Comparison of simulated and measured tomographic radar signalsradar signals

After successful manufacturing of the 3D-printed analogue and determination of the permittivity distribution of the target object, a preliminary tomographic microwave radar measurement was conducted in the anechoic chamber to validate the numer-ical model with experimental data. A single-point analysis on the match between the measured and simulated full wavefield data was carried out. The wavefields were simulated and measured for both the Homogeneous Model (HM), and the Detail Model (DM), analogues. The resulting frequency-domain measurement data was transformed to the time domain, and the measured data was compared to the simu-lated data for the HM and DM individually, the difference data between DM and HM were quantified for the simulated and measured data, and the moving peak signal-to-noise ratio was quantified to monitor the quality of the signal in the experiments.

The signal curves in Figure 5.6 show the electric field amplitude at the receiver at each time point specified as the signal round-trip time. The plots also contain colour coding of the zones outlined in Figure 4.7 and Table 4.4 giving a reference to the spatial regions from which the first echo in that time interval can originate from. In the HM data, the outer surface and the backwall echoes are clearly visible and form

the two highest peaks in both the measured and the simulated data. Juxtaposition of the HM and DM data shows that HM lacks most of the peaks observed in the DM data, giving evidence that the interior of the HM indeed is homogeneous and can be seen as the constant permittivity background distribution. In the DM data, the signal peaks are located at the time points predicted by the model zones, and the measurement and simulation peaks coincide very well, although especially the measured peak at the interior-mantle interface in the Mantle II zone (5) produces is nearly double the magnitude of the simulated value. The approximate maximum ob-served measurement error reflecting the credibility of the measurement is indicated by a shadowed region around the measurement data curves (red line). The deviation between the measurement and simulated data increases along with the time in both the HM and DM data and this is especially prominent in the higher order scattering zone.

The difference curves were calculated between the measured DM and HM data, the measured DM and simulated HM data, and the simulated DM and HM data.

The similarity between the first two difference curves and their peaks shown in the middle panel of Figure 5.6 by the blue and red curves, respectively, indicates that the measured and simulated HM signals give similar data, and therefore it could be cred-ible to use the simulated HM data in running the forward model for the background permittivity distribution needed for the inversion stage. However, the magnitude of the amplitudes between the measured and simulated differences is evident as the dashed black difference curve showing data for the simulated difference between the DM and the HM suggests that the measured DM data drives the magnitude of the amplitude data. The difference peaks at the Mantle I and Mantle II zones are the most prominent in the difference data curves containing measurement data, which can be expected as similar peaks are also found in the top panel.

The moving peak signal-to-noise ratio (SNR) in the bottom panel of Figure 5.6 shows the SNR between the measurement and simulation for the DM (dashed blue), HM (solid purple), and the difference between DM and HM (solid brown) signals.

The peak SNR comprises the effect of both the measurement and modelling accu-racy. The first of these is determined by the laboratory radar performance (SNR>

20 dB), target positioning and orientation errors (≤1 mm and≤1 degrees, respec-tively). The modelling accuracy includes errors in the numerical FETD simulation and in the modelled permittivity distribution, which depends on the accuracy of the

HM data DM data

Difference between DM and HM data

Moving peak SNR

Figure 5.6 A comparison of the between the measurements and finite element time-domain (FETD) simulation data for the centre frequency of12.9GHz and vertical (ΦΦ) polarisation at the central transmitter–receiver position. The approximate maximum observed measurement error is indicated by the shadowed region around the measurement data (red line). The top panel shows the measured and simulated data for the HM (left) and DM (right). The middle panel gives the difference between the DM and HM data in the case of measured or simulated differences. The bottom panel shows the moving peak SNR curves and the reference 10 dB threshold which has been found to enable reliable tomographic inversion of the data. Adapted from Publication V. Reprinted with permission.

analogue permittivity measurements (Table 5.3), and the accuracy of the analogue mesh edge inflation procedure, which may involve deviations of less than 1.5 % de-pending on the different surface curvatures of which more details are given in the Publication V. The mean power of the simulated signal was normalised with respect to that of the measured signal, and the length of the moving window is 0.5 ns. The dashed black line in the figure indicates the earlier found 10 dB threshold for obtain-ing a reasonable reconstruction[74, 75], and also supported by the findings in Figure 5.3 in the Section 5.1) of this thesis and Publication I.

The superior peak SNR is found for the measured DM data in which the peak SNR is maintained at or above 10 dB throughout the interval from 11.95 to 13.4 ns covering the two-way traveltime for the signal from the Mantle I to Void and the major part of the Mantle II zone. Also the early part of the Higher-order scattering zone yields a peak SNR above the threshold. The moving peak SNR for the HM is at its highest in the Mantle II zone, which can be expected from the signal data where the backwall echo is the most prominent source of scattering. The lowest peak SNR is obtained for the difference data between the measured DM and HM data, but also that is above 0 dB except for the later part of the time interval in the Higher-order scattering zone. This can also be expected because the difference data has an overall lower amplitude than either of the DM or HM signals alone.

5.5 Tomographic backpropagation of measured microwave