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Bias-sensitive transparent single-element ultrasound transducers using hot-pressed PMN-PT

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Abstract

Here we introduce electrostrictive hot-pressed lead magnesium niobate (PMN) with low lead titanate (PT) doping as a candidate transparent transducer material. We fabricate transparent high-frequency single-element transducers and characterize their optical, electrical, and acoustic properties. PMN-PT may offer sensitivity advantages over other transducer materials such as lithium niobate owing to its high electromechanical efficiency and bias-voltage sensitivity. The transparency of the fabricated transducer was measured ∼67% at 532 nm wavelength with a maximum electromechanical coefficient of ∼0.68 with a DC bias level of 100 V. The photoacoustic impulse response showed a center frequency of ∼27.6 MHz with a −6 dB bandwidth of ∼61% at a DC bias level of 40 V. Results demonstrate that the new transparent transducers hold promise for future optical-ultrasonic and photoacoustic imaging applications.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Emerging combined optical and ultrasonic imaging and sensing technologies have been limited by opaque ultrasound transducers. Transparent transducers would enable optical imaging and light delivery through the transducer, rather than around it. Photoacoustic imaging (PAI) is one such technology that offers rich optical contrast with ultrasonic - or even optical spatial resolution [1]. Most photoacoustic imaging methods require non-optimal light delivery methods where optical and acoustic paths are separated [2]. Transparent ultrasound transducers could enable improved light delivery and shorter acoustic path lengths, leading to high signal-to-noise ratios.

Transparent ultrasound transducers have recently been considered as an alternative to more conventional opaque transducers. Transparent Lithium niobate transducers were introduced some years ago using indium tin oxide electrodes, but initial work did not explore photoacoustic or imaging applications [3]. In 2019, Z. Li et al. demonstrated transparent single-element capacitive micromachined ultrasound transducers with accompanying through-illumination photoacoustic data [4]. Later the same year, Dangi et al. demonstrated a transparent single-element Lithium Niobate transducer for photoacoustic imaging [5]. The same group later demonstrated optical-resolution photoacoustic microscopy with similar devices [6]. R. Chen et al. successfully demonstrated PAI of mouse-ear vasculatures in vivo using a high-frequency transparent lithium niobate transducer [7]. The C. Kim group recently demonstrated multi-modality imaging with transparent ultrasound transducers, showing impressive imaging results in [8]. However, all these methods required mechanical scanning of the light source and/or the transducer to form images. Kashani et al. recently demonstrated transparent linear arrays for combined optical, ultrasonic, and photoacoustic imaging [9,10]. Transparent ultrasound arrays have also been implemented using optical detection methods, and include Fabry-Pérot etalon sensors, micro-ring resonators, etc. Fabry-Pérot etalons have demonstrated high sensitivity 3D photoacoustic imaging but require scanning of an interrogation beam over the etalon, and sometimes optical tuning to account for etalon non-uniformities.

Our long-term objective is to develop transparent ultrasound array transducers enabling 3D ultrasonic and photoacoustic imaging with fast electronic readout. Recently, Ceroici et al. demonstrated electrostrictive bias-sensitive row-column arrays with a novel Hadamard-biasing and readout scheme for fast 3D imaging [11,12]. This approach, however, used opaque row-column arrays. However, there may be an opportunity to achieve such arrays with transparent electrostrictive materials. Such materials would ideally be non-piezoelectric in the absence of a DC bias voltage, but become piezoelectric with an application of such voltage. Moreover, the phase of transmitted or received signals would ideally be shifted by 180 degrees with a bias polarity change to enable the required Hadamard bias readout schemes. As a step towards this goal, we here introduce a high-frequency transparent electrostrictive PMN-PT single-element transducer and demonstrate the feasibility of bias sensitivity.

2. Method

Here we present the fabrication and the first usage of hot-pressed lead magnesium niobate (PMN) with low PT doping (<0.1% PT [13]) as a bias-sensitive transparent ultrasound transducer with a higher electromechanical coefficient. The low PT doping leads to electrostrictive rather than piezoelectric behavior, such that at room temperature there is no hysteresis (i.e. no residual polarization) when cycling the electric field and measuring material polarization. This behavior is important for envisioned TOBE array bias-encoding operations as detailed in [14] with a fabricated high-frequency transducer in [15]. This relaxor material has an extremely large dielectric and electrostrictive constant. Hot-pressed PMN-PT has been used for electro-optic devices but to our knowledge, this is the first time this material has been investigated as a transparent ultrasound transducer. The transducer is fabricated by cutting down the bulk hot-pressed PMN-PT (Boston Applied Technologies, Inc., U.S.) into ∼1 mm thick samples using a diamond-wire saw (STX201, MTI Corporation, CA, U.S.) and then lapping to ∼80 µm thickness (Unipol 1202, Laizhou Weiyi experimental machine manufacturing Co., Ltd., China), followed by fine polishing on both sides [Fig. 1(b)]. The PMN-PT half-lambda thickness is the primary determinant of the resonance frequency, predicted to by ∼30MHz. A layer of ∼250 nm indium tin oxide (ITO) is deposited as a transparent electrode on both sides of the transducer with a measured sheet resistivity as low as 37.2 Ω/sq. To measure ITO resistivity, we used a four-point probe (Lucus Pro4 4000, CA, USA). The fabricated transducer showed transparency of 67% at 532 nm [Fig. 1(c)]. The transducer is diced into 4 × 4 mm squares and then mounted on a PCB with an open aperture to let the laser beam pass through. The bottom and top electrodes are connected to the PCB by a thin layer of gold masked during deposition with a photoresist patterned to create non-transparent metal bond-pads at the edge of the transducer. The transparent aperture measures ∼ 3.5 mm × 3.5 mm. Next, an SMA connector is connected to the PCB. A thick layer of transparent Epotek-301 with an acoustic impedance of ∼3 MRayls was used as a backing material. Figure 1(d),(e) illustrate the side view and the fabricated transducer, respectively.

 figure: Fig. 1.

Fig. 1. The fabricated transparent ultrasound transducer based on electrostrictive PMN-PT and transparency measurement. (a) The raw bulk hot-pressed PMN-PT measuring roughly 40 mm × 40 mm x 25 mm. (b) Precisely polished, and ITO coated ∼80 µm thick PMN-PT. (c) Transparency measurement of the fabricated transducer with maximum transparency of 67% at 532 nm. (d) diagram of the transducer cross section. (e) The fabricated transparent transducer mounted on a PCB with a transparent aperture of roughly 3.5 mm × 3.5 mm.

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As part of the characterization, the laser damage threshold was measured for separate material samples including a 3mm block of polished Epoxy-301, a ∼200 µm thick layer of transparent PMN, and a ∼250 nm layer of ITO sputtered on a glass wafer. A Nd:YAG pulsed 532 nm laser with a repetition rate of 10 Hz was guided to the samples. For the damage test, each sample was hit by 2000 laser shots for a few different energy levels. However, all the tested materials could withstand up to ∼60 mJ/cm2, without any apparent damage, which is three times the ANSI maximum permissible exposure used for biomedical applications. The laser damage threshold for Parylene C, however, was ∼23 mJ/cm2 for a ∼50 µm layer of Parylene C.

3. Results

The bias sensitivity and the electromechanical efficiency of the transducer were characterized by measuring the resonance and anti-resonance frequencies with an impedance analyzer for different DC bias voltages. Two different fabricated transducers were used for these measurements, the first one without a matching layer and another one with a layer of ∼20 µm (quarter-wavelength) Parylene C as a front matching layer. The deposition of the matching layer was obtained by evaporating ∼39 grams of Parylene C inside a vacuum chamber. Although the matching layer adds some damping to the transducer and decreases the operational center frequency, it showed an improvement in the transducer sensitivity and with non-noticeable electromechanical coefficient changes. Figure 2(a) and (c) are illustrating the magnitude of the unloaded input impedance for both transducers, with and without matching layer, respectively. The electromechanical coefficient (kt) value was calculated using measured resonance and anti-resonance frequencies, as detailed in [16] and expressed in Eq. (1), where ωS and ωP are the resonance and anti-resonance frequencies, respectively.

$${k_t} = \sqrt {\left( {\frac{{\pi \; {\mathrm{\omega }_s}}}{{2\; {\mathrm{\omega }_p}}}} \right)tan\left[ {\pi \frac{{({{\mathrm{\omega }_p}\; - \; {\mathrm{\omega }_s}} )}}{{2\; {\mathrm{\omega }_p}}}} \right]} $$

 figure: Fig. 2.

Fig. 2. The measured input impedance of the transducers without loading on the front surface. (a),(b) The magnitude and phase of the input impedance for the fabricated transducer without matching layer. (c),(d) The magnitude and phase of the input impedance for the fabricated transducer with a matching layer.

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As expected, the hot-pressed PMN-PT material shows no piezoelectric effect for a 0 Volt bias voltage while an increment on the kt was seen while the biasing voltage increases. Both the transducers showed almost the same kt for the same level of biasing with a maximum value of ∼0.68 for a voltage of 100V, which is higher than Lithium Niobate (with kt of ∼0.49). Single-crystal PMN-PT may provide even higher kt values, however, most PMN-PT materials have higher PT doping and thus are not purely electrostrictive as required in our envisioned applications.

The lower electrical impedance of the transducers is due to the high dielectric constant of the Hot-Pressed PMN-PT material and the large area of the transducers. Such a small input impedance causes a large electrical mismatch when transmitting on the transducer. For measuring the receive response of the transducer, a commercial broad-band 25 MHz transducer (V324-SM, Olympus Scientific Solutions Americas Inc. U.S.) with a focus point of half an inch was used as a transmitter while receiving on the fabricated transducers. A tank filled with deionized water was used for immersion testing. The 25 MHz transducer was placed 0.5 inches away from the fabricated transducer while transmitting the focused beam to the center of the transducer. The measurements are done for different values of DC bias voltages. The received signals were recorded after amplifying with a +28 dB, 5 to 75 MHz amplifier (PANAMETICS-NDT 5073PR). As shown in Fig. 3(a) for the measured impulse responses, the fabricated transparent transducer without a front matching layer has a center frequency of 27.5 MHz with a −6dB bandwidth of 36% at a DC bias voltage of 60 V. The transducer with a front matching layer showed a center frequency of 23.4 MHz with a bandwidth of 38% at the same DC biasing level. The matching layer slightly decreased the center frequency but increased the amplitude of the received signal from a peak-to-peak voltage (Vpp) of 780 mVpp to 1312 mVpp. The receive sensitivity of the transducers was measured by a Hydrophone at a 10 mm axial distance with a maximum sensitivity of ∼4.2 µV/kPa and ∼7.1 µV/kPa for the fabricated transducers with and without the matching layer, respectively. The hydrophone was first used to measure the acoustic pressure at a 10mm axial distance when transmitting on the 25MHz commercial transducer. The transmitter sends a negative short pulse to excite the transducer. Then the same 25MHz transducer was used at the same axial distance (10mm) to transmit the same acoustic wave and the signals were received on the fabricated transducers. For the given pressure and measured signal amplitude from each transducer, we have calculated the receive sensitivity for each fabricated transducer.

 figure: Fig. 3.

Fig. 3. The measured acoustic receive response and photoacoustic responses of the transducers. (a) The amplitude and phase of the impulse response for the fabricated transparent transducers, with and without matching layer at +60 V bias. (b) The PA response of the transducer without matching layer at +40 and −40 Volts bias.

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The photoacoustic (PA) response of the transducer was obtained only on the transparent transducer without a matching layer to avoid damage to the Parylene C layer. The characterization is done by guiding a pulsed 532 nm laser beam through the transducer and hitting a thin carbon fiber bundle inside a water tank filled with DI-Water. The diameter of the beam was ∼1mm when hitting the target with a measured power of ∼10 mW at a repetition rate of 10 Hz. Figure 3(b) illustrates the PA impulse response of the transducer with a center frequency of ∼27.6 MHz and a −6 dB bandwidth of ∼61% at a DC bias level of 40 V. Changing the polarity of the bias voltage keeps the sensitivity level the same but shifts the received signal’s phase by 180 degrees. This makes our bias-sensitive fabricated transducer a good candidate for aperture coding/decoding applications with adjustable sensitivity. The axial resolution of the single-element transparent transducer was estimated by taking the full-width at half-maximum (FWHM) of an envelope applied to the photoacoustic signal from the thin carbon fiber bundle shown in Fig. 3(b). The FWHM was found to be ∼60 ns, resulting in ∼90 µm in water. The obtained resolution is in a good agreement with ∼78.6 µm calculated by 0.88*c/BW as described in [17]. The resolution can be significantly improved by adding a high impedance backing layer, adding a matching layer, and designing an electrical matching network in future work.

We performed a simple photoacoustic imaging experiment, scanning a focused laser spot re-focused from a multi-mode fiber through the transducer. The lateral resolution in this experiment was determined by the laser spot size and was estimated from an edge-spread function by scanning a USAF 1951 resolution target and plotting the peak amplitude of the envelope detected photoacoustic responses, as illustrated in Fig. 4(b) and (c). The spatial resolution was estimated from the edge-spread function as ∼285 µm, as measured for a rise from 10% to 90% of the peak amplitude across the edge. The imaging resolution can be improved by tighter optical focusing in future work.

 figure: Fig. 4.

Fig. 4. PAI using the fabricated transparent PMN-PT transducer without a matching layer. (a) The laser setup for 1D scanning. (b) The linear PA scan was performed along a 3 mm line covering a line pair of element 3 in group −2. (c) The normalized PA amplitude of the scanned line for measuring the lateral resolution of the system.

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To demonstrate the potential advantages of our transparent transducers, we performed photoacoustic imaging experiments in a scattering phantom with an embedded blood tube. The phantom was a cornstarch-gelatin phantom (10% cornstarch, 10% gelatin powder, and 80% water, by weight) which previously was shown to exhibit ultrasonic and optical properties similar to tissues [18]. We investigated three different configurations: (a) trans-illumination through the fabricated unfocused transparent ultrasound transducer in direct contact with the scattering phantom (b) oblique illumination around the transducer (also in contact with the phantom) and (c) oblique illumination around a focused transducer (V324-SM, Olympus Scientific Solutions Americas Inc. U.S.) positioned with an ∼11mm standoff distance in water, as shown in Fig. 5. The oblique illumination scenario (b) suffered from a long optical propagation length through the scattering medium and thus produced a very weak photoacoustic signal compared to the trans-illumination scenario (a). Even when using a focused transducer with a water standoff to allow for oblique illumination to hit closer to the blood tube, signal-to-noise was still ∼4dB lower than the transparent transducer through illumination scenario. The through-illumination measurement was ∼25dB larger than the oblique illumination experiment b). This is primarily attributed to the long optical propagation distance through the scattering medium, greatly reducing the fluence at the blood tube. In all experiments, we used a 532-nm 8-ns pulsed laser with identical surface spot size and a laser surface fluence of ∼12mJ/cm2. The received photoacoustic signals were recorded after amplifying with a +28 dB, 5 to 75 MHz amplifier (PANAMETICS-NDT 5073PR).

 figure: Fig. 5.

Fig. 5. Comparison of PA signals obtained from a scattering phantom with an embedded blood tube. (a) illumination through the fabricated unfocused transparent transducer (b) oblique illumination around the opaque transducer (c) oblique illumination around the focused transducer positioned ∼11mm above the phantom (d) their photoacoustic received signals.

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4. Discussion

Current work is limited to single-element transparent transducers to establish feasibility of hot-pressed PMN-PT as a novel electrostrictive transducer material. Future work could involve development of linear or even 2D arrays, including top-orthogonal-to-bottom electrode arrays, which could enable bias-switchable readout of every element using only rows and columns.

Additional limitation of current work is the lack of a suitable backing material. Epoxy was tested as a backing material but it is not adequately impedance matched to the PMN-PT and thus ringing was observed in the transducer response. Future work could consider glass delay lines or fiber bundles as a backing material, which should be better impedance matched and thus provide a means of reducing ringing. Additional work is also needed to develop improved transparent matching layers which have a high optical damage threshold.

Transparent transducers could find important uses for wearable fiber-tethered photoacoustic devices to measure venous oxygen saturation, which cannot be measured with pulse oximetry. They could also be developed into arrays for improved deep-tissue photoacoustic imaging. They may further have applications to endoscopic or laparoscopic, trans-rectal or trans-vaginal form factors, where it is difficult to share optical and ultrasonic real-estate.

5. Conclusion

In conclusion, the fabrication steps and the preliminary results of a novel bias-sensitive transparent high-frequency ultrasound transducer made of hot-pressed PMN-PT are presented. The transparency of the transducers was measured ∼67% at 532 nm wavelength with a maximum electromechanical coefficient of ∼0.68 with a DC bias level of 100 V. The high bias voltages used here could be an electrical safety concern for human subject imaging without proper isolation. However, dielectric matching layers and/or additional grounding layers could provide suitable isolation for safe use. The effect of the matching layer on the transducer was investigated, which resulted in increasing the bandwidth from 36% to 38% and with a ∼168% improvement in the received signal peak-to-peak value. The center frequency of the transducer was slightly shifted from 27.5 MHz to 23.5 MHz due to the Parylene C matching layer. Our measured kt value of 0.68 is significantly improved compared to other transparent transducers such as lithium niobate with a reported kt of 0.49. However, our measured kt is less than that reported for single-crystal PMN-PT (>0.8), which could be a promising transparent technology in future work. However, electrostrictive PMN-PT with low-PT doping is not yet commercially available. In future work, we aim to fabricate top-orthogonal-to-bottom-electrode (TOBE) ultrasound arrays using these materials that should be capable of aperture coding/decoding, as well as sensitivity adjustment by changing the applied biasing polarity and voltages, respectively. Future work should investigate improved backing and the front matching layers that will be both transparent and be more immune to laser damage.

Funding

Mitacs; Natural Sciences and Engineering Research Council of Canada (RGPIN-2018-05788).

Acknowledgments

The authors are grateful for assistance with the laser’s and fiber’s initial setup from Matthew T. Martell and Nathaniel J. M. Haven.

Disclosures

R.J.Z. is a founder and shareholder of illumiSonics Inc. and CliniSonix Inc., which, however, did not support this work.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 41101 (2006). [CrossRef]  .

2. M. W. Schellenberg and H. K. Hunt, “Hand-held optoacoustic imaging: A review,” Photoacoustics 11, 14–27 (2018). [CrossRef]  

3. G. Brodie, Y. Qiu, S. Cochran, G. Spalding, and M. MacDonald, “Optically transparent piezoelectric transducer for ultrasonic particle manipulation,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 61(3), 389–391 (2014). [CrossRef]  

4. Z. Li, A. K. Ilkhechi, and R. Zemp, “Transparent capacitive micromachined ultrasonic transducers (CMUTs) for photoacoustic applications,” Opt. Express 27(9), 13204 (2019). [CrossRef]  

5. A. Dangi, S. Agrawal, and S.-R. Kothapalli, “Lithium niobate-based transparent ultrasound transducers for photoacoustic imaging,” Opt. Lett. 44(21), 5326 (2019). [CrossRef]  

6. H. Chen, S. Agrawal, A. Dangi, C. Wible, M. Osman, L. Abune, H. Jia, R. Rossi, Y. Wang, and S.-R. Kothapalli, “Optical-Resolution Photoacoustic Microscopy Using Transparent Ultrasound Transducer,” Sensors 19(24), 5470 (2019). [CrossRef]  

7. Y. Chen, J. He, C. Shi, J. Yung, L. v. Hwang, Q. Wang, and Zhou, “Transparent High-Frequency Ultrasonic Transducer for Photoacoustic Microscopy Application,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 67(9), 1848–1853 (2020). [CrossRef]  

8. J. Park, B. Park, S. Jeon, T. Y. Kim, D. H. Yoon, H. Kim, D. Lee, U. Yong, J. Jang, U. Jeong, H. H. Kim, and C. Kim, “Seamlessly integrated multi-modal imaging system through transparent ultrasound transducer in vivo,” in Photons Plus Ultrasound: Imaging and Sensing 2021, Mar.2021, p. 31, [CrossRef]  .

9. A. K. Ilkhechi, C. Ceroici, Z. Li, and R. Zemp, “Transparent capacitive micromachined ultrasonic transducer (CMUT) arrays for real-time photoacoustic applications,” Opt. Express 28(9), 13750 (2020). [CrossRef]  

10. A. Kashani Ilkhechi, C. Ceroici, and R. J. Zemp, “High sensitivity transparent capacitive micromachined ultrasound transducer linear arrays for optical, photoacoustic and ultrasound imaging,” in Photons Plus Ultrasound: Imaging and Sensing 2021, Mar.2021, p. 95, [CrossRef]  .

11. C. Ceroici, K. Latham, B. A. Greenlay, J. A. Brown, and R. J. Zemp, “Fast orthogonal row-column electronic scanning experiments and comparisons,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 66(6), 1093–1101 (2019). [CrossRef]  

12. C. Ceroici, K. Latham, R. Chee, B. Greenlay, Q. Barber, J. A. Brown, and R. Zemp, “3D photoacoustic imaging using Hadamard-bias encoding with a crossed electrode relaxor array,” Opt. Lett. 43(14), 3425 (2018). [CrossRef]  

13. H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Optoelectronic Devices and Integration 5644, 380 (2005). [CrossRef]  .

14. C. Ceroici, K. Latham, R. K. Chee, J. A. Brown, and R. J. Zemp, “Bias-sensitive crossed-electrode relaxor 2D arrays for 3D photoacoustic imaging,” in Photons Plus Ultrasound: Imaging and Sensing 2018, Feb. 2018, vol. 10494, p. 70, [CrossRef]  .

15. K. Latham, C. Samson, J. Woodacre, and J. Brown, “A 30 MHz, 3D Imaging, Forward Looking Miniature Endoscope based on a 128-element Relaxor Array,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 68(4), 1261–1271 (2021). [CrossRef]  .

16. “Foundations of Biomedical Ultrasound - Richard S. C. Cobbold - Google Books.”

17. Chi Zhang, Konstantin I. Maslov, Junjie Yao, and Lihong V. Wang, “In vivo photoacoustic microscopy with 7.6-µm axial resolution using a commercial 125-MHz ultrasonic transducer,” J. Biomed. Opt. 17(11), 116016 (2012). [CrossRef]  

18. Yan Jiang, Alex Forbrich, Tyler Harrison, and Roger J. Zemp, “Blood oxygen flux estimation with a combined photoacoustic and high-frequency ultrasound microscopy system: a phantom study,” J. Biomed. Opt. 17(3), 036012 (2012). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. The fabricated transparent ultrasound transducer based on electrostrictive PMN-PT and transparency measurement. (a) The raw bulk hot-pressed PMN-PT measuring roughly 40 mm × 40 mm x 25 mm. (b) Precisely polished, and ITO coated ∼80 µm thick PMN-PT. (c) Transparency measurement of the fabricated transducer with maximum transparency of 67% at 532 nm. (d) diagram of the transducer cross section. (e) The fabricated transparent transducer mounted on a PCB with a transparent aperture of roughly 3.5 mm × 3.5 mm.
Fig. 2.
Fig. 2. The measured input impedance of the transducers without loading on the front surface. (a),(b) The magnitude and phase of the input impedance for the fabricated transducer without matching layer. (c),(d) The magnitude and phase of the input impedance for the fabricated transducer with a matching layer.
Fig. 3.
Fig. 3. The measured acoustic receive response and photoacoustic responses of the transducers. (a) The amplitude and phase of the impulse response for the fabricated transparent transducers, with and without matching layer at +60 V bias. (b) The PA response of the transducer without matching layer at +40 and −40 Volts bias.
Fig. 4.
Fig. 4. PAI using the fabricated transparent PMN-PT transducer without a matching layer. (a) The laser setup for 1D scanning. (b) The linear PA scan was performed along a 3 mm line covering a line pair of element 3 in group −2. (c) The normalized PA amplitude of the scanned line for measuring the lateral resolution of the system.
Fig. 5.
Fig. 5. Comparison of PA signals obtained from a scattering phantom with an embedded blood tube. (a) illumination through the fabricated unfocused transparent transducer (b) oblique illumination around the opaque transducer (c) oblique illumination around the focused transducer positioned ∼11mm above the phantom (d) their photoacoustic received signals.

Equations (1)

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k t = ( π ω s 2 ω p ) t a n [ π ( ω p ω s ) 2 ω p ]
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