Abstract: Solidly mounted integrated transducers with a Bragg cell inserted between the piezoelectric film and the substrate are investigated for high frequency ultrasonic applications. A numerically stable recursive one dimensional transmission/reflection model was used to analyze the behavior of the periodic structure. This theoretical analysis includes the study of the influence of the acoustic properties of the constitutive layer, the effect of the number of cells and their arrangement. A 35 MHz integrated transducer consisting in a PZT ceramic laid down on a Au/PZT Bragg cell deposited on a porous substrate was fabricated and characterized. Both theoretical and experimental results highlight the interest of using a periodic structure for high frequency ultrasonic applications.

Abstract: A lens-focused single-element transducer designed for high-resolution medical imaging requires a high ratio of radius of curvature to source radius. Therefore, classical models neglecting the radial contribution may not be accurate. The objective of this study is to evaluate the contribution of radial displacement to the pressure response of the transducer, both in terms of focal spot and pulse response characteristics. To achieve this objective, two finite element method calculations (FEM) were performed (commercial ATILA software), namely those for free and clamped radial displacements. A propagation code adapted to an axisymmetric transducer geometry was implemented to compare the radiated fields, and FEM results for the transducer surface were used as inputs to obtain the radiated fields. Subsequently, the differences between the results of the two calculations results were determined. However, it was demonstrated that the radial displacements slightly affect the propagated field and can therefore be neglected in realistic transducer designs. Moreover, the effects of lens acoustic properties were studied for realistic configurations in terms of resolution and sensitivity to obtain an optimal ultrasound image quality.

Abstract: The goal of this work was to develop an extended ultrasound transducer model that would optimize the trade-off between accuracy of the calculation and computational time. The derivations are presented for a generalized transducer model, that is center frequency, pulse duration and physical dimensions are all normalized. The paper presents a computationally efficient model for lens-focused, circular (axisymmetric) single element piezoelectric ultrasound transducer. Specifically, the goal of the model is to determine the lens effect on the electro-acoustic response, both on focusing and on matching acoustic properties. The effective focal distance depends on the lens geometry and refraction index, but also on the near field limit, i.e. wavelength and source radius, and on the spectrum bandwidth of the ultrasound source. The broadband (80%) source generated by the transducer was therefore considered in this work. A new model based on a longitudinal-wave assumption is presented and the error introduced by this assumption is discussed in terms of its maximum value (16%) and mean value (5.9%). The simplified model was based on an extension of the classical KLM model for transducer structures and on the related assumptions. The validity of the implemented extended KLM model was evaluated by comparison with finite element modeling, itself previously validated analytically for the one-dimensional planar geometry considered. The pressure field was then propagated using the adequate formulation of the Rayleigh integral for both the extended KLM and finite element results. The simplified approach based on the KLM model delivered the focused response with good accuracy, and hundred-fold lower calculation time in comparison with a mode comprehensive FEM method. The trade-off between precision and time thus becomes compatible with an iterative procedure, used here for the optimization of the acoustic impedance of the lens for the chosen configuration. An experimental comparison was performed and found to be in good agreement with such an extension of the KLM model. The experiments confirm the accuracy of such a model in a validity domain up to -12 dB on the pulse-echo voltage within a relative error of 9% between experiment and modeling. This extended KLM model can advantageously be used for other transducer geometries satisfying the assumption of a predominantly longitudinal vibration or in an optimization procedure involving an adequate criteria for a particular application.

Abstract: Piezoelectric textured ceramics obtained by homo-template grain growth (HTGG) were recently demonstrated. A simple model with several assumptions has been used to calculate effective parameters of these new materials. Different connectivities have been simulated to show that spatial arrangements between the considered phases have little influence on the effective parameters, even through the 3-0 connectivity delivers the highest electromechanical thickness factor. A transducer based on a textured ceramic sample has been fabricated and characterised to show the efficiency of these piezoelectric materials. Finally, in a single element transducer configuration, simulation shows an improvement of 2 dB sensitivity for a transducer made with textured ceramic in comparison with a similar transducer design based on standard soft PZT (at equivalent bandwidths).

Abstract: A screen-printed PZT thick film with a final thickness of about 40 µm was deposited on a porous PZT substrate to obtain an integrated structure for ultrasonic transducer applications. This process makes it possible to decrease the number of steps in the fabrication of high-frequency, single-element transducers. The porous PZT substrates allow high acoustic impedance and attenuation to be obtained, satisfying transducer backing requirements for medical imaging. The piezoelectric thick films deliver high electromechanical performance, comparable to that of standard bulk ceramics (thickness coupling factor over 45%). Based on these structures, high-frequency transducers with a center frequency of about 25 MHz were produced and characterized. As a result, good sensitivity and axial resolution were obtained in comparison with similar transducers integrating a lead titanate (PT) disk as active material. The two transducers were integrated into a high frequency imaging system, and comparative skin images are shown.

Abstract: A successful fabrication process of textured ceramics by homo-template grain growth (HTGG) is described. Two samples fabricated with this technique were characterised. Functional properties obtained are competitive with for example a thickness coupling factor over 50%. Different characteristics were compared with those obtained by a unit cell model previously developed for piezocomposites and extended to the case of two piezoelectric phases. Behaviours of several connectivities (0-3, 3-0 and 3-3) are calculated and results show that the spatial arrangement does not have a great influence on effective parameters. A transducer based on a textured ceramic sample has been fabricated and characterised. The measured performance shows the efficiency of these new piezoelectric materials. Finally, electroacoustic responses of identical single element transducer configurations have been simulated. They show that a sensitivity increase of 3 dB can be obtained at equivalent relative bandwidth of 40% with textured ceramic sample in comparison with PMN-PT ceramic used as a matrix in the textured ceramic.

Abstract: High frequency electrical impedance measurements on PZT thick film structures were used to characterise thin layers of parylene for acoustic matching applications. The parylene properties (i.e. longitudinal wave velocity and acoustic impedance) were obtained in a realistic configuration for transducer applications. The measured parylene properties were compatible with medical imaging requirements, in particular for high frequency, since the deposited thickness can be controlled with high accuracy (around 1 µm). The mean longitudinal wave velocity was measured at 2135 m/s and corresponding acoustic impedance was 2.75 MRa. Three high frequency single element transducers were simulated to show that using parylene as a matching layer is a good trade-off between transducer performance and the technical process.

Abstract: In this paper, the use of a Bragg cell between the piezoelectric film and the substrate is investigated in high frequency ultrasonic transducers for non destructive testing or medical imaging. In this view, a recursive transmission / reflection model is presented. The influence of the constitutive layer properties of a Bragg cell is studied for two compatible sets of materials (Au/PZT or Pt/Al2O3). This model is then used in order to highlight the interest of a periodic structure loaded with a substrate. Finally, experimental results on a Bragg cell are reported and discussed.

Abstract: Pseudospectral methods are widespread techniques used in electromagnetics and geophysics to model wave propagation in fairly inhomogeneous media. Stability and high accuracy can be achieved from as few as two points per wavelength. A 2D pseudospectral time-domain (PSTD) algorithm was previously developed to simulate the transmit radiation pattern in water of an ultrasonic transducer using the front face pressure as input. Here, this algorithm is improved by taking into account the piezoelectric effect (with mechanical losses) in the active element of the transducer. For this, the PSTD algorithm is combined with a finite-difference time-domain (FDTD) method. From the piezoelectricity constitutive equations under quasi-static approximation, stress and velocity variables are calculated with the PSTD method. Since Poisson equation for the electrical potential is not time dependent, this variable is obtained from the FDTD method. Two different configurations have been investigated. In each case, the piezoelectric element is a PZT plate resonator with a 50 MHz thickness resonant frequency. The first one is composed of the piezoelectric element alone immersed in water. For the second one, a backing and a matching layer are added. Continuity of the electrical field is imposed at the borders of the piezoelectric material and perfectly matched layers (PML) are developed to avoid artifacts from waves reflected on the grid sides. The main characteristic values (displacement, stress and electrical potential) are calculated and are found to be in good agreement with those obtained using a finite element method (ATILA).

Abstract: In linear acoustics, the pressure field transmitted through a plate immersed in water is commonly used to determine the characteristics of the object. The aim of this work is to extend the approach to the quasi-linear case. The so-called insertion/substitution method consists in comparing the amplitude of the transmitted field with and without the sample whose parameters are to evaluate. An initially sinusoidal plane wave normally incident upon the plate is considered. The second order pressure field is described analytically, based on the solution to the Westervelt equation, from series of reflected and transmitted waves at the interfaces. Attenuation, dispersion and diffraction effects for the fundamental component are included in the model. Firstly, it is shown that the derived expression can be separated into three components according that harmonic generation occurs before, in or beyond the plate. Secondly, the source terms for harmonic generation are identified. Furthermore, experimental data obtained from aluminum plates are compared to results from the analytical expressions. The ability to deduce the nonlinear coefficient of a solid plate from such an experimental configuration is discussed.

Abstract: Based on previous work, screen-printing technology was used to elaborate an improved integrated piezoelectric structure relatively to a reference sample [1]. An active PZT layer doped with PGO to lower sintering temperature at 800°C was printed on a porous unpoled PZT substrate which was chosen to withstand such a temperature. Moreover, the acoustical impedance of this substrate is close to that of the deposited piezoelectric thick film, making it an adequate backing for a wideband device. Thus, a short pulse-echo response is obtained, but the resonance frequency is lowered. Additional layers such as a back electrode and a dense barrier layer were interposed between the substrate and the piezoelectric film. These passive and active layers have a significant influence on the performance of the high frequency transducer. Therefore, their thickness and acoustic propeties must be controlled precisely for an optimization of the structure. The center frequency and active source radius of the transducer were increased in comparison to the reference sample, resulting in an improved radiation pattern. In vivo human skin images were performed with an imaging system for two of the prototype broadband high frequency transducer.

Abstract: In previous work on acoustical lens effect, a model based on the annular decomposition of an axisymmetric focused piezoelectric transducer was described and found to be in agreement with FEM and experimental results. The design of a focused transducer must take into account both radiation and transduction properties. These complex models such as FEM, FDTD and PSTD methods take into account radial modes, but their influence is not significant compared to the thickness mode when the radius to thickness ratio of the piezoelectric source is high enough. This assumption was verified since the mean error was evaluated lower than 2% for the chosen lens materials and geometries. Therefore, an efficient transfer function to model the lens was proposed. This annular decomposition allows to determine the input acoustical impedance of the lens and it is shown that the lens can be considered as a semi-infinite propagation medium. For an experimental comparison, a transducer structure based on a 1-3 piezocomposite is chosen for its high thickness coupling factor kt = 64% and low acoustical impedance Z = 14 MRa. This piezoelectric source is damped by an epoxy backing and matched to the propagation medium with two quarter wavelength matching layers. Based on this structure, different types of focusing techniques are investigated: geometrical, concave lens with high velocity material and convex lens with low velocity material. Experimental results obtained on the manufactured transducers are finally compared to simulated ones and the performance of the different focusing strategies is discussed.

Abstract: The purpose of this study is to present a new pseudospectral time-domain (PSTD) algorithm to model wave propagation in axisymmetric multi-layer propagation media. The approach consists in meshing the medium and in solving local differential equations at each node. This paper describes first the model. Then, the validation is performed for a classical geometrically focused wave front configuration. The results are shown to be in good agreement with an analytical diffraction model. In the next section, a 10.5 MHz center frequency lensfocused transducer is modeled. The electro-acoustical response is calculated by coupling a KLM-based model of the transducer to the PSTD propagation code. Results are very similar to those obtained with other methods involving a KLM model extended to axisymmetric geometry coupled to an analytical propagation code using an axisymmetric formulation of the Rayleigh integral [1]. Finally, the variation of the focal distance as a function of the Poisson ratio in the lens’s material is shown and discussed.

Abstract: A screen-printed PZT thick film with a final thickness around 40 μm is deposited on a porous PZT substrate to tend toward an integrated structure for ultrasonic transducer applications. This process allows to decrease the number of fabrication steps of high frequency single-element transducers. The porous PZT material has high acoustical impedance and attenuation, satisfying conditions as a backing for medical imaging. The piezoelectric thick film delivers high electromechanical performance comparable to those of standard bulk ceramic (thickness coupling factor near 50 %). Based on these structures, high frequency transducers with a center frequency around 25 MHz are fabricated and characterized. As a result, a good sensitivity and axial resolution are obtained in comparison with similar transducer integrating a PT disk as active material. The two types of transducers are integrated in high frequency imaging system and comparative skin images are shown.

Abstract: The purpose of this study is to compare two methods for calculating the electroacoustic response of a transducer at the focal point through an acoustic focusing lens. The theoretical conditions depend on the degrees of freedom taken into account as well as on the boundary conditions for the propagation. The most widely used conditions, i.e. longitudinal vibration and rigid baffle boundary condition are considered here. The theoretical approach consists in calculating the electroacoustic response using each electroacoustic model, both of these results being then propagated with the Rayleigh integral for a focused source. The first section consists in a modeling of the electroacoustic response based either on the modified classical KLM electrical equivalent circuit (1D) or on the finite element method (FEM) ATILA (axisymmetric 2D). Both models are applied to an axisymmetric configuration, and a classical propagation operation is used to obtain the response at the focal point. The second part deals with the experimental verification of the modeling methods. Measurements on a series of 10 MHz focused transducers are compared to theoretical curves, and results are discussed as a function of geometry and properties of the acoustical lens.

Abstract: Focusing ultrasound is needed for high resolution imaging applications such as non destructive testing (NDT) or medical imaging. Its effects are explored in the case of a single-element transducer focused with a lens, and electrically driven with a broadband excitation. The electro-acoustic response very near the surface of the transducer is first modelled using a finite element method (ATILA). This response in the very near-field is then propagated in water thanks to two codes. These results are presented and compared. Using these tools, the electro-acoustic response is investigated at the focal point, as a function of the acoustic impedance of the lens.

Abstract: The determination of a surface roughness with translation velocity was investigated with an ultrasonic backscattered technique based on the Doppler effect. The difficulty of the Fourier analysis to detect with accuracy the changes of roughness induce a time-frequency analysis. We demonstrate that the Doppler spectrum is related to the spatial spectrum of the surface roughness and the velocity of the surface. A accurate detection of roughness has been derived thanks to the spectrogram representation.

Abstract: The determination of a calibrated surface roughness with translation velocity of v=15 m/s was investigated with an ultrasonic backscattered technique based on the Doppler effect. The difficulty of the Fourier analysis to detect with accuracy the instantaneous changes of roughness induce a time-frequency analysis. The need to analyze both frequency and temporal nature of data is due to the non stationarity of measured signals. The theoretical study demonstrates that the Doppler spectrum is the product of the spatial spectrum of the surface roughness and the velocity of the surface. A accurate detection of roughness has been derived thanks to the spectrogram representation.

Abstract: Applications of ultrasonic imaging such as medical diagnostics and non-destructive testing tend to require improvement of resolution. Resolution being mainly linked to the operating frequencies of the systems, there is a need for ultrasonic transducers having a high center frequency, large bandwidth as well as strong focusing. Here, several modeling methods of the transducer and its radiation diagram are implemented in order to describe an acoustically focused source. The electroacoustic response and radiated field are evaluated and compared for various materials. In order to optimize transducer performance, new compositions and thick film deposition techniques of piezoelectric materials are tested and compared with classical fabrication methods. Several transducers are manufactured and their performance compared to those predicted by our models. Finally, they are integrated in a real-time high frequency ultrasonic scanner and used to produce in vivo images of human skin.