Verification of optimal discretization in multi-plane phaseless diagnostics

The paper deals with the reconstruction of the excitation coefficients of a planar array antenna from phaseless near-field data. To solve this non linear inverse problem, the iterative minimization of a non quadratic functional of the data by the conjugate gradient method is performed. A novel non- uniform measurement grid is applied to collect the data over a planar observation surface. According to the number of unknowns, i.e. the elements of the array source, the number of scanning planes is to be increased in order to achieve the solution. Therefore, a criterion providing the optimal distance between them is applied, leading to a non uniform spacing. Compared with a standard uniform spacing approach, array coefficients reconstructions are obtained by far less number of data with similar reliability. Finally, numerical results, including both noiseless and noisy conditions and a diagnostics application, prove the correctness and validity of the assumed mathematical findings