## 8 Validation with Measurements  
To validate the new phase reconstruction method with measurements, a subset of the simulated antennas was measured, namely the cavity-fed dipole array at 30 GHz and at 60 GHz and the horn loaded with a slot array at 30 GHz and at 90 GHz (see Figure 1). These measurements are performed using the cDASY6 mmWave module (EUmmWVx) [20] shown in Figure 11.  
The EUmmWVx probe is based on the pseudo-vector probe design, which not only measures the field magnitude but also derives its polarization ellipse. This probe concept also has the advantage that the sensor angle errors or distortions of the field by the substrate can be largely nullified by calibration. This is particularly important as, at these very high frequencies, field distortions by the substrate are dependent on the wavelength. The design entails two small 0.8 mm dipole sensors mechanically protected by high-density foam, printed on both sides of a 0.9 mm wide and 0.12 mm thick glass substrate. The body of the probe is specifically constructed to minimize distortion by the scattered fields. The probe consist of two sensors with different angles arranged in the same plane in the probe axis. Three or more measurements of the two sensors are taken for different probe rotational angles to derive the amplitude and polarization information. These probes are the most flexible and accurate currently available for measuring field amplitude. Their design allows measurements at distances as small as 2 mm from the sensors to the surface of the device under test (DUT). The closest measurement plane (corresponding to the plane of equivalent currents) was placed at a distance \(z_{1}=2\) mm from the AUT and the procedure for phase reconstruction and FT was the same as described in Section 2. Figure 11: Measurement of the radiation profile using the EUmmWVx Module. Figure 10: Mean absolute error in psPD\({}_{n}\) (left column, (a,c,e)) and psPD\({}_{tot}\) (right column, (b,d,f)) for different distances \(z_{1}\) of the plane of equivalent currents for the 10 GHz antennas. Different noise levels (\(y\)-axis of each figure) and FT to different distances are shown (title of each subplot). The plane of equivalent currents was placed at \(z_{1}=2\) mm (a,b), \(z_{1}=4\) mm (c,d), and \(z_{1}=6\) mm (e,f). Mean values and standard deviations over 20 simulations per noise level are shown. The uncertainty is bounded by the acceptable level for \(z_{1}\geq 4\) mm. The radiation efficiency of the antennas was determined using the psPD\({}_{n}\) averaged over 1 cm\({}^{2}\) at a large distance (i.e., at 50 mm). The FT was evaluated at distances of 5, 10, 20, 50 and 150 mm from the AUT, and the resulting psPD was compared to two different reference values: one was a measurement at the respective distance and the other was the simulated value. The noise levels in the measurements were below \(-30\) dB; note that in the simulation study (Section 7), deviations from reference values were within approximately 0.5 dB for these noise levels. The results are shown in Figure 12. It can be seen that, when comparing FT results to measurements, all results are within 0.6 dB of the measurement reference. This is well within the expected deviations from the simulation study, especially when considering that only Gaussian noise on the sensors was modeled without considering other effects such as positioning errors or sensor isotropy. As an example, the simulated, measured and reconstructed radiation patterns at a 5 mm distance from the AUT are illustrated in Figure 13 for the two cases of the cavity-fed dipole array and horn antenna loaded with slot arrays. In comparison to the simulation reference, deviations are within 1.1 dB. These larger deviations compared to measurements may be attributed to modeling uncertainty (agreement between exposure setup and simulated setup). Figure 12: Errors in psPD (averaged over 1 cm\({}^{2}\)) for FT from measurements at \(z_{1}=2\) mm to evaluation planes at different distances (indicated in the subplot titles).