Multi-Probe Array Design for Partially-Coherent Phase Retrieval in Near-Field Measurements

Phase retrieval, in particular for the operators arising from near-field measurements, is a non-convex task suffering from a severe lack of reliability due to local minima and false solutions. Approaches to tackle this issue, in turn, suffer from strict and often unrealistic oversampling requirements and possibly unfeasible computational complexities—in particular when larger scenarios are considered. In this paper, we analyze the sampling requirements for convex phase retrieval based on partially coherent observations which are captured with multi-probe arrays. We discuss requirements for the orientation and positioning of the probe antennas in the probe arrays. Following these conditions, a recently introduced linearized method is able to reconstruct a unique global solution reliably. The theoretical deliberations are corroborated with simulated near-field data.