Resolution effects in radarclinometry
Data from the Cassini-Huygens mission, in particular images from the Cassini Titan Radar Mapper (RADAR) have revealed Saturn's giant moon, Titan to be a world whose geologic diversity and complexity approach those of the Earth itself. Estimates of topographic relief are, naturally, of enormous interest in the effort to understand the nature of Titan's surface features and quantify the processes by which they formed. Such data are available from a variety of sources, including altimetry and, increasingly, stereo imaging by the RADAR, but radarclinometry (radar shape-from-shading) has received considerable attention because it provides the highest resolution topographic measurements and can be applied to single images, wherever topographic shading dominates intrinsic variations in radar backscattering strength. In this abstract, we attempt to explain the surprising result that the majority of topographic measurements of Titan by radarclinometry appear to be asymmetric: slopes facing the RADAR instrument tend to be really extensive but shallow, whereas slopes facing away are limited in area but relatively steep. We describe how this is a natural consequence of the inability of the instrument to resolve the foreshortened facing slopes, causing them to be over-represented (by area, but underestimated in magnitude) when we attempt to reconstruct the surface from the image. We quantify this effect by constructing models of the imaging and reconstruction of idealized symmetrical mountains, and show that the magnitudes of slopes facing away from the instrument are estimated relatively accurately. As a result, height estimates from radarclinometry can be at least approximately corrected for the effects of limited resolution. This result is of obvious geoscientific significance for Titan: it indicates that some mountainous areas approach 2 km in local relief. Our modeling should also be useful to the interpretation of radarclinometric models of features at the limit of resolution in other SAR images, such as Magellan data for Venus, as well as current earth-based and planned orbital imaging of the Moon.