## 2 Materials and Methods: Transducers Design and Fabrication
### Transducer Design and Fabrication Method  
Flat and spherically focused transducers were tried. In all cases aperture was circular (15 mm diameter). Two different radii of curvature were tried for the spherically focused transducers: 22 and 35 mm. In all cases, the FE film is glued to a heavy backing block (brass) and provided with aluminum housing, ground connected for radio frequency RF shielding (see Figure 1). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Thickness** & **Density** & **\(\uplambda\)/2 Resonant Frequency, Thickness Mode** & **Impedance** \\  & **(\(\upmu\)m)** & **(kg/m\({}^{3}\))** & **(MHz)** & **(MRayl)** \\ \hline HS03 & 70 & 530 & 0.638 & 0.046 \\ \hline HS06 & 90 & 370 & 1.120 & 0.065 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the ferroelectret FE films employed [10]. The possibility of using matching layers for water-coupled FE transducers was studied in [8]. The purpose was to improve the transducer sensitivity and to provide a protection of the FE front surface and electrode. However, the main problem is that there are no available materials with the required properties to produce these matching layers. For the ferroelectric materials shown in Table 1, the required impedance for the matching layer is about 0.28 MRayl for one single matching layer and about 0.07 and 0.23 MRayl for a stack of two matching layers. Such low impedance materials can be found in porous materials like those presented in [11], however the open-cell nature of the pores of these materials makes it impossible to use them in water. Closed-cell porous materials were also tried as matching layers [12], but it is not easy to obtain close-cell porous materials with impedance below 0.3 MRayl; specially, considering that the pore size must be much smaller than the matching layer thickness. Finally, [8] revealed that the use of available materials produces a moderate improvement of the transducer sensitivity together with an unacceptable reduction in the transducers' frequency band. For this reason, the use of matching layers was discarded, however, methods to protect the transducer front surface and electrode that do not interfere with the frequency band nor reduce sensitivity have been considered in this work and are explained later. Circles were cut out of the FE sheets, of diameter 15 mm, and glued to a brass backing block using double-sided electrically conductive tape. The front face of the FE circle is electrically connected to the cylindrical transducer housing (aluminum) that is connected to the ground electrode of the transducer. For the focused transducer, the backing block has a spherical shape. The FE film is pressed against the spherical surface, this permits the accommodation of the film to this curvature, though it also produces some wrinkles. The number and size of these wrinkles depend on the radius of the spherical backing block and the transducer aperture. The problem of adapting the flexible (but non-stretchable) ferroelectric film to non-developable surfaces has already been addressed in [13], where it was avoided by dividing the surface into small portions. When this is not possible some wrinkles may appear in the  
Figure 1: Transducer design for flat and spherically focused prototypes. 1: Connector, 2: wire, 3: backing block, 4: aluminum housing, 5: conductive tape, 6: insulating seal, 7: ferroelectret film, 8: Au coating, 9: Polymer coating. film as is the case for spherically focused transducers. A similar effect has been observed previously in [14] for air-coupled spherically focused transducers. The HS03 has one surface metalized with aluminum; this face is used as transducer external surface and the aluminum metallization can be used as ground electrode. The HS06 has no electroded surface. Therefore, in this case the outer surface is sputtered with gold. However, the stability of the aluminum electrode is very poor, and it can be easily removed with film manipulation or even when the transducer is operated in water.