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Waveguides allow grating lobe free beamforming for air-coupled ultrasonic phased-arrays by reducing the effective inter-element spacing to half wavelength. Since the sound waves propagate through the waveguide ducts, additional time delays are introduced. In this work, we present analytical, numerical, and experimental methods to estimate these time delays. Afterwards, two different waveguides are compared. The first one consists of equal-length ducts, requiring a time-consuming assembly process of the ultrasonic phased-array. In contrast, the second waveguide consists of Bézier-shaped ducts of unequal lengths but a planar input port allowing fast assembly. The analytical model is based on the geometric lengths of the waveguide ducts. The numerical model relies on a transient finite element analysis. All simulations are validated in an anechoic chamber using a calibrated microphone. The analytical (7.6% deviation) and numerical (3.2% deviation) propagation time models are in good agreement with the measurements. By using the analyzed propagation times for the compensation of the unequal waveguide duct lengths, we restored the beamforming capability without significant sound pressure level (SPL) loss. This work shows the possibility of reduced transducer assembly time for waveguided air-coupled phased-arrays without a reduced SPL.

Waveguided air-coupled ultrasonic phased arrays offer grating-lobe-free beam forming for many applications such as obstacle detection, non-destructive testing, flow metering or tactile feedback. However, for industrial applications, the open output ports of the waveguide can be clogged due to dust, liquids or dirt leading to additional acoustic attenuation. In previous work, we presented the effectiveness of hydrophobic fabrics as a protection layer for acoustic waveguides. In this work, we created a numerical model of the waveguide including the hydrophobic fabric allowing the prediction of the insertion loss (IL). The numerical model uses the boundary element method (BEM) and the finite element method (FEM) in the frequency domain including the waveguide, the hydrophobic fabric and the finite-sized rigid baffle used in the measurements. All walls are assumed as ideal sound hard and the transducers are ideal piston transducers. The specific flow resistivity of the hydrophobic fabric, which is required for the simulation, is analyzed using a 3D-printed flow pipe. The simulations are validated with a calibrated microphone in an anechoic chamber. The IL of the simulations are within the uncertainties of the measurements. In addition, both the measurements and the simulations have no significant influence on the beamforming capabilities.

Ultrasonic flow meters (UFMs) have the advantage of noninvasive flow metering of liquids, gases and multi-phase mixtures with or without particles. However, one challenge is a restricted measurement range of UFMs. The sound drift effect is causing a significant reduction of the signal to noise ratio (SNR) at larger flow velocities. In this paper, we extend our previous work by providing ray-tracing simulation of the sound drift effect for high flow velocities to predict the compensation angles and therefore increase the SNR, allowing measurements, of up to a flow velocity of 100 ms−1in a pipe with a diameter of 31.5 cm, The 3D-ray-tracing calculation for each sound path of a multipath UFM takes into account the flow velocity distribution and the sound velocity within the flow meter. The pre-characterized velocity distribution is used in a boundary value problem, solving each sound ray path for a given compensation angle in flow velocity steps of 0.1 ms−1. For validation, a 3D-printed flowmeter consisting of an 8 x 8, λ/2 phased-array for transmission and 14 individual single receivers for upstream and downstream sound paths are used. The correct steering angle maximizing the received power of the direct sound wave corresponds to the ideal compensation angle for each flow velocity and transducer. In general, the measured and simulated ideal compensation angles are in excellent agreement with a root mean square deviation of 2.88°. In upstream direction, the simulation no longer converges for flow velocities above 34.9 ms−1for the outermost sound path above 78.9 ms−1for the middle sound path.

Ferroelectrets are typical cellular polymer foams that exhibit high flexibility and an excellent matching to air. Recently, biodegradable cellular polylactic acid (PLA) ferroelectrets have been introduced, exhibiting a large longitudinal piezoelectric coefficient. In this work, we present a combination of a PLA film and a printed PLA backplate using fused deposition modeling to build a ferroelectret air-coupled ultrasonic transducer. The ultrasonic transducer consists of three main components all made from PLA: the film presenting the vibrating plate, the printed backplate with well-defined groves, and the printed holder. The PLA film and the printed backplate build together the ferroelectret with artificial air voids. The printed holder clamps the film on the backplate and fixes the ferroelectret together. After poling, the trapped surface charge density serves as electrical bias as well as a mechanical pre-stress due to the permanent electrostatic forces. The resulting sound pressure is measured with a calibrated microphone (Type 4138, Bruel & Kjaer) at 30 cm distance. The sound pressure of the transducer is measured at the resonance frequency for different applied AC voltages (from 30 to 70 Vrms). The biodegradable ultrasonic transducer exhibits a large bandwidth of approximately 45 kHz and fractional bandwidth of 70 %. The resulting sound pressure at the resonance frequency can be increased from 98 dB up to 106 dB for driving voltages from 30 to 70 Vrms. respectively.

Lamb wave excitation in sheet materials is possible using non-contact, non-destructive evaluation methods such as air-coupled transducers, pulsed Laser excitation and electro magnetic acoustic transducers (EMATs). However, these methods are limited to specific groups of materials or lack flexibility when testing specimens with different geometries or compositions. In previous work we demonstrated air-coupled Lamb wave excitation using a custom ultrasonic phased array (UPA). In this work we utilized the UPA for localizing two different discontinuities in a steel sheet specimen. The steering capability of the UPA is used in order to find the optimum coupling angle. The time of flight (TOF) of the Lamb wave, reflected at the discontinuities, is measured using a laser Doppler vibrometer (LDV). The defect location is calculated using the group velocity derived from the coupling angle and the theoretical value from the dispersion diagram. The setup is characterized and our results show mean localization errors of 1.39 mm and 1.42 mm at distances of up to 800 mm using the optimum coupling angle. This can be further optimized using a finer angular step size. This way, the system is suitable for a wide range of non destructive evaluation (NDE) applications.

Ultrasound propagation in liquids is highly influenced by its attenuation due to viscous damping. The dissipated energy will be partially absorbed by the liquid due to its dynamic viscosity as well as its bulk viscosity. The former results in the generation of a flow that is called acoustic streaming, and the latter is associated with the vibrational and rotational relaxation of liquid molecules. Measuring the ultrasonic wave attenuation due to the bulk viscosity is presented as a novel method in this article. Poly(N-isopropylacrylamide) (PNIPAM) microgels, which are soluble in several solvents such as water, were used as acousto-responsive markers in water, which upon absorption of ultrasonic energy undergo a volume phase transition due to the breakage of their hydrogen bonds. Thus, they become insoluble in water, and due to shrinking, their optical density increases. As a result, their agglomeration can be seen as a turbid medium. We managed to visualize the ultrasonic energy absorption due to the bulk viscosity using the turbidity since the excess acoustic energy on top of the absorbed energy for the translational motion of liquid is spent to break the hydrogen bonds between PNIPAM and water. In addition, to quantify the turbidity phenomenon, the total energy required for breaking hydrogen bonds in the solution is calculated, and its evolution, according to the input power intensity, is quantified by image processing. The effect of viscosity by changing the microgel concentration was investigated, and it is shown that an increasing microgel concentration increases the acoustic energy absorption rate much greater than its dynamic viscosity. Therefore, the bulk viscosity, as the responsible parameter for this increase, is measured directly from the energy of broken hydrogen bonds. The results show that at low solution concentration (0.2 wt %) the bulk viscosity is in the same order of magnitude as its dynamic viscosity. Increasing the concentrations to 1 and 5 wt % increases the bulk viscosity and consequently the structural relaxation time by 1 and 2 orders of magnitude, respectively.

Air-coupled ultrasonic sonar systems are a valuable complement to lidar sensors for safe navigation of autonomous vehicles, especially in environments with optically transparent and reflective surfaces. Consequently, sonar systems based on phased arrays and beamforming are a promising compact solution, providing precise and unambiguous 3D localization of multiple objects in a wide field of view. However, a cost-effective and viable integration is challenging due to the increased component count and computational effort. Therefore, we present an embedded phased array sonar system requiring a minimum number of low-cost components, and providing high frame rates. The system contains 36 digital MEMS microphones, one 40 kHz transducer, an FPGA for CIC-filtering and communication with the main processor (Nvidia Jetson Nano) via Hi-Speed USB or WiFi. The GPU accelerated frequency-domain signal processing consisting of matched filtering, optimized conventional narrow-band beamforming and envelope extraction, enables frame rates up to 30 Hz. In an anechoic chamber, a field of view of ±80° and an angular resolution of 14° have been measured using two O100 mm spheres. Therefore, this self-contained phased array sonar allows a practicable sensor fusion with lidar data for a more reliable monitoring of the environment.

The Least Absolute Shrinkage and Selection Operator (LASSO) was recently introduced for imaging of sparse scenes in low sample size scenarios. In this paper, we investigate the imaging capabilities of LASSO for ultrasonic phased arrays operating in air. Using sparse regularization and a dictionary of measured array point responses, 3D images can be generated with only a few, single pulse measurements. A priori, the dictionary of point responses is learned by calibrating the array. The underlying low-rank structure can be adequately expressed by fitting rank-one vectors. A proof of concept shows the imaging potential of our proposed scheme with a real ultrasonic phased array.

Schlieren photography is widely used for visualization of acoustic or shock waves, e.g. in ballistics and aerodynamics. Due to the low molar refractivity of air the visualization of acoustic waves requires sensitive equipment or high sound pressure levels. We present a Schlieren system utilized in a nondestructive test setup, that is capable to visualize leaky Lamb waves, radiating from a steel sheet specimen. The Lamb wave is excited with our air-coupled ultrasonic phased array. Image processing includes averaging, substraction of a phase-shifted image and filtering in the frequency domain. We analyze the detection limit of our setup and discuss measurements with two different specimen. Leaky Lamb waves with SPLs down to 101.5 dB can be visualized. The exit angles above and beneath the specimen, measured in the Schlieren images are in good agreement with the excitation angles for 0.5 mm and 0.8 mm thick steel sheets.

Spiral-shaped phased arrays are widely used for sound source localization and are trending in other fields, e.g. 3D medical ultrasound imaging. The non-uniform element geometry allows grating lobe free beamforming without an inter-element spacing of half wavelength. We demonstrate the 3D imaging capabilities of an air-coupled ultrasonic 40-kHz phased array based on 64 Murata MA40S4S transducers, spirally arranged on a 200 mm aperture. The 3D image is generated by sequentially transmitting beamformed pulses in discrete directions and capturing the corresponding echo signals, using all transducers. The GPU accelerated array signal processing consists of matched filtering, conventional beamforming and envelope extraction. The origins of the echos are visualized in B-Scans and 3D-Scans using OpenGL. We characterize the far-field transmit and receive directivity patterns, as well as the angular resolution in an anechoic chamber. The main lobe widths and maximum side lobe levels of the transmit (2.6°, -11.5 dB), the receive (2.6°, -11.6 dB) and the ideal model directivity patterns (2.4°, -13.4 dB) are in good agreement. Two laterally positioned rods (O10 mm) are separately detectable with an angular resolution of 2.3 °. The localization of multiple scatterers at the same range (2 m) is demonstrated by a test pattern of corner reflectors. Overall, the spiral array allows highly directional sound beam steering and localization, making it ideal for imaging and other in-air applications.

Air-coupled ultrasonic phased arrays with acoustic waveguides offer grating-lobe-free beamforming for different applications such as obstacle detection, range finding, flow metering, acoustic levitation or tactile feedback. However, for real world applications the open outputs of the waveguide must be protected against fluids and dust in order to prevent clogging in the waveguide openings resulting in additional acoustic attenuation. In this work, we compare a hydrophobic fabric and a low density polyethylene (LDPE) foil regarding the insertion loss (IL), the influence on the beamforming, the blind zone in pulse-echo mode and the watertightness. Measurements are conducted in an anechoic chamber in transmit, receive and pulse-echo mode. The watertightness is determined with a submersion experiment in a water column of up to 2 m. The hydrophobic fabric has an IL of 1.8 dB±1 dB and does not effect the blind zone, whereas the LDPE foil has a higher IL of 7.5 dB±1 dB and increases the blind zone by 22%. The LDPE foil reaches IPX8, whereas the hydrophobic fabric reaches IPX7. However, in pulse-echo mode it is possible with both protection layers to detect a 10 mm-hollow steel sphere at a distance of 1 m. Their influence on the beamforming is within the measurement uncertainty.

We present an air-coupled ultrasonic imaging system based on a 40-kHz $8\times 8$ phased-array for 3-D real-time localization of multiple objects in the far-field. By attaching a waveguide to the array, the effective interelement spacing is reduced to half wavelength. This enables grating lobe-free transmit and receive beamforming with a uniform rectangular array of efficient low-cost transducers. The system further includes custom transceiver electronics, an field programmable gate array (FPGA) system-on-chip and a PC for GPU accelerated frequency domain signal processing, consisting of matched filtering, conventional beamforming, and envelope extraction using Nvidia Compute Unified Device Architecture (CUDA) and OpenGL for visualization. The uniform rectangular layout allows utilizing multiple transmit and receive methods, known from medical imaging applications. Thus, the system is dynamically adaptable to maximize the frame rate or detection range. One implemented method demonstrates the real-time capability by transmitting a hemispherical pulse (HP) with a single transducer to irradiate the surroundings simultaneously, whereas all transducers are used for echo reception. The imaging properties, such as axial and lateral resolution, field of view and range of view, are characterized in an anechoic chamber. The object localization is validated for a horizontal and vertical field of view of ±80° and a range of view of 0.5–3 m with 29 frames/s. Using the same system, a comparison between the HP method and the dynamic transmit beamforming method, which transmits multiple sequential beamformed pulses for long-range localization, is provided.

We present a simulation of an acoustic waveguide array consisting of 64 circular-shaped ducts with equal lengths. The waveguide reduces the acoustic aperture to an effective element pitch of half lambda. In order to optimize the waveguide geometry regarding sound pressure level and time delay between the channels and directivity, we use the acoustic boundary element method of COMSOL Muliphysics 5.4. The main objective for this work, is to simulate and measure the directivity pattern in the far field region based on the wave propagation inside the waveguide in order to extend our previous simulation of ultrasonic phased arrays. The complexity of the model was reduced using two symmetry planes. The wave propagation is calculated in the frequency domain based on the Helmholtz equation. A finite-sized rigid baffle at the acoustic aperture side of the array, identical to the one used in the measurements, is included. Our model allows visualizing the wave propagation in our waveguide. As the geometry intended, all waveguides emit the ultrasound in phase. Due to a different distribution of the normal velocity of the real transducers, the half power beam width differs only 4° and the side lobe level 3 dB compared to measurements.

We present a simulation of an ultrasonic transducer element with piezoelectric and electrostatic transduction combined and with two bending plates. It combines the high SPL of a piezoelectric transducer with the tunable resonance frequency of a CMUT due to spring softening effect. In this work, we compare two state-of-the-art transducers with our approach: First, a piezoelectric bending plate transducer, based on a Murata MA40S4S transducer; second, a piezoelectric bending plate positioned above an additional electrode (piezoelectric and electrostatic transduction principle combined) and, third, a new structure, based on two bending plates with piezoelectric and electrostatic transduction combined (piezoelectric and electrostatic double-bending plate transducer). We use COMSOL Multiphysics 5.4 for creating a multiphysical model, including the electrical, mechanical and acoustical domain. We simulate mechanical total displacement and the directivity pattern. Thermoviscous losses in the air gap between the two bending plates are considered as well. The double-bending plate transducer has an increased amplitude of up to 570% at 80% of the pull-in voltage and a tunable resonance frequency of up to 21%. Compared to piezoelectric and electrostatic bending plate transducer, the total displacement is doubled. In addition, the radiation pattern is approximately omnidirectional, and, thus, beneficial for various applications such as obstacle detection, flow metering, distance measurement or anemometry.

We present a fully-populated 8×8 2D-phased array, capable of emitting directed air-coupled ultrasound at 40 kHz with λ/2-pitch size for zero grating lobes. In comparison to our previous work, in which we describe a 1D-phased array, we use 3D-printing to realize the wave guide structure. Besides the key idea to separate the vibrating from the acoustic aperture, the 3D-printing approach allows implementing a versatile fullypopulated air-coupled 2D-phased array transducer with superior performance. We are using commercially available transducers with a diameter of 10mm on the vibrating aperture side. Focal laws and beam steering true time delays are calculated by a custom FPGA board, extended with ultrasound pulsers. The array features beam steering in two directions over an opening angle of 110° with outstanding sound pressure levels (SPL) exceeding 145 dB SPL and 136 dB SPL at a distance of 0.3m and 1 m, respectively. The main lobe is symmetric and has a full angle of about 14° (− 3 dB). Our results prove that the approach of using the 3D-printed waveguide structure has the potential to be useful for numerous ultrasonic air-coupled applications.

We present a versatile ultrasonic one-dimensional (1D) air-coupled phased array transducer with a focus on its receive performance. In addition to its beam steering capability in transmit mode, it can be used to listen to ultrasonic waves at 40 kHz and below. We fulfill the half-wavelength criteria for the element spacing by introducing an additional layer, consisting of many tapered sound tubes (waveguides). These sound tubes separate the effective acoustic aperture from the actual receiving aperture of several ultrasonic transducers. This ensures that the array is not affected by grating lobes over a wide range of steering angles, and, thus, the array is capable of receiving directed ultrasound with only one primary receive direction for an adjustable angle (receive-beam forming). Based on this approach, we built and characterized a proof-of-concept prototype device. Our results prove that the array is able to receive ultrasonic waves over a wide range of 110° in total, with a receive sensitivity of −55.9 dB (0 dB equal 1 V/Pa). Thus, the device has huge potential for new sensory applications and the approach is compatible with micromachined ultrasonic transducers as well.

We introduce an ultrasonic one-dimensional (1D) air-coupled phased array transducer, operating at 40 kHz without any grating lobes. It is well known, that this achievement is only possible when each transducer element is small enough for an element pitch that is equal to or less than half of the wavelength, i.e. ≤ 4.3 mm for 40 kHz operation frequency. As far as we know, conventionally low frequency array designs for air-coupled transducer applications were not possible at 40 kHz due to this inter element spacing requirement. The main idea is to separate the acoustic aperture from the actual radiating aperture of the ultrasonic transducer. We use acoustic waveguides, forming a smart packaging layer, to fulfill the half-wavelength criteria for the pitch and to benefit from concentrating the acoustic energy from several single ultrasonic transducers into a smaller effective aperture. A proof-of-concept prototype array was built and characterized. An impressive 130 ± 1 dB sound pressure level (SPL) is observed at a distance of 1 m. The opening angle of the array is 110° in total, without any grating lobes. For future work, we plan extending the approach to build an air-coupled fully populated 2D phased array transducer as well.

We present an efficient numerical method to analyze the diffraction loss of an ultrasonic air-coupled phased array transducer to an arbitrary located receiving aperture. The objective is the efficient calculation of diffraction loss for applications in which such an array is excited with arbitrary input signals on all channels for different beam steering angles. Available software, such as Field II, provide the pressure field in front of the phased transducer array, i.e. they assume a point source receiver. Our calculation method, however, is focused on directly calculating the diffraction loss to a given receiving aperture, such as a microphone or a receiving transducer, with arbitrary location and orientation. The boundary element method (BEM) is used for an efficient calculation. The entire model is implemented in the commercially available software package Mathematica V10 from Wolfram Research. Excellent agreement between calculation results and microphone measurements validate the approach. For future work, we will use this model for further optimizing the development of high-performance air-coupled phased array transducer designs.