Measurement strategies for a confined microwave circular scanner

Figures & data

Figure 1. Schematic of the current microwave circular scanner measurement configuration.

Figure 2. Evolution with water content and frequency of the real part (a) and imaginary part (b) of the dielectric permittivity for an homogeneous sample of soil made of 20% of sand and 30% of clay, at 20°C.

Figure 3. Map of the exact permittivity profile which is used to create the synthetic dataset.

Figure 4. Reconstructed permittivity profile when ϵ_r,r = ϵ_r,b and (x_c, y_c) = (0, 0) and when no noise has been added to the dataset, except for the modelling errors. The profile is obtained after 38 iterations. The colour scale is identical to the one plotted in Figure 3. Available in colour online.

Figure 5. Reconstructed permittivity profile when ϵ_r,r = ϵ_r,b and (x_c, y_c) = (0, 0) and when white Gaussian noise with an SNR of 30 dB has been added to the dataset. The profile is obtained after 11 iterations. The colour scale is identical to the one plotted in Figure 3. Available in colour online.

Figure 6. Reconstructed permittivity profile when ϵ_r,r = ϵ_r,b and for various eccentricity positions of the monolith. White Gaussian noise with an SNR of 30 dB has been added to all datasets. The profile is provided when the cost functional is reaching a plateau. The colour scale is the same as the one plotted in Figure 3. Available in colour online.

Figure 7. Behaviour of the error functions 𝒥 and 𝒥 when the monolith is off-centred. In all cases, the ring is filled with water and white Gaussian noise with an SNR of 30 dB has been added to the datasets: (a) Data error function 𝒥; (b) Image error function ℐ.

Figure 8. Influence of the annulus permittivity ϵ_r,r and its width on the electrical energy ratio. Available in colour online.

Figure 9. Reconstructed permittivity profile when (x_c, y_c) = (0, 0) and an adaptation annulus of permittivity ϵ_r,r = 34 + 3j with an outer radius of R_r = 15.5 cm has been positioned around the soil column. White Gaussian noise with an SNR of 30 dB has been added to the dataset. The profile is obtained after 15 iterations. The colour scale is the same as the one plotted in Figure 3. Available in colour online.

Figure 10. Reconstructed permittivity profile for various eccentricity positions of the monolith. The impedance matching annulus of outer radius R_r = 15.5 cm is filled with a liquid of permittivity ϵ_r,r = 34 + 3j. White Gaussian noise with an SNR of 30 dB has been added to all datasets. The profile is provided when the cost functional is reaching a plateau. The colour scale is the same as the one plotted in Figure 3. (a) (x_c, y_c) = (8.05, 0.00); (b) (x_c, y_c) = (10.00, 0.00). Available in colour online.

Figure 11. Behaviour of the error functionals 𝒥 and 𝒥 when the monolith is off-centred. The adaption annulus of outer radius R_r = 15.5 cm is filled with a liquid of permittivity ϵ_r,r = 34 + 3j. White Gaussian noise with an SNR of 30 dB has been added to the datasets: (a) Data error function 𝒥; (b) Image error function ℐ.

Figure 12. Behaviour of the electrical energy ratio r^e when the monolith is off-centred. Two cases are considered: there is no adaption ring, or there is an impedance matching ring filled with a liquid of permittivity ϵ_r,r = 34 + 3j and an outer radius R_r = 15.5 cm.