SAR Imaging Distortions Induced by Topography: A Compact Analytical Formulation for Radiometric Calibration

Modeling of synthetic aperture radar (SAR) imaging distortions induced by topography is addressed and a novel radiometric calibration method is proposed in this paper. An analytical formulation of the problem is primarily provided in purely geometrical terms, by adopting the theoretical notions of the differential geometry of surfaces. The novel and conceptually simple formulation relies on a cylindrical coordinate system, whose longitudinal axis corresponds to the sensor flight direction. A 3D representation of the terrain shape is then incorporated into the SAR imaging model by resorting to a suitable parametrization of the observed ground surface. Within this analytical framework, the area-stretching function quantitatively expresses in geometrical terms the inherent local radiometric distortions. This paper establishes its analytical expression in terms of the magnitude of the gradient of the look-angle function uniquely defined in the image domain, thus resulting in being mathematically concise and amenable to a straightforward implementation. The practical relevance of the formulation is also illustrated from a computational perspective, by elucidating its effective discrete implementation. In particular, an inverse cylindrical mapping approach is adopted, thus avoiding the drawback of pixel area fragmentation and integration required in forward-mapping-based approaches. The effectiveness of the proposed SAR radiometric calibration method is experimentally demonstrated by using COSMO-SkyMed SAR data acquired over a mountainous area in Italy.