An apodized spherical transducer: Analytical solution

： In order to study acoustic radiation from the spherical cap transducer, a theoretical model was used by solving the wave equation in spherical coordinates using the method of separation of variables, based on the spherical harmonic Fourier transform and boundary condition. The calculation formulas for far field radiated pressure and directivity of spherical cap are derived. Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angle of spherical cap, radius of sphere baffle and operating frequency. The diameter of sphere baffle and wavelength in the media determine the directivity of acoustic radiation from a spherical cap. When the frequency is low or the wavelength is longer than the diameter of the sphere baffle, the acoustic radiation from a spherical cap is omnidirectional. With the increasing of the frequency or the diameter of the sphere baffle, the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle, furthermore the ripple in the beam is more obvious. Finally, the high frequency spherical cap transducer was fabricated and the directivity pattern were tested. As a result, the measurement data coincides with the theoretical calculation results and at the same time it verifies the correctness of theoretical formulas. This research can provide a guideline for designing the spherical cap transducers and arrays.

Japanese Journal of Applied Physics

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 fiel...

Design of different type of transducers to enhance image quality by forming narrow beams at the principals of nonlinear acoustics is considered in the paper. Thus, the nonlinear pressure fields of elliptical and rhomboid transducers were simulated in three dimensions. The simulation method presented in this study is based on Aanonsen's model for circular sources, and closely follows the model that recently explored for the nonlinear wave propagation due to square and rectangular sources in three dimensions [Kaya et al. "Pressure field of rectangular transducers at finite amplitude in three dimensions," Ultrasound in Med. Biol., vol. 32, no. 2, pp. 271-280, 2006]. It is assumed that elliptical and rhomboid sources are plane sources, and driven at 2.25 MHz fundamental frequency. Typical results of nonlinear acoustical pressure field simulation are presented there in three dimensions for elliptical and rhomboid sources and compared with the results for rectangular source. The similarities and differences between the nonlinear pressure field of rectangular, ellip tical and rhomboid sources are discussed. The numerical results show that diffraction effects and acoustical beam cross section depend on the source geometry a lot. It is noticeable that the nonlinear pressure field of a rectangular source has a broader beam profile than elliptical and rhomboid source.

2003

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 acoustical impedance of the lens.

arXiv: Applied Physics, 2019

In this paper, we present an analytical modeling technique for circularly symmetric piezoelectric transducers, also called as Fresnel Lens. We also present the design of a flat/piston transducer that can generate unique acoustic wave patterns, having both converging and vortexing effects. The converging effect is generated by designing the transducer electrodes in the shapes of circular rings using Fresnel formula and exciting it with an RF signal of resonant frequency. The vortexing effect is achieved by cutting the rings to different sector angles: 90, 120, 180 and 270 degrees. We use the analytical model to simulate the performance of these transducers.

IMA Journal of Applied Mathematics, 2015

This article considers the theoretical modelling of a novel electrostatic transducer in which the backplate consists of many spherical resonators. Three analytical models are considered, each of which produce impedance profiles of the device, in addition to transmission voltage responses and reception force responses, all of which closely agree. Design parameters are then varied to investigate their influence on the resonant frequencies and other model outputs.

Journal of the Acoustical Society of America, 2013

The main purpose of the paper is to contribute at presenting an analytical and a numerical modeling which would be relevant for interpreting the couplings between a circular membrane, a peripheral cavity having the same external radius as the membrane, and a thin air gap (with a geometrical discontinuity between them), and then to characterize small scale electrostatic receivers and to propose procedures that could be suitable for fitting adjustable parameters to achieve optimal behavior in terms of sensitivity and bandwidth expected. Therefore, comparison between these theoretical methods and characterization of several shapes is dealt with, which show that the models would be appropriate to address the design of such transducers. V

Ultrasonics, 2007

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 À12 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.

Journal of Magnetism and Magnetic Materials, 1983

The possibility of the optimization of a maximum sensitivity of a unaxial inclination transducer with ferrofluid is discussed.

Ultrasonics, 2008

The article is devoted to theoretical analysis of light diffraction in a non-homogeneous acoustic field created by a wedge-shaped piezoelectric transducer. Relationships describing electrical, acoustic and acousto-optic properties of the acousto-optic cell are derived in the approximation of a small thickness of the piezoelectric plate. Principal characteristics of acousto-optic interaction are examined such as dependences of the light diffraction efficiency on the phase mismatch and the acoustic wave amplitude. It is shown that the acoustic field has a complicated amplitude-phase structure changing with the acoustic frequency. It is demonstrated that the diffraction efficiency in the Bragg regime can approach 100% in spite of a noticeable phase mismatch. The appropriate optimal values of ultrasound power and incidence angles of light are found.