The accurate determination of the transfer function of ultrasound transducers is important for their design and operational performance. However, conventional methods for quantifying the transfer function, such as hydrophone measurements, radiation force balance, and pulse-echo measurements, are costly and complex due to specialized equipment required. In this study, we introduce a novel approach to estimate the transfer function of ultrasound transducers by measuring the acoustic streaming velocity generated by the transducer. We utilize an experimental setup consisting of a water tank with a millimeter scale, an ink-filled syringe, and a camera for recording the streaming phenomenon. Through streaming velocity measurements in the frequency range from 2 to 8 MHz, we determined the transfer function of an unfocused circular transducer with a center frequency of 5 MHz and a radius of 5.6 mm. We compared the performance of our method with hydrophone and pulse-echo measurements. At the center frequency, we measured a transmit efficiency of 1.9 kPa/V using the streaming approach, while hydrophone and pulse-echo measurements yielded transmit efficiencies of 2.1 kPa/V and 1.8 kPa/V, respectively. These findings demonstrate that the proposed method for estimating the transfer function of ultrasound transducers achieves a sufficient level of accuracy comparable to pulse-echo and hydrophone measurements.

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In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

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Ultrasonic flow meters (UFMs) based on transducer arrays offer several advantages. With electronic beam steering, it is possible to tune the steering angle of the beam for optimal signal-tonoise ratio (SNR) upon reception. Moreover, multiple beams can be generated to propagate through different travel paths, covering a wider section of the flow profile. Furthermore, in a clamp-on configuration, UFMs based on transducer arrays can perform self-calibration. In this manner, userinput is minimized and measurement repeatability is increased. In practice, transducer array elements may break down. This could happen due to aging, exposure to rough environments, and/or rough mechanical contact. As a consequence of inactive array elements, the measured transit time difference contains two offsets. One offset originates from non-uniform spatial sampling of the generated wavefield. Another offset originates from the ill-defined beam propagating through a travel path different from the intended one. In this paper, an algorithm is proposed that corrects for both of these offsets. The algorithm also performs a filtering operation in the frequency-wavenumber domain of all spurious (i.e., flow-insensitive) wave modes. The advantage of implementing the proposed algorithm is demonstrated on simulations and measurements, showing improved accuracy and precision of the transit time differences compared to the values obtained when the algorithm is not applied. The proposed algorithm can be implemented in both in-line and clamp-on configuration of UFMs based on transducer arrays.

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The semiconductor industry needs to fit ever more devices per unit area to improve their performance; hence a trend towards increasingly complex structures by varying material combinations and 3D geometries with increasing aspect ratios. The new materials used may be optically opaque, posing problems for traditional optical metrology methods. One solution is to use acoustical waves, which present the double advantage of not being hampered by optically opaque layers and allowing for penetration depths of 10's of μm at sub-μm wavelengths; which is considerably larger than most traditional optical methods (O(100 nm's - μm's)). Here, we present a novel acoustic metrology method using GHz ultrasound waves to measure deeply buried subsurface features (>5 μm). The concept consisted of a GHz acoustic transducer integrated above the tip of a custom designed probe, which is then scanned across a sample. The method uses non-damaging solid-solid contact without the need for liquid coupling layers - in contrast to conventional acoustical microscopy. This allows for the use of much higher acoustic frequencies, hence higher on-axis resolutions. The transducer is used in pulse-echo mode and a stage controller is used to move the probe for scanning. An experimental setup was built with a 4 GHz transducer and tested successfully on 1.5-2 μm size features buried below a 5 μm PMMA or 10 μm SiO₂layer, respectively. A good match was further obtained between the measurements and the model predictions. These results demonstrated the feasibility of the new method, opening new opportunities for metrology and inspection applications.

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Over the last 15 years, literature on nondestructive testing has shown that the generation of higher harmonics and nonlinear mixing of waves could be used to obtain the nonlinearity parameters of an elastic medium and thereby gather information about its state, e.g., aging and fatigue. To design ultrasound measurement setups based on these phenomena, efficient numerical modeling tools are needed. In this paper, the iterative nonlinear contrast source method for numerical modeling of nonlinear acoustic waves is extended to the one-dimensional elastic case. In particular, nonlinear mixing of two collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic medium is considered, taking into account its third-order elastic constants ( A,  B,  and  C). The obtained results for nonlinear propagation are in good agreement with a benchmark solution based on the modified Burgers equation. The results for the resonant waves that are caused by the one-way and two-way mixing of primary waves are in quantitative agreement with the results in the literature [Chen, Tang, Zhao, Jacobs, and Qu, J. Acoust. Soc. Am. 136(5), 2389-2404 (2014)]. The contrast source approach allows the identification of the propagating and evanescent components of the scattered wavefield in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the resonant wave.@en

Common clamp-on ultrasonic flow meters consist of two single-element transducers placed on the pipe wall. Flow speed is measured noninvasively, i.e., without interrupting the flow and without perforating the pipe wall, which also minimizes safety risks and avoids pressure drops inside the pipe. However, before metering, the transducers have to be carefully positioned along the pipe axis to correctly align the acoustic beams and obtain a well-calibrated flowmeter. This process is done manually, is dependent on the properties of the pipe and the liquid, does not account for pipe imperfections, and becomes troublesome on pipelines with an intricate shape. Matrix transducer arrays are suitable to dynamically steer acoustic beams and realize self-alignment upon reception, without user input. In this work, the design of a broadband 37×17 matrix array (center frequency of 1 MHz) to perform clamp-on ultrasonic flow measurements over a wide range of liquids (c=1000-2000m/s, α≤1 dB/MHz · cm) and pipe sizes is presented. Three critical aspects were assessed: efficiency, electronic beam steering, and wave mode conversion in the pipe wall. A prototype of a proof-of-concept flowmeter consisting of two 36-element linear arrays (center frequency of 1.1 MHz) was fabricated and placed on a 1-mm-thick, 40-mm inner diameter stainless steel pipe in a custom-made flow loop filled with water. At resonance, simulated and measured efficiencies in water of the linear arrays compared well: 0.88 and 0.81 kPa/V, respectively. Mean flow measurements were achieved by electronic beam steering of the acoustic beams and using both compressional and shear waves generated in the pipe wall. Correlation coefficients of R2>0.99 between measured and reference flow speeds were obtained, thus showing the operational concept of an array-based clamp-on ultrasonic flowmeter.

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Clamp-on ultrasonic flow meters (UFMs) are installed on the outside of the pipe wall. Typically, they consist of two single-element transducers mounted on angled wedges, which are acoustically coupled to the pipe wall. Before flow metering, the transducers are placed at the correct axial position by manually moving one transducer along the pipe wall until the maximum amplitude of the relevant acoustic pulse is obtained. This process is time-consuming and operator-dependent. Next to this, at least five parameters of the pipe and the liquid need to be provided manually to compute the flow speed. In this work, a method is proposed to obtain the five parameters of the pipe and the liquid required to compute the flow speed. The method consists of obtaining the optimal angles for different wave travel paths by varying the steering angle of the emitted acoustic beam systematically. Based on these optimal angles, a system of equations is built and solved to extract the desired parameters. The proposed method was tested experimentally with a custom-made clamp-on UFM consisting of two linear arrays placed on a water-filled stainless steel pipe. The obtained parameters of the pipe and the liquid correspond very well with the expected (nominal) values. Furthermore, the performed experiment also demonstrates that a clamp-on UFM based on transducer arrays can achieve self-alignment without the need to manually move the transducers@en

Coatings with dynamic surface structures are appealing to many applications like haptics and soft robotics. Restrictively, the speed of the surface dynamics in these coatings is often limited to frequencies below 1 kHz, which makes them unsuitable for applications like acoustics and communication optics. This work describes a method to create high-frequency surface dynamics controlled by alternating electric fields on a substrate-contact-modulated coating that consists of an elastic poly(dimethyl siloxane) network supported by SU-8 microstructures. The principle is based on the global application of Maxwell stress that is locally resisted by the supporting SU-8 microstructures. In-between the microstructures the elastic material is stretched, causing a large deformation of the surface topography, which is supported by the authors’ finite element method models. By applying a high-frequency alternating field, they discovered resonance effects at frequencies up to 230 kHz, where the surface of the coating vibrates at high speeds and large amplitudes. At these high frequencies, the coatings can produce and detect ultrasound waves underwater, indicating their potential for ultrasound transducers in the future.

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In this work, we investigate the feasibility of extracting velocity profile information with clamp-on transit-time ultrasonic flow meters. By using time delay inversion on multiple acoustic paths generated with clamp-on array transducers we extract the velocity profile inside the pipe. Monte-Carlo simulations with 1ns random jitter on the transit-times show good agreement with input velocity profiles. Measurements to test the algorithm on experimental data are ongoing. @en

Acoustic wave propagation in ultrasonic flow measurements is typically assumed to be linear and reciprocal. However, if the transmitting transducer generates a sufficiently high pressure, nonlinear wave propagation effects become significant. In flow measurements, this would translate into more information to estimate the flow and therefore a higher precision relative to the linear case. In this work, we investigate how the generated harmonics can be used to measure flow. Measurements in a custom-made flow loop and simulations using the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation will show that the second harmonic component provides similar transit time differences to those obtained from the fundamental component, their linear combination results in more precise flow measurements compared to the estimations with the fundamental component alone.

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Shear wave elastography (SWE) has the potential to determine cardiac tissue stiffness from non-invasive shear wave speed measurements, important, e.g., for predicting heart failure. Previous studies showed that waves traveling in the interventricular septum (IVS) may display Lamb-like dispersive behaviour, introducing a thickness-frequency dependency in the wave speed. However, the IVS tapers across its length, which complicates wave speed estimation by introducing an additional variable to account for. The goal of this work is to assess the impact of tapering thickness on SWE. The investigation is performed by combining in vitro experiments with acoustic radiation force (ARF) and 2D finite element simulations, to isolate the effect of the tapering curve on ARF-induced and natural waves in the heart. The experiments show a 11% deceleration during propagation from the thick to the thin end of an IVS-mimicking tapered phantom plate. The numerical analysis shows that neglecting the thickness variation in the wavenumber-frequency domain can introduce errors of more than 30% in the estimation of the shear modulus, and that the exact tapering curve, rather than the overall thickness reduction, determines the dispersive behaviour of the wave. These results suggest that septal geometry should be accounted for when deriving cardiac stiffness with SWE.

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Current ultrasonic clamp-on flow meters consist of a pair of single-element transducers that are carefully positioned before use. This positioning process consists of manually finding the distance between the transducer elements, along the pipe axis, for which maximum signal-to-noise ratio (SNR) is achieved. This distance depends on the sound speed, thickness, and diameter of the pipe and on the sound speed of the liquid. However, these parameters are either known with low accuracy or completely unknown during positioning, making it a manual and troublesome process. Furthermore, even when sensor positioning is done properly, uncertainty about the mentioned parameters, and therefore on the path of the acoustic beams, limits the final accuracy of flow measurements. In this research, we address these issues using an ultrasonic clamp-on flow meter consisting of two matrix arrays, which enables the measurement of pipe and liquid parameters by the flow meter itself. Automatic parameter extraction, combined with the beam-steering capabilities of transducer arrays, yields a sensor capable of compensating for pipe imperfections. Three parameter extraction procedures are presented. In contrast to similar literature, the procedures proposed here do not require that the medium be submerged nor do they require a priori information about it. First, axial Lamb waves are excited along the pipe wall and recorded with one of the arrays. A dispersion curve-fitting algorithm is used to extract bulk sound speeds and wall thickness of the pipe from the measured dispersion curves. Second, circumferential Lamb waves are excited, measured, and corrected for dispersion to extract the pipe diameter. Third, pulse-echo measurements provide the sound speed of the liquid. The effectiveness of the first two procedures has been evaluated using simulated and measured data of stainless steel and aluminum pipes, and the feasibility of the third procedure has been evaluated using simulated data.

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Several methods are being researched to detect and characterize buried nanoscale structures in hard solid samples. The most common acoustic method is acoustic microscopy. An acoustic microscope is based on a single element transducer operating in pulse-echo mode. The acoustic waves are coupled into a sample using a liquid couplant (eg water) and the beam is focused using a geometric lens to obtain a good lateral resolution. Thus, the frequency is limited by the attenuation in the coupling layer (water 3.5\{dB}/{m} at 4 GHz) and the typically low transmission coefficients at the transducer-liquid couplant and liquid-sample interfaces. Here, we present a novel method for high frequency acoustic metrology of buried structures in solid samples. The concept consisted of a 4 GHz acoustic transducer integrated above the tip of a custom designed probe. It operated in pulse-echo mode, and used solid-solid contact with the sample without the need for liquid coupling layers. A prototype was built and successfully tested experimentally on samples consisting of silicon with 1D and 2D arrays ofmu\{m} sized features buried below 5-10{m} of PMMA or SiO2 top layers. Moreover, a good match was obtained between model predictions and measurements of the pulse-echo performance of the novel GHz acoustic metrology method. The technique features a penetration depth of O(10s ofmu\{m}), is nondamaging and is not hampered by optically opaque layers.

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Current ultrasonic clamp-on flow meters are manually calibrated. This process is based on manual placement of two single-element transducers along a pipe wall. Due to the usually unknown pipe properties and inhomogeneities in the pipe geometry, the axial distance of the transducers needs to be manually calibrated to align the location of the emitted beam on the receiver. In this work it is presented an automatic calibration procedure, based on matrix transducer arrays, to provide calibration information that would normally be entered into the instrument manually prior to ultrasonic clamp-on flow measurements. The calibration consists of two steps: First, along the axial direction of the pipe, Lamb waves are excited and recorded. Then, the measured time signals are combined with the Rayleigh-Lamb dispersion equation to extract pipe wall thickness and bulk wave sound speeds. Second, along the circumferential direction of the pipe, a specific Lamb wave mode is excited and recorded, from which the pipe diameter is estimated. The potential of both calibration procedures is shown, and the necessity of a matrix transducer array (i.e. small elements) is highlighted@en

In Subsurface Scanning Probe Microscopy (SSPM), Atomic Force Microscopy (AFM) is combined with ultrasound. The AFM cantilever is used as a receiver. At low frequencies (O(MHz)) the method can be used to measure the stiffness contrast in a sample and at high frequencies (O(GHz)) to measure scattering based contrast. Both variants use modulated excitation signals in combination with the nonlinear tip-sample interaction to downmix the sample top surface displacement close to the resonance frequency of the cantilever. This concept has three advantages: 1) the resonance of the cantilever is used to boost the sensitivity, 2) the downmixing allows the system to record signals in an extremely wide range of carrier frequencies (kHz - GHz), and 3) the cantilever tip-sample contact diameter is usually much smaller than 10 nm. The latter implies that spatial averaging effects are negligible up to 100 GHz. Said advantages mean that AFM cantilevers could be useful to characterize acoustic sources. Here, we investigate the suitability of AFM cantilevers as acoustic point receivers to characterize acoustic sources. Investigation with an AFM setup and two sources - one O(MHz) and one O(GHz) - show a good match between the measured response, KLM simulations and the transducers bandwidth, which are promising results for the use of a cantilever as a wideband receiver for high resolution acoustic (transducer) characterization.

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Design, fabrication and acoustic characterization of a transducer array for ultrasonic clamp-on flow measurements. @en

During ultrasonic clamp-on flow metering, Lamb waves propagating in the pipe wall may limit the measurement accuracy by introducing absolute errors in the flow estimates. Upon reception, these waves can interfere with the up and downstream waves refracting from the liquid, and disturb the measurement of the transit time difference that is used to obtain the flow speed. Thus, suppression of the generation of Lamb waves might directly increase the accuracy of a clamp-on flow meter. Existing techniques apply to flow meters with single element transducers. This paper considers the application of transducer arrays and presents a method to achieve a predefined amount of suppression of these spurious Lamb waves based on appropriate amplitude weightings of the transducer elements. Finite element simulations of an ultrasonic clamp-on flow measurement setting will be presented to show the effect of array aperture control on the suppression of the Lamb waves in a 1-mm-thick stainless steel pipe wall. Furthermore, a proof-of-principle experiment will be shown that demonstrates a good agreement with the simulations.@en

The characterization of buried nanoscale structures nondestructively is an important challenge in a number of applications, such as defect detection and metrology in the semiconductor industry. A promising technique is Subsurface Scanning Probe Microscopy (SSPM), which combines ultrasound with Atomic Force Microscopy (AFM). Initially, SSPM was used to measure the viscoelastic contrast between a subsurface feature and its surrounding medium. However, by increasing the ultrasonic frequency to >1 GHz, it has been shown that SSPM can also measure acoustic impedance based contrasts. At these frequencies, it becomes difficult to reliably couple the sound into the sample such that the AFM is able to pick up the scattered sound field. The cause is the existence of strong acoustic resonances in the sample, the transducer, and the coupling layer-the liquid layer used to couple the sound energy from the transducer into the sample-in combination with the nonlinearity of the tip-sample interaction. Thus, it is essential to control and measure the thickness of the coupling layer with nanometer accuracy. Here, we present the design of a mechanical clamp to ensure a stable acoustic coupling. Moreover, an acoustic method is presented to measure the coupling layer thickness in real-time. Stable coupling layers with thicknesses of 700 ± 2 nm were achieved over periods of 2-4 h. Measurements of the downmixed AFM signals showed stable signal intensities for >1 h. The clamp and monitoring method introduced here makes scattering based SSPM practical, robust, and reliable and enables measurement periods of hours.

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In nondestructive testing, nonlinear wave mixing could be used to obtain the nonlinearity parameters of an elastic medium and thereby get information about its state, e.g., aging and fatigue. To better understand the mixing mechanisms and optimize the design of measurement setups, a physics-oriented tool for the simulation of nonlinear elastic wave propagation would be valuable. In this presentation, we extend the iterative nonlinear contrast source method (INCS) to study the nonlinear mixing of two plane, collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic, elastic medium with two independent coefficients of nonlinearity (βL and βT). The method successfully captured the resonant wave generated due to the mixing (one-way and two-way) of primary waves of different frequencies. The obtained results for the resonant wave were in good agreement with the results reported in the literature. In addition, the contrast source allowed the propagating and evanescent components of the scattered wave field to be studied in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the scattered wave. Thus, the INCS method seems to be a useful tool to investigate and predict wave mixing in nonlinear elastic media.@en

Current ultrasonic clamp-on flow meters are based on single-element transducers that require manual calibration by aligning these to a fixed acoustic path. Moreover, the size and operational frequency of the transducers cannot be adapted to the parameters of the pipe and the liquid, which are in practice not precisely known a priory. A set of two transducer arrays could be used to solve these issues. With an array, properties of the pipe and the liquid can be estimated before measuring flow. Furthermore, electronic beam steering can be used for auto-alignment of the acoustic beam, reducing the need for manual calibration. Moreover, an array allows for the use of signal processing to suppress the effects of spurious Lamb waves propagating in the pipe wall. This research work describes the acoustic design process of a transducer array for ultrasonic clamp-on flow measurements for a wide range of conditions. First, performance requirements are defined. Then, the design models are presented, and a step by step process of the acoustic stack design of the transducer array is described. At each design step, material dimensions are optimized to achieve a thickness resonance mode at 1 MHz within a bandwidth of interest between 0.2 MHz and 2 MHz. Finally, the expected performance of the designed array is reported, based on simulation results.

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