Experimental Exposure Evaluation from the Very Close Near- to the Far-Field Using a Multiple-Multipole Source Reconstruction Algorithm

Kristian S. Cujia, Arya Fallahi, Sylvain Reboux, and Niels Kuster, IEEE Transactions on Antennas and Propagation, September 2022, Volume 70, Issue 9, pp. 8461–8472, online 30 May 2022; doi: 10.1109/TAP.2022.3177564 

Exposure assessment of wireless devices operating at ≥6 GHz requires measurement with minimal uncertainty of the power density (PD) at a distance of 2 mm (≥λ/25) from the surface of the device, i.e., the reactive near field, to the far field. These measurements present several challenges, including field distortion and backscattering by the probe, spatial resolution, sensitivity, isotropy, and phase accuracy. In addition, the surfaces of devices may not be planar. Today, plane-to-plane phase reconstruction (PR) methods based on phaseless amplitude measurements are widely applied to obtain the field phasors. The phasors obtained in conjunction with Maxwell’s equations allow the fields in the whole volume of interest to be evaluated. Although these methods meet the compliance criteria for the PD of flat surfaces at distances as near as λ/5, they are unsuited for curved surfaces and shorter distances. To overcome these limitations, we present a method based on a multiple-multipole expansion for accurate PD evaluation in all field regions by means of sparse phaseless electric (E-) field measurements. We construct a physically relevant vectorial basis in terms of elementary electric or magnetic dipoles and optimize their amplitudes such that the measured fields are reproduced with minimal error. The proposed procedure yields current distributions that resemble those of the physical radiation source and accurately reconstruct the electromagnetic (EM) field from the reactive near-field to the far-field regions with an uncertainty of <0.6 dB. Our approach does not impose any geometric requirements on the measurement or evaluation surfaces and, thus, supports conformal assessments, providing a potential solution for accurate evaluation of the PD of 5G devices and beyond.

The scientific and technical impact of the study can be summarized as:

• We use phaseless, i.e., amplitude-only, E-field measurements to construct the physically-relevant equivalent sources used to reconstruct complex EM fields in the space surrounding the device-under-test
• Both simulated and experimental measurement data were used to validate the method on various millimeter (mm-) wave sources operating from 10 – 90 GHz, taking the peak spatial-average PD as a figure-of-merit to demonstrate an intrinsic reconstruction uncertainty <0.6 dB on evaluations ranging from the reactive near-field (>λ/25) to far-field regions
• Our strategy does not impose any requirements on the distribution of measurement or evaluation points and supports both forward and backward field propagation, i.e., field reconstruction at distances closer than the measurement location
• The above features enable PD assessments on non-planar geometries where direct access to the transmitter may be restricted, e.g., camera modules on modern smartphones, providing a potential solution for the conformal assessment and measurement-based simulation of 5G devices and beyond