# 2D Ultrasonic Antenna System for Imaging in Liquid Sodium
## 4 Experimental FMC/TFM Images Performed in Water and Associated Simulations with CIVA
### Signal-to-Noise Ratio Improvement  
During full matrix capture, each probe's element of the antenna operating in emission is fired individually and emits a spherical wave that propagates in the medium and gives rise to an elementary echo when meeting a target. This emission process, while it allows to insonify a large volume, transmits a limited acoustic power as only one element is used. In order to increase the acoustic power sent into the medium, the Plane Wave Imaging (PWI) method [7] can be used. The principle of this method is to emit plane wave fronts generated by all the elements of the probe at different angles instead of the spherical elementary wave front emitted by one element. As all the probe's elements are excited together, the acoustic power sent in the medium is much higher. Then, for the FMC, the backscattered signals are recorded on every element of the probe and the signals are coherently summed up to  
Figure 8: Measured and simulated FMC/TFM results for targets placed far from the antenna: (**a**) The spherical target is at the position surrounded with a blue circle in the 2D diagram of the experimental trial configuration (top of the figure). (**b**) The spherical target (\(\O\): 6 mm) is at the position surrounded with a blue circle in the 2D diagram. For each position of the target, the measured and CIVA simulated 3D and 2D TFM images are displayed. The 3D TFM image was computed in a 3D zone centered on the spherical target and represented on the figure. The 2D TFM image is in the XY plane and was extracted from the 3D image at the position of the maximum amplitude.  
obtain an image similar to the one obtained by TFM. The sole difference when applying the TFM is the computation of the incident wave's time of flight (spherical for the FMC and plane for PWI). In order to take into account cylindrical wave fronts emitted by the element curved surface in the orthogonal plane, some modifications were added to the \"classical\" PWI method that deals with emitted planar wave fronts. Another possibility to improve the SNR is to use encoded transmissions like Hadamard spatial codes [8]. With this method, all the probe's elements are excited simultaneously, but for every transmission, N electric signals applied to the N elements are multiplied by a combination of a +1/\(-\)1 coefficient. A coded matrix is thus formed. The equivalent impulse response matrix (i.e., FMC) can be obtained with a decoding operation. The Hadamard coded excitation increases the SNR by an \(\sqrt{\text{N}}\) factor compared to a conventional FMC.  
The improvements resulting from the application of these two methods (PWI and Hadamard) are not illustrated for our configuration of interest because it requires new experimental trials, where the FMC will be replaced by a PWI or Hadamard acquisitions. These acquisitions are not completed at the moment. Thus, instead of illustrating for telemetry applications (long-distance case), we illustrate the methods for a highly attenuating medium (short-distance case). In each case, a high-level noise is induced by attenuation (by the propagation distance or the high attenuation coefficient) and the same methods can be applied to reduce it. Figure 9 shows the images obtained with three methods (TFM, Hadamard, and PWI) for a side-drilled hole (diameter of 2 mm) at a 25-mm depth in a strongly attenuating High-Density Polyethylene (HDPE) component with a 5-MHz, 64-element probe. The noticeable increase in SNR with the Hadamard coding and PWI demonstrates the benefit that can be expected from these methods.