any pixel may vary from that given by the flat (or curved) Earth assumption, the second, being that the wrong elevation angle may be used in correcting for the radiometric variation of the antenna pattern. In tracking radars, simultaneous amplitude or phase measurements made by the same radar antenna, but modulated differently, are compared to determine the angular position of targets. This is known as the monopulse principle. In the present paper, the authors show how polarimetric SAR data can be used in a novel application of the monopulse principle to determine the elevation angle and thus, the height at the different parts of the image. The authors´ approach begins with the observation that, provided like- and cross-polarized backscatter are uncorrelated, then the algorithm described in van Zyl (1990) for calculating antenna crosstalk yields a measurable quantity whose amplitude (and phase) depends only on elevation angle (or off-boresight angle). Thus, if one determines the crosstalk for a given point in the image, one can relate that measurement to the elevation angle appropriate to that point. Knowledge of the slant range to the point then allows determination of the height of the platform above it. This operation, repeated at many locations throughout the image, allows a topographic map of the height of the aircraft above each location to be built up. The approach described in this paper gives sufficient resolution in elevation to allow the antenna pattern radiometric correction to be done properly, since it allows the determination of elevation angles at a grid of points in the image. Knowledge of the slant range to each point and the height of the aircraft then allows a grid of height estimates for the imaged area to be built up. Unfortunately, the spatial resolution of the grid was not sufficient to turn the height maps into usable maps of local incidence angle. The approach may be improved upon, using an active, phased array antenna