1. Introduction
Ferroelectrets (FE) are polymeric foam films with elongated pores in the film plane that can be poled and present a piezoelectric response [1,2]. They have been widely researched and used. One of the most interesting uses of FE films is for air-coupled ultrasonic transducers, where flat and focused designs have been used in Nondestructive Tests NDT [3,4,5]. The very low impedance of this type of materials permits the construction of transducers without matching layers, though the response is quite resonant and, hence, the bandwidth reduced, alternatively they have also been used as active matching layers [6].
Flat transducers were first tried for water immersion in [3,7] where they demonstrated a poor sensitivity but a very wide band response. Later, in [8], the use of matching layers was tried to increase both sensitivity and water resistance with limited succeed. In spite of the poor sensitivity, the large bandwidth together with other advantages, like the flexibility and the possibility to miniaturize the transducers, motivated further study of this application. In particular, the use of different FE materials, different protective coatings and focused designs to improve resolution.
In this work, we present the pulse-echo response in water immersion of transducers based on two different FE materials with the purpose of providing some insight into the path to improve FE material properties for water coupled ultrasonic transducers. Flat and spherically focused prototypes were fabricated and tested and the use of different thin polymeric coatings intended to protect the transducer surface without having any negative impact on either the sensitivity or the frequency bandwidth were tried. Transducer response in pulse-echo operation mode (both time domain and sensitivity in the frequency domain) was measured as well as the acoustic field distribution.
2. Materials and Methods: Transducers Design and Fabrication
The purpose of this work is to study the feasibility of using ultrasonic transducers based on FE films for pulse-echo water immersion. To this end, FE transducers were designed, fabricated and tested. Two different FE materials (HS03 and HS06) were used to make ultrasonic transducers that were then tested in pulse-echo mode in water immersion. For the FE material providing the best results, spherically focused transducers were then produced and tested. Finally, different techniques and materials were investigated with the purpose of providing further protection of the transducer radiating surface without affecting transducer performance.
2.1. Ferroelectret Materials
Two different polypropylene ferroelectret films were employed to produce and test water immersion transducers. Both materials were purchased from EMFI, their commercial names are: HS03 and HS06. The properties of these materials have been widely studied before (see, for example [9,10]). The main properties of the employed FE films are summarized in Table 1. These two materials permit determination of whether the resonant frequency of the film has any effect on the pulse-echo frequency band of the transducer when operated in water immersion and if the differences in the material impedance have any impact on the transducers’ sensitivity. Furthermore, these two materials present a somewhat different microstructure; see [10], where pores in HS06 are more open giving rise to a lower material density and deformability in the thickness direction. It is of interest to determine what is the material microstructure that provides better water-coupled transducers is, as this information could be used to further engineer FE properties for this application.
2.2. 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).
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 ferroelectret 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) ferroelectret 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 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. For this reason, in all cases a thin layer of gold was sputtered on the radiating surface, this electrode presents a much better resistance compared with the evaporated aluminum electrode. The Au-sputtering was performed using a Leica EM ACE200 coater with directional coating and coating time between 30 and 60 s.
Figure 2 shows a picture of some of the fabricated transducer prototypes. Wrinkles in the FE film can be seen in the focused designs, as well as the fact that there are more wrinkles and wrinkle size is larger in the transducer with the smaller radius.
2.3. Methods for Transducer Characterization
2.3.1. Preliminary Transducer Verification: Pulse-Echo in Air
A first verification of the proper FE film behavior in the transducer was performed by measuring the transducer response in pulse-eco in air. As it is well known, the FE film glued to a backing block and operating in air is quite a resonant device and the resonant mode is the quarter wavelength thickness resonance of the FE film. Sensitivity (SNS) in pulse echo is measured as:
(1)
where FFT denotes the Fast Fourier Transform, sTx is the signal applied to transducer terminals and sRx is the electrical signal generated in the transducer when the echo is received. In order to obtain these signals a temporal square gate is applied. In the first case the gate is located at t = 0 s, while in the second case the gate is located at the time of arrival of the echo. We used an Olympus 4077 pulser-receiver PR in pulse-echo mode to drive the transducer with a half cycle square pulse, 400 V amplitude, 1.0 MHz center frequency, and to receive and amplify (40 dB) the received echo. Signals where digitized and stored using a Tektronix DPO oscilloscope.The advantage of this way of verifying transducer fabrication is that it is simple and fast. Any lack of resonant response or a response more damped than expected or a significant deviation of the resonant frequency away from the expected value (λ/4 thickness resonance) can easily be interpreted as defective design that can be attributed to a damaged FE film, or electrode, or to an imperfect binding of the FE film to the backing block.Table 1 shows the value of the λ/2 thickness resonance measured in [10] in free standing films, so the λ/4 frequency is simply ½ of the λ/2 resonant frequency shown in Table 1.
2.3.2. Transducer Characterization: Pulse-Echo Measurements in Water Immersion
The experimental set-up for pulse-echo measurements is shown in Figure 3; transducers and a flat steel block (53 mm thick) used as reflector were immersed in a water tank. The transducer is driven by the an Olympus 5058 pulser/receiver, the received echo is received through the receiver stage of the Olympus 5058 PR, filtered, amplified (40 dB) and then sent to an oscilloscope where the signal is digitized and stored. For the focused transducers, the reflector is located at the transducer focal distance, while for the flat transducer, the separation was 40 mm (which is close to the transition between near and far field).
2.3.3. Transducer Characterization: Acoustic Field Measurements in Water Immersion
An XYZ scanner DIS300 and a Difrascope pulse-echo ultrasound equipment were used, both from DASEL SL (Madrid, Spain). For each transducer, the acoustic field was measured over a rectangular grid, using a 1 mm diameter needle hydrophone (Precision Acoustics, Dorchester, Dorset, UK) connected to the reception stage of the pulse-receiver system. The excitation, acquisition and movement were synchronized by a rotary encoder in one of the scanner axes, with a resolution of 0.1 mm.
A single negative square pulse of −400 V amplitude and 250 ns width was used for excitation, and a band-pass filter between 30 kHz and 5 MHz was applied on reception, along with averaging by 8 to improve signal to noise ratio. For each position of the measurement grid, the peak-to-peak value was registered, to build the normalized field plots. The time-of-flight between the transducer and the hydrophone was also registered, to account for measurement gap near the transducer surface. Measurement grid resolution was 1 mm for the flat transducer, 0.5 mm for the f = 35 mm transducer, and 0.2 mm for the f = 22 mm transducer. Signal processing and image reconstruction were performed in Matlab (Matworks Inc., Beltsville, MD, USA).
2.4. Methods for Radiating Surface Protection
Different techniques and materials were tried to provide an additional protection of the transducer surface while avoiding any reduction in either sensitivity or bandwidth: polymethylmethacrylate PMMA deposited by spin coating and polytetrafluoroethylene PTFE, varnish and acrylic lacquer (used for conformal coating for insulation and circuit boards environmental protection) deposited by spray coating, see Table 2.
PMMA powder was first dissolved in anisole (5%), deposited on transducer surface and then spin coated in two steps, first, 10 s at 1000 rpm and then 10 s at 2000 rpm. Continuity and uniformity of the coating were verified by observing the transducer surface under a microscope. The employed lacquer and varnish are UV fluorescent, so UV illumination was used to make the presence of the coating material clearer. All coatings were allowed to cure or dry for 24 h at room conditions. Thicknesses of the layers of coating were estimated from the frequency shift of the transducer thickness resonance, measured in pulse-echo in air, and from properties of the deposited materials (see Table 2).
3. Results
3.1. Preliminary Verification of the FE Film Response
This preliminary verification is performed as explained in Section 2.4. This procedure was applied to uncoated flat and focused transducers to verify the proper integration of the FE layer in the transducer design and to coated flat transducers to determine the influence of the coating.
3.1.1. Basic Design: Transducers without Surface Protection.
The resonant frequency in air of the HS03 and the HS06 transducers corresponds to the λ/4 thickness resonance of the FE film. Hence, the resonant frequency is expected to be located close to 0.32 and 0.56 MHz, for HS03 and HS06, respectively (see Table 1). Measured SNS of the gold coated transducers operated in pulse-echo mode in air is shown in Figure 4.
In all cases, the resonant response is clearly observed, however, the resonance is located at a lower frequency compared with the expected λ/4 thickness resonant frequency (see Table 1). This is an expected result and is due to the effect of the layer of gold, as the gold loads the resonance and then shifts the resonant frequency towards lower values. Nonetheless, it can be confirmed that the thickness resonance is preserved and that the frequency shift is moderated. This deviation in the resonant frequency (about 10%) is common in all Au coated transducers, this permits to estimate the thickness of the Au layer which is typically in the range 65–110 nm, for sputtering times between 30 and 60 s.
For the HS03 film the first two orders of resonances have been observed, revealing the effect of the increase in the ultrasound attenuation in the FE material with the frequency. For the HS06 film a lower sensitivity and more damped resonance is observed. This can be due to the increase in the attenuation with the frequency, or the higher impedance of this film (poorer matching to the air), or a reduced piezoelectric response compared with HS03, which could be due to a lower polarization level or to a lower piezoelectric constant that could be related to the different cellular structure of these two films, see [10].
For the HS03 focused transducer a similar resonant behavior is observed with the same resonant frequency, though it presents a somewhat lower peak SNS value that can be due to the wrinkles introduced in the FE film when it is glued to the spherical backing block. Figure 4 shows, as an example, the SNS in air of the HS03 transducer with the smaller radius of curvature.
3.1.2. Transducers with a Polymer Coating
HS03 transducers with different coatings were fabricated and the pulse-echo response in air compared before and after coating deposition. The purpose was to estimate the effect of the coating on the resonant response of the FE film: the thicker the coating, the larger the frequency shift and the lower the coating uniformity the larger the reduction in the resonance Q-factor. The measured SNS in pulse-echo mode in air, using the same equipment as in the previous section is shown in Figure 5. The frequency shift of the λ/4 thickness resonance of the transducer operated in air in pulse-echo mode is shown in Table 3.
3.2. Water Immersion Response in Pulse-Echo Mode
All measurements presented in this section were performed as described in Section 2.3.2 of methods for transducer characterization.
3.2.1. Frequency Domain Response
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Response of transducers made with different FE materials
The measured SNSs in pulse-echo mode in water immersion for flat HS03 and HS06 transducers without any coating (apart from the layer of sputtered Au) are shown in Figure 6. The response of the HS03-transducers is clearly better than that of the HS06-transducer. The sensitivity of the HS03 transducer is about 15 dB higher. The bandwidth of the flat transducers made with the HS06 film is narrower, more resonant and centered at a lower frequency (about 0.6 MHz). In addition, for frequencies over 1.2 MHz the signal to noise ratio is very poor and peaks observed for HS06 between 2 and 3 MHz are due to the noise. On the contrary, the HS03 transducer presents a wider frequency band: rather flat between 0.4 and 1.3 MHz. Between 1.5 and 4.0 MHz it is also flat but 6 dB below. Beyond 4.0 MHz, the signal to noise ratio becomes very low, in part due to the lower energy output of the pulser at those frequencies. The main drawback of these transducers is the reduced peak sensitivity that is about −117 and −130 dB for HS03 and HS06, respectively.
Due to the worse performance of HS06-transducers the rest of the study (performance of focused transducers and effect of surface coating) is limited to HS03-transducers.
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Response of focused transducers.
Figure 7 shows the measured sensitivity (SNS) for the flat and the spherically focused transducers with focal distance of 22 and 35 mm. The obtained response is pretty similar, so it can be concluded that the effect of adapting the FE film to the spherical surface of the backing block has a limited effect on the transducer performance.
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Response of transducers with different surface protection coatings.
Figure 8 shows the measured SNS vs. frequency for the HS03 flat transducers with different coatings. The response below 1.5 MHz is similar, but above 1.5 MHz the signal to noise ratio SNR is poorer in this case compared with the uncoated transducers.
3.2.2. Time Domain Response
All measurements presented in this section were performed as described in Section 2.3.2 of methods for transducer characterization.
-
Flat and focused transducers.
The received echoes for the HS03 flat and focused transducers corresponding to the experimental set-up shown in Figure 3 are shown in Figure 9. For the flat transducer it is possible to see the first reflection from the water/steel surface (echo #1 in Figure 5) that appears at ~57 μs (Figure 9, top), and the first reverberation in this cavity (transducer-reflector), at ~115 μs (Figure 9, top). In addition, echoes from: (i) the back surface of the steel block (echo #2 in Figure 5), at ~75 μs (Figure 9, top), (ii) the bottom surface of the water tank (echo #3 in Figure 5), at ~87 μs (Figure 9, top), and (iii) reverberations in those cavities can also be appreciated. For the focused transducers (focal distances of 22 and 35 mm) only the reflections from the front steel reflector surface (and reverberations in the transducer–reflector cavity) are observed as the other interfaces mentioned above are well out of focus. For the 22 mm radius of curvature transducer, the first reflection from the steel reflector front face (at ~29 μs) plus two reverberations in the cavity between the transducer and the reflector can be observed (at ~57 μs and ~85 μs).
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Transducers with coating.
The received echoes corresponding to the experimental set-up shown in Figure 5 for the HS03 flat transducers with different coatings are shown in Figure 10.
3.2.3. Acoustic Field
All measurements presented in this section were performed as described in Section 2.3.3.
The measured acoustic field (axial and transverse, at focal distance) distribution is shown in Figure 11, Figure 12 and Figure 13 for HS03 transducers: flat and spherically focused with radii of curvature of 35 mm and 22 mm, respectively.
The measured center frequency, focal distance and beam width at focus are shown in Table 4. In addition, the theoretical beam width (BW) calculated according to Equation (2) is also shown.
(2)
where F is the focal distance, λ is the wavelength and D the transducer aperture diameter.4. Discussion
The objective of this work was to test the possibility of using FE films to produce water immersion transducers for pulse-echo operation. Two different FE materials were employed: HS03 and HS06. The former has a lower resonant frequency, a more flattened pore structure (that makes the pores and the film more deformable in the thickness direction), and a lower acoustic impedance. Results with these two materials reveal that transducers produced with the HS03 film have a sensitivity about 15 dB better and a wider frequency bandwidth (Figure 6). Considering that the impedance of the HS06 film is better coupled to the water, this better response of the HS03 film could be related with either a better piezoelectric response of HS03 or a more efficient response of the cellular structure of HS03 when operated with a water load.
Water is a huge mechanical load for the FE film; hence, thickness resonances are expected to be completely damped out. As a matter of fact, no trace of the film thickness resonance is found in the pulse-echo response in water, where the film could be expected to operate in the lambda/2 thickness mode (Figure 6). This huge load imposed by the water is expected to produce a very large frequency bandwidth and a very low sensitivity. Pulse duration (under spike excitation) is about 2–3 us long (Figure 9 and Figure 10), while the 6 dB frequency band expands from 0.29 up to 2.7 MHz (161%), and the 12 dB band expands up to 4.5 MHz (Figure 6 and Figure 7). The main counterpart is the reduced sensitivity. The observed peak sensitivity values for the different prototypes are in the range of −114 to −118 dB (Figure 6, Figure 7 and Figure 8). Nonetheless, even with this low sensitivity it was possible to observe the front and back echoes of a 53 mm thick steel block (see Figure 9 and Figure 10).
Different techniques and materials were tried to provide protection for the radiating surface. The main idea is to provide a uniform and thin coating with acoustic properties similar to the water, so that the effect of this coating on the acoustic performance could be negligible. Measured response in pulse echo mode in water immersion revealed a somewhat better sensitivity (about 5 dB) for transducers with varnish and lacquer compared with PMMA and PTFE coted transducers. This can be due to the fact that the acoustic impedance of PMMA and PTFE coatings is expected to be higher that of the water. However, the SNR of coated transducers seems to be poorer in coated transducers (Figure 7 and Figure 8). This has to be confirmed in further studies.
Finally, we have shown that it is possible to produce spherically focused transducers, by using a backing block with a spherical surface and gluing the FE film to it. Adapting the FE film to the curved surface produces some wrinkles in the film, however the effect on the ultrasonic response is reduced (Figure 4 and Figure 7) and no artifacts can be observed in the acoustic fields (Figure 11, Figure 12 and Figure 13). SNS and the signal in the time domain (Figure 9) are very similar for flat and focused transducers. The measured acoustic field of the focused transducers revealed a field distribution very close to the expected one. For the transducer with a radius of curvature of 22 mm, the measured focal distance was 19 mm and the focal spot size was 1.8 mm. In this case the calculated focal spot size was 1.67 mm, very close to the measured value. For the transducer with a radius of curvature of 35 mm, the measured focal distance was 32 mm and the focal spot size was 3.7 mm. In this case the calculated focal spot size was 2.88 mm.
5. Conclusions
This work shows the response of ferroelectret film-based transducers for pulse-echo operation in water. Two FE films were tried and the best results were obtained with the film (HS03) with the highest density and the lowest impedance. As the impedance matching is poorer for this film, the better response must be due to a better piezoelectric response of the HS03 film. As expected, and due to the large load of the water, the thickness resonance of the film is completely damped out, giving rise to a poor sensitivity (around −115 dB) and a very wide band response with a short signal duration. It has been shown that it is also possible to produce spherically focused transducers with a similar response compared with flat ones, but with the advantage of a better spatial resolution, with a focal spot size <2 mm.
In spite of the reduced peak sensitivity, the huge bandwidth and the observed SNR values still permit to consider the use of this kind of transducers for different water immersion applications related to materials characterization, NDT and medical imaging, in applications where large bandwidth, moderate frequencies (0.5–4.0 MHz) and good axial resolution are required. In addition to the large frequency bandwidth and short signal duration, the FE transducers offer other advantages related to the flexibility of the material and the reduced size of the required backing block. Further studies are needed to determine if the transducer sensitivity can be improved. The first step can be to try techniques that have already been tested for FE air-coupled transducers. They include the use of a high voltage excitation to make the FE film work under the electrostrictive regime and the use of a bias voltage [15]. In addition, spread spectrum signals with programable excitation spectral shape can be used to compensate the 10 dB spectral losses beyond 2.0 MHz, making received signals even more broadband [16]. In addition, further studies of transmission and reception sensitivity and frequency bands could be beneficial in order to optimize transducer design.
Author Contributions
Conceptualization, L.S. and T.G.A.-A.; methodology, T.G.A.-A. and J.C.; software, J.C.; validation, J.Q., and T.G.A.-A.; resources, T.G.A.-A., L.S., and J.C.; writing—original draft preparation, J.Q.; writing—review and editing, T.G.A.-A., L.S. and J.C.; funding acquisition, T.G.A.-A., J.C. and L.S. All authors have read and agreed to the published version of the manuscript.
Funding
This work was supported in part by Ministerio de Economía y Competitividad under grants ECERES (DPI2016- 78876-R, AEI/FEDER, UE) and AIMUT (RTI2018-099118-A-I00, MCIU/AEI/FEDER, UE) and received partial funding (LS) from European Regional Development Fund (project No. 01.2.2-LMT-K-718-03-0026) under grant agreement with the Research Council of Lithuania (LMTLT).
Conflicts of Interest
The authors declare no conflict of interest and the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Figures and Tables
Enlarge this image.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.
Enlarge this image.Figure 2. Picture of transducer prototypes, from left to right: HS03 focused (radius of curvature: 22 mm), HS03 focused (radius of curvature: 35 mm), HS06 flat, HS03 flat.
Enlarge this image.Figure 4. Au-sputtered transducers in pulse-echo response, air-coupled operation.
Enlarge this image.Figure 5. Sensitivity (SNS) vs. frequency for flat HS03 transducers with different coatings in pulse-echo mode in air.
Enlarge this image.Figure 7. SNS vs. frequency for HS03 transducers in pulse-echo mode in water: flat and spherically focused (two focal distances: 22 and 35 mm).
Enlarge this image.Figure 8. SNS vs. frequency for flat HS03 transducers in pulse-echo mode in water with different coatings.
Enlarge this image.Figure 9. Response in the time domain in pulse-echo mode in water for the HS03 flat and focused transducers, radii of curvature of 22 and 35 mm.
Enlarge this image.Figure 10. The response in the time domain in pulse-echo mode in water for HS03 transducers with different coatings (varnish, PTFE, lacquer and PMMA).
Enlarge this image.Figure 11. HS03 flat transducer acoustic field. (a) axial section, (b) transversal section.
Enlarge this image.Figure 12. HS03 spherically focused transducer (radius of curvature 35 mm) acoustic field. (a) axial section, (b) transversal section.
Enlarge this image.Figure 13. HS03 spherically focused transducer (radius of curvature 22 mm) acoustic field. (a) axial section, (b) transversal section.
Properties of the ferroelectret FE films employed [10].
| Material | Thickness |
Density |
λ/2 Resonant Frequency, Thickness Mode |
Impedance |
|---|---|---|---|---|
| HS03 | 70 | 530 | 0.638 | 0.046 |
| HS06 | 90 | 370 | 1.120 | 0.065 |
Coating material properties and method employed.
| Material | Density |
Ultrasound Velocity |
Acoustic Impedance |
Coating Method |
|---|---|---|---|---|
| PMMA | 1150 | 2700 | 3.11 | Spin coating |
| PTFE | 2200 | 1400 | 3.10 | Spray coating |
| Varnish | 950 ** | 1800 * | 0.95 | Spray coating |
| Acrylic Lacquer | 800 ** | 1800 * | 0.88 | Spray coating |
* Estimated.; ** According to manufacturer data.
Table 3Frequency shift due to the coting and estimated coating thickness.
| Coating | λ/4 Resonance |
Relative Variation |
Estimated Coating Thickness |
|
|---|---|---|---|---|
| Before Coating | After Coating | |||
| PMMA | 285.6 | 283.2 | 0.85 | 0.3 |
| PTFE | 290.5 | 288.0 | 0.84 | 0.15 |
| Varnish | 280.8 | 200.2 | 28.7 | 25 |
| Lacquer | 285.0 | 200.0 | 29.8 | 26 |
Focal distance and beam width at focus.
| Transducer |
Measured Center Frequency | Measured Focal Distance | Beam Width at Focus | |
|---|---|---|---|---|
| Theoretical | Measured | |||
| 22 mm | 1.30 MHz | 19 mm | 1.67 mm | 1.8 mm |
| 35 mm | 1.20 MHz | 32 mm | 2.88 mm | 3.7 mm |
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; Camacho, Jorge 1 ; Tomas Gomez Alvarez-Arenas 1
1 Instituto de Tecnologías Físicas y de la Información, CSIC, 28006 Madrid, Spain;
2 Department of Electronics Engineering, Kaunas University of Technology, LT-51368 Kaunas, Lithuania;