Reconstruction of Squared Field Magnitudes and Relative Phases from Magnitude-Only Near-Field Measurements

An optimization-free method is presented for the retrieval of the individual phases of phaseless antenna measurements in the near-field (NF) zone of an antenna under test (AUT). Based on a bilinear expression for the magnitude-only measurements, the result for any desired magnitude-only measurement sample is synthetically calculated as a linear combination of sufficiently many previous measurement samples. In this way, signals, which allow for a straightforward computation of the phase difference between a pair of measurement samples, are obtained. Its high numerical complexity limits the algorithm to problems of moderate size, but understanding and using the algorithm delivers new insight into the phase retrieval problem and allows to evaluate the feasibility of specific measurement procedures and configurations. In particular, we show that there exist at most N-mathrm DOF^2 independent phaseless measurements for an AUT with N-mathrm DOF degrees of freedom (DoFs). Any additional phaseless measurement can be calculated as a linear combination of those N-mathrm DOF^2 measurement samples. Under certain circumstances, much less than N-mathrm DOF^2 measurement samples are sufficient to retrieve the magnitude and phase of the measured field at desired locations. A numerical example shows that the presented method is capable, in principle, to reconstruct all relevant NF information needed for a conventional NF far-field transformation (NFFFT) from noiseless irregularly distributed squared magnitude field samples only. In addition, it is shown that measurements with specialized probes can bring more information into the problem than measurements on surfaces with different distances to the AUT. When it comes to true noisy measurement data, the presented method can reconstruct NF magnitudes reliably, but the reconstruction of phase information is sensitive to noise.