Three-Dimensional processing for (circular) high resolution SAR imaging of non planar targets

When acquisition trajectory is linear, synthetic aperture radar (SAR) focusing, i.e. the phase history of image points during signal integration time, depends only of the position (range & azimuth) of the point in the image. Due to the invariant trajectory with rotation around its axis, focusing is also correct for points above the ground for the same range and azimuth. It just appears projected closer towards the acquisition track because it is closer to the sensor than the point directly at its nadir on the ground. This is not the case when the acquisition trajectory deviates significantly from a straight line. The first order contribution to phase history variation with target point altitude are the deviation perpendicular to the imaging direction during integration. Circular SAR at high resolution, hence wide integration angle, is particularly challenging in this matter because, as seen from a given target point, the nominal acquisition trajectory is an ellipse close to a circle centred at the zenith, hence the integrated signal is sampled from a path curved upwards. As the desired azimuth resolution increases, the path length increases (more or less in proportion) hence, its curvature amounts to an increasing deviation perpendicular to imaging direction (more or less quadratically), hence an higher defocusing of any point above the ground or the processed terrain altitude (the tolerance of altitude for correct focusing decreases more or less quadratically with desired azimuth resolution). Here, a three-dimensional processing is proposed for accurately focusing a non planar target (typically a vehicle or a non-modelled building) in such a condition. It is illustrated with circular SAR acquisitions at X-band with azimuth resolution of 3.5 cm of small aircraft. This azimuth resolution requires an integration angle of 24deg, inducing a focusing width in altitude far below the 5 m typical extension in altitude of the target. Two 3D processing algorithms are assessed, one mathematical morphology filter derived from the CLEAN technique, and a fast & simple contrast maximisation autofocus applied locally. Byproducts such as target 3D modelling, geographical projection and circular multilooking are proposed.