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Modeling, design and characterization of limited diffraction ultrasonic transducers
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Physics Procedia 00 (2009) 000–000 Physics Procedia 3 (2010) 577–583 www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
International Congress on Ultrasonics, Universidad de Santiago de Chile, January 2009
Modeling, Design and Characterization of Limited Diffraction Ultrasonic Transducers Alina Auleta*, José A. Eirasb and Carlos Negreiraa. a Laboratorio de Acústica Ultrasonora, Instituto de Física- Facultad de Ciencias Universidad de la República - Iguá 4225, esq. Mataojo CC 10773, Montevideo 11400, Uruguay b Laboratorio de Cerámicas Ferroeléctricas - Departamento de Física - UFSCar, Rod.Washington Luis, km 235, 13.565-905 San Carlos, SP , Brasil
Elsevier use only: Received date here; revised date here; accepted date here
Abstract Ultrasound piezoelectric transducers are used in medical applications and for non-destructive testing of materials. Among them, a special type, the so named limited diffraction ultrasonic transducers present a great depth of acoustic field, without important effects of diffraction, besides other qualities, which make them optimal in applications of medical images. In this paper, the design of a class of these transducers is explained through a simple technology that uses a method of direct polarization. The application of the Finite Elements Method to simulations in the design process of not uniformly poled transducers, as well as the experimental characterization of their dynamic behaviour, is described. The comparison of the experimental results with those simulated, using Finite Element Analysis, guarantees with an excellent agreement the use of this powerful method of simulation, during the construction and characterization of limited diffraction transducers. PACS: 43.38; 77.65.D; 02.70.D; 81.70C Keywords: Finite elements method; ultrasonic transducers; vibration modes.
1. Introduction Ultrasound piezoelectric transducers are used in medical applications and for non-destructive testing (NDT) of materials, among others applications. The transducers and/or the mechanisms of ultrasound generation, must exhibit different properties that should make them efficient for each type of application. The limited diffraction ultrasonic transducers (LDUT), and in particular the so named Bessel transducers, present a great depth of acoustic field, without important effects of diffraction, besides other qualities, which make them optimal in applications of medical
* Corresponding author. Tel.: +598 2 E-mail address: [email protected]
doi:10.1016/j.phpro.2010.01.074
5258624; fax: +598 2 5250580.
578
A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
images [1]-[5]. According to how they are manufactured, the effects of cross-coupling between the vibration modes can also be diminished. In this work, the design of transducer of Bessel type, through a simple technology, that uses a method of direct polarization, is explained. Three electrodes in the form of concentric rings in both faces of a ferroelectric ceramic disk, were used, being applied a profile of non-uniform polarization. The Finite Element Method (FEM) to simulate the dynamic behavior of the Bessel Transducers was used. In order to experimentally characterize their vibration modes, the electric impedance and phase were measured as a function of frequency.
2. Design and modeling The Bessel transducer was constructed using a 2 MHz ceramic disk of PZT (53/47 + 1wt% Nb) and diameter ~25 mm. Three rings were formed on the faces of the disk with silver painting, in order to act as electrodes (separated each from other 2 mm), and each ring was poled individually, during a constant time, varying the polarization field. In the process of direct polarization to each ring, an electric field was applied following the profile of the first kind and zero order Bessel function during a constant time interval. The inner ring was polarized with a value of electric field E=3 kV/mm, the intermediate ring with E=1.2 kV/mm and the external ring with E= 0.9 kV/mm. For the intermediate ring, the poled field was inverted. This simple method of polarization is shown in Figure 1. After the polarization process was realized, a deposition of gold layers was made in each face of the ceramics by means of the technique of sputtering in order to conform the final electrodes. A backing of low impedance and a front matching layer were added [6] and placed all the elements in a copper tube for its characterization. In order to compare with the performance of this Bessel device, also a conventional piezoelectric transducer of similar dimensions was constructed, in this later case, uniformly poled.
Fig.1 Direct poled method following the profile of the Bessel function of order zero.
The computer technical program used to simulate the mechanical vibrations of the transducers excited through piezoelectric effect was the Finite Element Method. The elastic, dielectric and piezoelectric constants corresponding to a material of composition PZT5A [7], were used in all the simulations, having obtained the electrical impedance and phase based on the frequency of all the resonant modes. Due to the circular geometry of the conventional Bessel transducers, a axi-symmetrical model was used in the simulation method, doing possible to reduce the three-dimensional problem to a bi-dimensional one, with the axis "x" and the axis "y" corresponding to the radial direction and the center line of the circular transducer respectively.
A. Aulet et al. / Physics Procedia 3 (2010) 577–583
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Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
This diminishes the time of computer calculation. With a view to clarify these ideas, we show in Figure 2 the bidimensional (2-D) geometry used. The Finite Elements Method (FEM) allows obtaining an approximate numerical solution of a set of discrete algebraic equations that describe the answer of a continuous system. Was made a division of the structure in discrete elements (mesh) with the formation of “nodes” that define the elements in which the problem will be solved [8]. Once defined the geometry of the problem and the equations of the system for its solution, the continuous solution is transformed in a set of discrete solutions.
Fig.2 Axi-symmetrical model used for the computer simulation in 2-D [9].
In Figure 3, bi-dimensional geometries for (a) the conventional (uniformly poled) and (b) the Bessel ceramic (poled, non uniform) used in the Finite Element Method are show.
(a)
(b) Fig.3 Bi-dimensional geometry for (a) the conventional (uniformly poled), and (b) the Bessel ceramic (poled, non uniform) to be used in the Finite Element Method.
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A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
The colour code represents the percentage of polarization of the electric field applied to each ring [10]. In Figure 3a), the conventional ceramic uniformly poled (100 %) is shown, and in Figure 3b), it can be distinguished between the central ring, which was poled with 100%, the intermediate ring which was poled with 40% and the external ring, poled with 30%, of the value of the electric field, respectively.
3. Characterization and results The electric impedances (modulus and phase) were measured at room temperature using an Impedance Analyzer HP4194-A. The measures were made in the corresponding interval of frequencies between 100 Hertz and 3 MHz, having contemplated therefore the main vibration modes of this circular geometry: radial and thickness. The characterization of the vibration modes of the conventional and Bessel transducers, through the measures and simulations of the electrical impedance amplitude in function of the frequency, is shown in the Figure 4. Here, the results have been divided in two ranges, the one of low frequency concerning the radial (a), and the other for high frequencies related to thickness vibration modes (b).
Fig.4 Electrical impedance as a function of the frequency, showing vibration modes of radial and thickness type, for: a) the conventional and b) the Bessel transducers. (Red: experimental, and Black: simulated results).
A. Aulet et al. / Physics Procedia 3 (2010) 577–583
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Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
In this Figure, with the object of comparison, the simulated and experimental results of the radial vibration mode in the conventional uniformly poled and in the Bessel ceramics are observed, on the one hand the radial modes characteristic are shown of the conventional transducer and on the other hand, the suppression of the fundamental radial mode and several of their overtones in Bessel case. With this Bessel transducer, the thickness vibration modes appear clearly decoupled of the radial vibration modes, as it is desired in a transducer designed for applications in medical imaging. The experimental resonance frequencies of the Bessel transducer are in agreement with the FEM simulated results in the low and high frequency ranges. The behaviour of the Bessel is shown in Figure 5 when the rings are excited of independent form and when they are excited like a whole. The excited modes of radial vibration are presented of individual form, and altogether these are compensated giving rise to the reinforcing of the one of the harmonic modes and elimination of the others.
Fig.5 Composition of the radial modes exciting each Bessel’s ring and then exciting Bessel transducer (dark: measured curves and light: simulated curves) [11].
This results show that some mechanical resonant modes (i.e. radials: fundamental and several harmonics modes) are suppressed when an “in phase” excitation of the rings is applied. That is not the case for uniformly poled disks or conventional ceramics. The simulated mechanical displacements in the frequencies of the mechanical resonance, of the here studied transducers, are presented in Figure 6. The presence of different conditions of edges of each ring influences in this behaviour of the radial vibration.
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A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
Fig.6 Simulated mechanical displacements in the fundamentals frequencies of a) the conventional and b) the Bessel ceramic.
The radial and thickness mechanical displacements simulated by FEM, of the Bessel, ceramics are shown. In both cases is a half of the diameter of the ceramics the part shown (following the geometries presented in Figure 3). It can be noted that, between the rings, PZT material that is not polarized is also present. In this Figure: 6b) for the radial frequency of 342 kHz of the Bessel ceramic, it is shown that, while the central ring is contracted radially, the inner ring and outer expand in the same direction, and in Figure 6b) for frequency of 2.04 MHz, the same happens but this time in the direction of thickness.
4. Conclusions In this paper, Bessel transducers were designed with a new variable direct poling method. The vibration modes of these special Bessel transducers were studied, numerically and experimentally. Due to, this method of polarization follows the profile of the Bessel function, it was verified that the radial fundamental vibration mode and several overtones are suppressed when the rings are excited in phase, with the decrease of the effects of connection between the vibration modes. The uncoupling of the vibration modes favours the transducer efficiency in the MHz range for medical imaging. The excellent agreement in the comparison of the experimental results with those simulated on the construction and characterization of these limited diffraction transducers, using FEM, guarantees the use of this powerful method of simulation. These simulations allow to optimize the project of new LDUT transducers and the evaluation of new materials in their construction. It is a low-cost process, which accurately predicts their dynamic behaviour when the parameters, characteristics and properties of the constituent materials change.
Acknowledgements The authors would like to thank to CLAF (Latin American Center of Physics) and PEDECIBA (Uruguayan agency), for financial support. Special acknowledgements to Francisco Picon of the Ferro-electric Ceramic Laboratory of the UFSCar (Brazil) and Eduardo Moreno of the Ministry of Science, Technology and Environment of Cuba.
A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
References [1] Jian-yu Lu et al., Ultrasound in Medicine and Biology, Vol. 20, No. 5, 403 (1994). [2] Jian-yu Lu, Acta Physica Sinica. Vol. 8, Chin. Phys. Soc. (1999). [3] J. Durnin, Optical Society of America. Vol. 4, No. 4, 651 (1987). [4] Jian-yu Lu, “Limited diffraction array beams” John Wiley & Sons, Inc. Vol. 8, 126 (1997). [5] D. K. Hsu et al., Appl. Phys. Lett. 55(20), (1989). [6] G. Kossoff, IEEE Transactions on Sonic and Ultrasonic Vol. SU-13, No. 1 (1966). [7] G. Hayward et al., J.Acoust. Soc. Am. Vol. 98 No.4, 2187 (1995). [8] R. Lerch IEEE Trans. Ultrason., Ferroelec., and Freq. Contr., Vol. 37, No. 2, 233 (1990). [9] G. Nader, Doctoral Thesis (Doctor in Engineering) - Escola Politécnica da Universidade de São Paulo, SP, Brasil, (2002). [10] A. Aulet, Doctoral Thesis (PhD) – Dpto. Física da Universidade Federal de São Carlos, SP, Brasil (2006). [11] A. Aulet, et al., Ferroelectrics 333, 131 (2006).
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Physics Procedia 00 (2009) 000–000 Physics Procedia 3 (2010) 577–583 www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
International Congress on Ultrasonics, Universidad de Santiago de Chile, January 2009
Modeling, Design and Characterization of Limited Diffraction Ultrasonic Transducers Alina Auleta*, José A. Eirasb and Carlos Negreiraa. a Laboratorio de Acústica Ultrasonora, Instituto de Física- Facultad de Ciencias Universidad de la República - Iguá 4225, esq. Mataojo CC 10773, Montevideo 11400, Uruguay b Laboratorio de Cerámicas Ferroeléctricas - Departamento de Física - UFSCar, Rod.Washington Luis, km 235, 13.565-905 San Carlos, SP , Brasil
Elsevier use only: Received date here; revised date here; accepted date here
Abstract Ultrasound piezoelectric transducers are used in medical applications and for non-destructive testing of materials. Among them, a special type, the so named limited diffraction ultrasonic transducers present a great depth of acoustic field, without important effects of diffraction, besides other qualities, which make them optimal in applications of medical images. In this paper, the design of a class of these transducers is explained through a simple technology that uses a method of direct polarization. The application of the Finite Elements Method to simulations in the design process of not uniformly poled transducers, as well as the experimental characterization of their dynamic behaviour, is described. The comparison of the experimental results with those simulated, using Finite Element Analysis, guarantees with an excellent agreement the use of this powerful method of simulation, during the construction and characterization of limited diffraction transducers. PACS: 43.38; 77.65.D; 02.70.D; 81.70C Keywords: Finite elements method; ultrasonic transducers; vibration modes.
1. Introduction Ultrasound piezoelectric transducers are used in medical applications and for non-destructive testing (NDT) of materials, among others applications. The transducers and/or the mechanisms of ultrasound generation, must exhibit different properties that should make them efficient for each type of application. The limited diffraction ultrasonic transducers (LDUT), and in particular the so named Bessel transducers, present a great depth of acoustic field, without important effects of diffraction, besides other qualities, which make them optimal in applications of medical
* Corresponding author. Tel.: +598 2 E-mail address: [email protected]
doi:10.1016/j.phpro.2010.01.074
5258624; fax: +598 2 5250580.
578
A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
images [1]-[5]. According to how they are manufactured, the effects of cross-coupling between the vibration modes can also be diminished. In this work, the design of transducer of Bessel type, through a simple technology, that uses a method of direct polarization, is explained. Three electrodes in the form of concentric rings in both faces of a ferroelectric ceramic disk, were used, being applied a profile of non-uniform polarization. The Finite Element Method (FEM) to simulate the dynamic behavior of the Bessel Transducers was used. In order to experimentally characterize their vibration modes, the electric impedance and phase were measured as a function of frequency.
2. Design and modeling The Bessel transducer was constructed using a 2 MHz ceramic disk of PZT (53/47 + 1wt% Nb) and diameter ~25 mm. Three rings were formed on the faces of the disk with silver painting, in order to act as electrodes (separated each from other 2 mm), and each ring was poled individually, during a constant time, varying the polarization field. In the process of direct polarization to each ring, an electric field was applied following the profile of the first kind and zero order Bessel function during a constant time interval. The inner ring was polarized with a value of electric field E=3 kV/mm, the intermediate ring with E=1.2 kV/mm and the external ring with E= 0.9 kV/mm. For the intermediate ring, the poled field was inverted. This simple method of polarization is shown in Figure 1. After the polarization process was realized, a deposition of gold layers was made in each face of the ceramics by means of the technique of sputtering in order to conform the final electrodes. A backing of low impedance and a front matching layer were added [6] and placed all the elements in a copper tube for its characterization. In order to compare with the performance of this Bessel device, also a conventional piezoelectric transducer of similar dimensions was constructed, in this later case, uniformly poled.
Fig.1 Direct poled method following the profile of the Bessel function of order zero.
The computer technical program used to simulate the mechanical vibrations of the transducers excited through piezoelectric effect was the Finite Element Method. The elastic, dielectric and piezoelectric constants corresponding to a material of composition PZT5A [7], were used in all the simulations, having obtained the electrical impedance and phase based on the frequency of all the resonant modes. Due to the circular geometry of the conventional Bessel transducers, a axi-symmetrical model was used in the simulation method, doing possible to reduce the three-dimensional problem to a bi-dimensional one, with the axis "x" and the axis "y" corresponding to the radial direction and the center line of the circular transducer respectively.
A. Aulet et al. / Physics Procedia 3 (2010) 577–583
579
Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
This diminishes the time of computer calculation. With a view to clarify these ideas, we show in Figure 2 the bidimensional (2-D) geometry used. The Finite Elements Method (FEM) allows obtaining an approximate numerical solution of a set of discrete algebraic equations that describe the answer of a continuous system. Was made a division of the structure in discrete elements (mesh) with the formation of “nodes” that define the elements in which the problem will be solved [8]. Once defined the geometry of the problem and the equations of the system for its solution, the continuous solution is transformed in a set of discrete solutions.
Fig.2 Axi-symmetrical model used for the computer simulation in 2-D [9].
In Figure 3, bi-dimensional geometries for (a) the conventional (uniformly poled) and (b) the Bessel ceramic (poled, non uniform) used in the Finite Element Method are show.
(a)
(b) Fig.3 Bi-dimensional geometry for (a) the conventional (uniformly poled), and (b) the Bessel ceramic (poled, non uniform) to be used in the Finite Element Method.
580
A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
The colour code represents the percentage of polarization of the electric field applied to each ring [10]. In Figure 3a), the conventional ceramic uniformly poled (100 %) is shown, and in Figure 3b), it can be distinguished between the central ring, which was poled with 100%, the intermediate ring which was poled with 40% and the external ring, poled with 30%, of the value of the electric field, respectively.
3. Characterization and results The electric impedances (modulus and phase) were measured at room temperature using an Impedance Analyzer HP4194-A. The measures were made in the corresponding interval of frequencies between 100 Hertz and 3 MHz, having contemplated therefore the main vibration modes of this circular geometry: radial and thickness. The characterization of the vibration modes of the conventional and Bessel transducers, through the measures and simulations of the electrical impedance amplitude in function of the frequency, is shown in the Figure 4. Here, the results have been divided in two ranges, the one of low frequency concerning the radial (a), and the other for high frequencies related to thickness vibration modes (b).
Fig.4 Electrical impedance as a function of the frequency, showing vibration modes of radial and thickness type, for: a) the conventional and b) the Bessel transducers. (Red: experimental, and Black: simulated results).
A. Aulet et al. / Physics Procedia 3 (2010) 577–583
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Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
In this Figure, with the object of comparison, the simulated and experimental results of the radial vibration mode in the conventional uniformly poled and in the Bessel ceramics are observed, on the one hand the radial modes characteristic are shown of the conventional transducer and on the other hand, the suppression of the fundamental radial mode and several of their overtones in Bessel case. With this Bessel transducer, the thickness vibration modes appear clearly decoupled of the radial vibration modes, as it is desired in a transducer designed for applications in medical imaging. The experimental resonance frequencies of the Bessel transducer are in agreement with the FEM simulated results in the low and high frequency ranges. The behaviour of the Bessel is shown in Figure 5 when the rings are excited of independent form and when they are excited like a whole. The excited modes of radial vibration are presented of individual form, and altogether these are compensated giving rise to the reinforcing of the one of the harmonic modes and elimination of the others.
Fig.5 Composition of the radial modes exciting each Bessel’s ring and then exciting Bessel transducer (dark: measured curves and light: simulated curves) [11].
This results show that some mechanical resonant modes (i.e. radials: fundamental and several harmonics modes) are suppressed when an “in phase” excitation of the rings is applied. That is not the case for uniformly poled disks or conventional ceramics. The simulated mechanical displacements in the frequencies of the mechanical resonance, of the here studied transducers, are presented in Figure 6. The presence of different conditions of edges of each ring influences in this behaviour of the radial vibration.
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A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
Fig.6 Simulated mechanical displacements in the fundamentals frequencies of a) the conventional and b) the Bessel ceramic.
The radial and thickness mechanical displacements simulated by FEM, of the Bessel, ceramics are shown. In both cases is a half of the diameter of the ceramics the part shown (following the geometries presented in Figure 3). It can be noted that, between the rings, PZT material that is not polarized is also present. In this Figure: 6b) for the radial frequency of 342 kHz of the Bessel ceramic, it is shown that, while the central ring is contracted radially, the inner ring and outer expand in the same direction, and in Figure 6b) for frequency of 2.04 MHz, the same happens but this time in the direction of thickness.
4. Conclusions In this paper, Bessel transducers were designed with a new variable direct poling method. The vibration modes of these special Bessel transducers were studied, numerically and experimentally. Due to, this method of polarization follows the profile of the Bessel function, it was verified that the radial fundamental vibration mode and several overtones are suppressed when the rings are excited in phase, with the decrease of the effects of connection between the vibration modes. The uncoupling of the vibration modes favours the transducer efficiency in the MHz range for medical imaging. The excellent agreement in the comparison of the experimental results with those simulated on the construction and characterization of these limited diffraction transducers, using FEM, guarantees the use of this powerful method of simulation. These simulations allow to optimize the project of new LDUT transducers and the evaluation of new materials in their construction. It is a low-cost process, which accurately predicts their dynamic behaviour when the parameters, characteristics and properties of the constituent materials change.
Acknowledgements The authors would like to thank to CLAF (Latin American Center of Physics) and PEDECIBA (Uruguayan agency), for financial support. Special acknowledgements to Francisco Picon of the Ferro-electric Ceramic Laboratory of the UFSCar (Brazil) and Eduardo Moreno of the Ministry of Science, Technology and Environment of Cuba.
A. Aulet et al. / Physics Procedia 3 (2010) 577–583 Alina Aulet et al./ Physics Procedia 00 (2010) 000–000
References [1] Jian-yu Lu et al., Ultrasound in Medicine and Biology, Vol. 20, No. 5, 403 (1994). [2] Jian-yu Lu, Acta Physica Sinica. Vol. 8, Chin. Phys. Soc. (1999). [3] J. Durnin, Optical Society of America. Vol. 4, No. 4, 651 (1987). [4] Jian-yu Lu, “Limited diffraction array beams” John Wiley & Sons, Inc. Vol. 8, 126 (1997). [5] D. K. Hsu et al., Appl. Phys. Lett. 55(20), (1989). [6] G. Kossoff, IEEE Transactions on Sonic and Ultrasonic Vol. SU-13, No. 1 (1966). [7] G. Hayward et al., J.Acoust. Soc. Am. Vol. 98 No.4, 2187 (1995). [8] R. Lerch IEEE Trans. Ultrason., Ferroelec., and Freq. Contr., Vol. 37, No. 2, 233 (1990). [9] G. Nader, Doctoral Thesis (Doctor in Engineering) - Escola Politécnica da Universidade de São Paulo, SP, Brasil, (2002). [10] A. Aulet, Doctoral Thesis (PhD) – Dpto. Física da Universidade Federal de São Carlos, SP, Brasil (2006). [11] A. Aulet, et al., Ferroelectrics 333, 131 (2006).
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