## 3 Sample, Experimental Devices, and Protocols
### Transmitted and Received Signals

Table 2: Time and frequency (\(-6\) dB) parameters of the transmitted signal, generated using the pulse-receiver generator and recorded using a 0.5 mm needle hydrophone; f\({}_{0}\) = 500 kHz, 1 MHz, 2.25 MHz (\(c_{0}\) = 1486 m/s). The challenge for the WCE-mode method was therefore to determine the signal \(\mathrm{e(t)}\) transmitted to the generator:  
\[\mathrm{e(t)}=\psi_{j}(t)\,\frac{\otimes}{\otimes}\,\left[h_{T}^{*}(t)\right]^{ ref} \tag{34}\]  
where \(\frac{\otimes}{\otimes}\) denotes the operation of deconvolution. The reference signal \(\left[h_{T}^{*}(t)\right]^{ref}\) was obtained by reflection of a pulse wave on the reference plate (Figure 5, Configuration B), the impulse response of which was assimilated to a Dirac delta function (\(p(t)\approx\ \delta(t)\)). A system identification procedure based on a \"black-box\" model detailed in [27] was used to determine \(\mathrm{e(t)}\). The time and frequency (\(-6\) dB) parameters for the transducers are presented in Table 4 for the WCE-mode method. The simulated signal was sent to the waveform generator, and a pseudo-wavelet was transmitted. All the experiment signals reflected from the objects under study were filtered by the same wavelet function, as explained in Section 2.2 (Equation (18)). The algorithm is more detailed in [26]. Signal processing for a complete sinogram took about 1 min. Figures 6-8 show the comparison of the temporal representations and frequency spectra of the theoretical analyzing wavelet, the transmitted pulse signal, and the pseudo-wavelet for each transducer, recorded using the hydrophone at a distance of 150 mm in the Fresnel zone (Configuration A). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter (\(-6\) dB)** & **500 kHz** & **1 MHz** & **2.25 MHz** \\ \hline Nominal frequency & 553 kHz & 744 kHz & 2.23 MHz \\ Broadband width & 458 kHz & 900 kHz & 1.8 MHz \\ Bandwidth & (267–725) kHz & (0.5–1.4) MHz & (1.1–2.9) MHz \\ AUC (normalized) & 0.347 & 0.655 & 1.42 \\ Pulse duration (\(t_{pulse}\)) & 2.2 μs & 1.2 μs & 0.56 μs \\ Axial resolution & 3.2 mm & 1.8 mm & 832 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time and frequency (\(-6\) dB) parameters of the transmitted signal, generated using the waveform generator and recorded using a \(0.5\) mm needle hydrophone; \(t_{0}=500\) kHz, \(1\) MHz, \(2.25\) MHz (\(\alpha_{0}=1486\) m/s). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Theoretical Parameter** & **500 kHz** & **1 MHz** & **2.25 MHz** \\ \hline \(j\) & \(-9\) & \(-8\) & \(-7\) \\ Center frequency (\(v_{j}^{0}\)) & 651 kHz & 1.3 MHz & 2.6 MHz \\ Bandwidth \(\left[v_{j}^{1};\ v_{j}^{2}\right]\) & (0.325–1.3) MHz & (0.651–2.6) MHz & (1.3–5.2) MHz \\ \hline \multicolumn{4}{c}{\(-6\) dB Parameters} \\ \hline Broadband width & 458 kHz & 900 kHz & 1.66 MHz \\ Bandwidth & (248–706) kHz & (0.5–1.4) MHz & (1.04–2.7) MHz \\ AUC (normalized) & 0.349 & 0.694 & 1.38 \\ Pulse duration (\(t_{pulse}\)) & 2.2 μs & 0.74 μs & 0.5 μs \\ Axial resolution & 3.2 mm & 1.1 mm & 743 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time and frequency (theoretical and \(-6\) dB) parameters of the theoretical analyzing wavelets. The scale \(j\) was determined for each transducer with the sampling frequency \(F_{e}=500\) MHz, and a number of samples \(N=65\),536. Figure 6: Comparison of the temporal representations (**top**) and frequency spectra (**bottom**) of the theoretical analyzing wavelet (solid line), the transmitted pulse signal (dashed line), and the pseudo-wavelet (dotted line) for the 500 kHz-transducer. Figure 8: _Cont_. Figure 7: Comparison of the temporal representations (**top**) and frequency spectra (**bottom**) of the theoretical analyzing wavelet (solid line), the transmitted pulse signal (dashed line), and the pseudo-wavelet (dotted line) for the \(1\) MHz-transducer.