Three-Dimensional inverse modelling of the Atmospheric Phase Screen in Ground-Based SAR systems

Ground-Based Synthetic Aperture Radar (GB-SAR) systems are increasingly used for the monitoring of slopes and civil structures, thanks to their sub-millimetric precision, wide field of view, and short acquisition times. However, the electromagnetic waves emitted by such systems are affected by atmospheric disturbances, producing a phase delay known as the Atmospheric Phase Screen (APS). Accurate estimation and removal of this contribution are essential to isolate the actual ground deformation. This thesis presents a new physical–mathematical approach based on the formulation and solution of an inverse problem for the three-dimensional reconstruction of the APS, using multiple ArcSAR radar systems. The atmospheric volume is divided into voxels crossed by radar rays; their intersections define a sparse interaction matrix describing the forward model. The inversion, inherently ill-posed, is stabilized through second-order Tikhonov regularization, ensuring smooth and physically consistent refractivity estimates. A sensitivity analysis confirmed the non-uniform voxel illumination and validated the effectiveness of the adopted regularization. The proposed method, implemented in MATLAB and tested on ArcSAR data, successfully compensates for atmospheric effects and improves the reliability of interferometric measurements, offering a robust framework for future applications.