# 2D Ultrasonic Antenna System for Imaging in Liquid Sodium
## 4 Experimental FMC/TFM Images Performed in Water and Associated Simulations with CIVA  
A two-antenna prototype was designed in 1999 by CEA and manufactured by IMASONIC French company to perform tests in a water tank using large curves and rough surfaces [5]. The number of elements of each antenna is 128, the element length in the focusing plane is 1.8 mm, the gap between two adjacent elements is 0.2 mm, the element dimension in the orthogonal plane is 20 mm, the radius of the convex surface in the orthogonal plane is 35 mm, the centre frequency is 1 MHz, and the bandwidth of the excitation signal is 50%. The relative positions of the two antennas are given in Figure 6.  
Various experimental FMC and TFM images of spherical and planar targets were performed in order to assess the antennas' capabilities in terms of sensitivity and spatial resolution. The associated FMC and TFM were also computed with CIVA (the model used for the echoes computation of the spherical targets presented below was the SOV (Separation of Variable) model). For example, some FMC acquisitions of the echoes of a spherical target (diameter \(\mathcal{O}\) = 6 mm) located at a 850-mm depth were carried out for 12 different positions of the target in the antennas field of vision (Figure 6). Figure 6: Diagram of the experimental trial configuration: (**a**) 3D diagram of the two-antenna system and successive positions of the spherical targets at a 850-mm depth (red points): the spherical target’s FMC were measured one after the other for each of the twelve positions of the sphere. (**b**) Top view of the same configuration. The sphere located at X = 0\({}^{\circ}\) and Y = 0\({}^{\circ}\) (surrounded by a green circle) is used as a reference for the amplitudes (see in the text). The TFM measured images obtained for four positions of the sphere are presented Figures 7 and 8. They show the good capability of system imaging as, even for the target far from the R antenna axis, the TFM image's quality is good in terms of SNR and resolution in the three cases of Figure 7a,b and Figure 8a. It is only when the sphere is far from both the E and R antenna axes (Figure 8b, where the sphere is distant 235 mm from the E antenna and 227 mm from the R antenna) that the SNR becomes too low to allow a good experimental image of the sphere. The SNR values measured on the experimental TFM are 9.5 dB for Figure 7a, 8 dB for Figure 7b, 8 dB for Figure 8a, and 2 dB for Figure 8b. It should be noted that, to calculate these SNRs, both attenuation and grating lobes were included in the noise measurement. The four results also show a good qualitative agreement between CIVA and the measures regarding the evolution of the target image with the position of the sphere in the field of vision. A good quantitative agreement was also obtained for the maximum amplitude of the TFM images: the discrepancy between CIVA and the twelve measures was less than 3 dB (the reference for the amplitude is the TFM amplitude obtained for the sphere located at X = 0\({}^{\circ}\) and Y = 0\({}^{\circ}\), which is surrounded by a green circle in Figure 6). However, the model used for the FMC simulation in CIVA does not predict the noise observed on the experimental image as it is not taken into account for the computation. Figure 7: Measured and simulated FMC/TFM results: (**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.