Diffraction effects in hydrophone measurements

Ultrasonic needle hydrophone calibration in air by a parabolic off-axis mirror focused beam using three-transducer reciprocity

An acoustic field distribution investigation in air requires a small receiving sensor. Needle hydrophones seem to be an attractive solution, and it has previously been demonstrated that needle hydrophones designed for use in water can be used in air. The metrology problem is that an absolute sensitivity calibration is needed, because needle hydrophones are not characterized in air, especially for frequencies below 1 MHz, which is of interest for air-coupled ultrasound. Conventional, three-transducer/microphone reciprocity calibration requires measurements to be done in the far field. However, when transducer diameter is large and the frequency is high, the required measurement distance becomes very large: 3 m for a 20 mm source, transmitting at 1 MHz. Large propagation distance leads to high attenuation and nonlinear effects in air propagation, and distortion and losses accumulate. Small needle hydrophones have low sensitivity, so that high excitation amplitudes would be required, which can lead to transducer heating and increase nonlinearity effects. A derivative of the three-transducer reciprocity calibration method is proposed, where a large aperture transducer is focused onto a hydrophone, using hybrid of plane wave and spherical wave reciprocity. Use of a focused source minimizes the frequency-dependent diffraction effects, and the spherical wave approximation is valid at the focal distance, and low level excitation signals can be used. Focusing is accomplished using a parabolic off-axis mirror. Calibration is in transmission, which reduces the complexity of the electrical measurements. The corresponding equations have been derived for this setup. Calibration of the transducer and needle hydrophone absolute sensitivity is obtained.

Ultra-Low-Voltage Capacitive Micromachined Ultrasonic Transducers with Increased Output Pressure Due to Piston-Structured Plates

Capacitive micromachined ultrasonic transducers (CMUTs) represent an accepted technology for ultrasonic transducers, while high bias voltage requirements and limited output pressure still need to be addressed. In this paper, we present a design for ultra-low-voltage operation with enhanced output pressure. Low voltages allow for good integrability and mobile applications, whereas higher output pressures improve the penetration depth and signal-to-noise ratio. The CMUT introduced has an ultra-thin gap (120 nm), small plate thickness (800 nm), and is supported by a non-flexural piston, stiffening the topside for improved average displacement, and thus higher output pressure. Three designs for low MHz operation are simulated and fabricated for comparison: bare plate, plate with small piston (34% plate coverage), and big piston (57%). The impact of the piston on the plate mechanics in terms of resonance and pull-in voltage are simulated with finite element method (FEM). Simulations are in good agreement with laser Doppler vibrometer and LCR-meter measurements. Further, the sound pressure output is characterized in immersion with a hydrophone. Pull-in voltages range from only 7.4 V to 25.0 V. Measurements in immersion with a pulse at 80% of the pull-in voltage present surface output pressures from 44.7 kPa to 502.1 kPa at 3.3 MHz to 4.2 MHz with a fractional bandwidth of up to 135%. This leads to an improvement in transmit sensitivity in pulsed (non-harmonic) driving from 7.8 kPa/V up to 24.8 kPa/V.

Optimal quantization for amplitude and phase in computer-generated holography

Owing to the characteristics of existing spatial light modulators (SLMs), the computer-generated hologram (CGH) with continuous complex-amplitude is conventionally converted to a quantized amplitude-only or phase-only CGH in practical applications. The quantization of CGH significantly affects the holographic reconstruction quality. In this work, we evaluated the influence of the quantization for both amplitude and phase on the quality of holographic reconstructions by traversing method. Furthermore, we considered several critical CGH parameters, including resolution, zero-padding size, reconstruction distance, wavelength, random phase, pixel pitch, bit depth, phase modulation deviation, and filling factor. Based on evaluations, the optimal quantization for both available and future SLM devices is suggested.

Holographic extraction of plane waves from an ultrasound beam for acoustic characterization of an absorbing layer of finite dimensions

For the acoustic characterization of materials, a method is proposed for interpreting experiments with finite-sized transducers and test samples in terms of the idealized situation in which plane waves are transmitted through an infinite plane-parallel layer. The method uses acoustic holography, which experimentally provides complete knowledge of the wave field by recording pressure waveforms at points on a surface intersected by the acoustic beam. The measured hologram makes it possible to calculate the angular spectrum of the beam to decompose the field into a superposition of plane waves propagating in different directions. Because these waves cancel one another outside the beam, the idealized geometry of an infinite layer can be represented by a sample of finite size if its lateral dimensions exceed the width of the acoustic beam. The proposed method relies on holograms that represent the acoustic beam with and without the test sample in the transmission path. The method is described theoretically, and its capabilities are demonstrated experimentally for silicone rubber samples by measuring their frequency-dependent phase velocities and absorption coefficients in the megahertz frequency range.

A Harmonic Dual-Frequency Transducer for Acoustic Cluster Therapy

Acoustic Cluster Therapy (ACT) is a two-component formulation of commercially available microbubbles (Sonazoid; GE Healthcare, Oslo, Norway) and microdroplets (perfluorated oil) currently under development for cancer treatment. The microbubbles and microdroplets have opposite surface charges to form microbubble/microdroplet clusters, which are administered to patients together with a drug. When the clusters and drug reach the target tumour, two ultrasound (US) exposure regimes are used: First, high-frequency (>2.0 MHz) US evaporates the oil and forms ACT bubbles that lodge at the microvascular level. Second, low-frequency (0.5 MHz) US induces stable mechanical oscillations of the ACT bubbles, causing localized micro-streaming, radiation and shear forces that increase the uptake of the drugs to the target tumour. This report describes the design and testing of a dual-frequency transducer and a laboratory setup for pre-clinical in vivo studies of ACT on murine tumour models. The dual-frequency transducer utilizes the 5th harmonic (2.7 MHz) and fundamental (0.5 MHz) of a single piezoceramic disk for the high-frequency and low-frequency regimes, respectively. Two different aperture radii are used to align the high-frequency and low-frequency beam maxima, and the high-frequency -3 dB beam width diameter is 6 mm, corresponding to the largest tumour sizes we expect to treat. The low-frequency -3 dB beam width extends 6 mm. Although unconventional, the 5th harmonic exhibit a 44% efficiency and can therefore be used for transmission of acoustic energy. Moreover, both in vitro and in vivo measurements demonstrate that the 5th harmonic can be used to evaporate the microbubble/microdroplet clusters. For the in vivo measurements, we used the kidneys of non-tumour-bearing mice as tumour surrogates. Based on this, the transducer is deemed suited for pre-clinical in vivo studies of ACT and replaces a cumbersome test setup consisting of two transducers.

Spatial averaging effects of hydrophone on field characterization of planar transducer using Fresnel approximation

The purpose of this work was to improve the existing models that allow spatial averaging effects of piezoelectric hydrophones to be accounted for. The model derived in the present study is valid for a planar source and was verified using transducers operating at 5 and 20MHz. It is based on Fresnel approximation and enables corrections for both on-axis and off-axis measurements. A single-integral approximate formula for the axial acoustic pressure was derived, and the validity of the Fresnel approximation in the near field of the planar transducer was examined. The numerical results obtained using 5 and 20MHz planar transmitters with an effective diameter of 12.7mm showed that the derived model could account for spatial averaging effects to within 0.2% with Beissner's exact integral (Beissner, 1981), for k(a+b)2≫π (where k is the circular wavenumber, and a and b are the effective radii of the transmitter and hydrophone, respectively). The field distributions along the acoustic axis and the beam directivity patterns are also included in the model. The spatial averaging effects of the hydrophone were generally observed to cause underestimation of the absolute pressure amplitudes of the acoustic beam, and overestimation of the cross-sectional size of the beam directivity pattern. However, the cross-sectional size of the directivity pattern was also found to be underestimated in the "far zone" (beyond Y0=a(2)/λ) of the transmitter. The results of this study indicate that the spatial averaging effect on the beam directivity pattern is negligible for π(γ(2)+4γ)s≪1 (where γ=b/a, and s is the normalized distance to the planar transducer).

Primary reciprocity-based method for calibration of hydrophone magnitude and phase sensitivity: complete tests at frequencies from 1 to 7 MHz

A primary reciprocity-based method for calibration of hydrophone magnitude and phase sensitivity is proposed. The method starts determining the transmit transfer function of an auxiliary transducer, based on the self-reciprocity method and using a stainless steel cylinder as reflecting target. Afterwards, the hydrophone, to be calibrated, is positioned facing the auxiliary transducer. The pressure field waveform, calculated at the hydrophone spot and based on the transmit transfer function of an auxiliary transducer, is used together with the output end of cable voltage waveform signal from the hydrophone to yield the calibrated hydrophone sensitivity. The method was tested with two similar membrane hydrophones, at frequencies within the 1.0-7.0 MHz range, in steps of 1.0 MHz. Results for magnitude sensitivity agree, within a confidence level of 95%, with those from previous calibration of same hydrophones at the National Physical Laboratory, in the UK (Enor⩽1.0). Phase sensitivity results agree with literature reported ones concerning the achieved uncertainty. Additionally, the phase sensitivities measured at 5.0 MHz for two similar hydrophones and employing two distinct auxiliary transducers presented no statistical significant difference. The method yielded a relative expanded uncertainty (p=0.95) for the sensitivity magnitude ranging between 6.6 and 7.0%, and an expanded uncertainty (p=0.95) ranging between 12° and 17° for the phase sensitivity. The results obtained so far lead to conclude that the proposed hydrophone calibration method is a validated alternative to the different existing methods.

Quantitative reconstruction of a disturbed ultrasound pressure field in a conventional hydrophone measurement

Among various techniques enabling absolute measurements of ultrasound pressure, light refractive tomography (LRT) is so far the only one which is noninvasive, omnidirectional, and provides time-resolved results in pascals. By exploiting all these advantages, LRT shows suitability for investigations of ultrasound pressure fields, even in the case of adjacent medium boundaries which may cause considerable sound reflections. To demonstrate the potential research possibilities offered by this technique, we apply LRT to investigating the disturbance to a pressure field caused by a hydrophone. A commercial capsule hydrophone is placed in front of an ultrasound transducer excited by 1-MHz burst signals. We reconstruct the disturbed ultrasound pressure field between the hydrophone and the transducer in both spatial and temporal dimensions. Good agreement has been achieved between the reconstructed pressure field and the prediction made by a numerical simulation. Moreover, a comparison between the results provided by LRT and hydrophone shows that multiple reflections can jeopardize the reliability of hydrophone measurement when a hydrophone is placed very close to a medium boundary (e.g., <5 mm in our case). On the contrary, LRT achieves reasonable results at all distances. Finally, as a proof of the reliability of LRT, we compare the pressure amplitudes offered by LRT and hydrophone measurements at 27 mm away from the transducer in the absence of obstacles. The comparison shows a relative difference of 7.07%.

Diamond-based capacitive micromachined ultrasonic transducers in immersion

Diamond is a superior membrane material for capacitive micromachined ultrasonic transducers (CMUTs). By using ultrananocrystalline diamond (UNCD) membrane and plasma-activated wafer bonding technology, a single diamond-based circular CMUT is demonstrated and operated in immersion for the first time. The diamond-based CMUT, biased at 100 V, is excited with a 10-cycle burst of 36 V(p-p) sine signal at 3.5 MHz. Pressure generated on a 2-D plane coincident with the normal of the CMUT is measured using a broadband hydrophone. Peak-to-peak hydrophone voltage measurements along the scan area clearly indicate the main lobe and the side lobes, as theoretically predicted by our directivity function calculations. The peak-to-peak hydrophone voltage on the axial direction of the CMUT is found to be in agreement with our theoretical calculations in the Fraunhofer region (-45 mm <y <-15 mm). The spectrum of the diamond-based CMUT is measured for a dc bias of 100 V, and ac excitation with 30-cycle bursts of 9, 36, and 54 V(p-p) sine signal. A peak response at 5.6 MHz is measured for all ac amplitudes. Overall, diamond is shown to be an applicable membrane for CMUT devices and applications.

Super-harmonic imaging: development of an interleaved phased-array transducer

For several years, the standard in ultrasound imaging has been second-harmonic imaging. A new imaging technique dubbed "super-harmonic imaging" (SHI) was recently proposed. It takes advantage of the higher - third to fifth - harmonics arising from nonlinear propagation or ultrasound-contrast-agent (UCA) response. Next to its better suppression of near-field artifacts, tissue SHI is expected to improve axial and lateral resolutions resulting in clearer images than second-harmonic imaging. When SHI is used in combination with UCAs, a better contrast-to-tissue ratio can be obtained. The use of SHI implies a large dynamic range and requires a sufficiently sensitive array over a frequency range from the transmission frequency up to its fifth harmonic (bandwidth > 130%). In this paper, we present the characteristics and performance of a new interleaved dual frequency array built chiefly for SHI. We report the rationale behind the design choice, frequencies, aperture, and piezomaterials used. The array is efficient both in transmission and reception with well-behaved transfer functions and a combined -6-dB bandwidth of 144%. In addition, there is virtually no contamination of the harmonic components by spurious transducer transmission, due to low element-to-element crosstalk (< 30 dB) and a low transmission efficiency of the odd harmonics (< 46 dB). The interleaved array presented in this article possesses ideal characteristics for SHI and is suitable for other methods like second-harmonic, subharmonic, and second-order ultrasound field (SURF) imaging.

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important. We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function. The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior. We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.

Steady state spherically focused, circular aperture beam patterns

This review was written to aid ultrasonic investigators using spherically focused transducers. It introduces a new direct method for computing steady state focused beam patterns on personal computers in nonattenuating and attenuating fluids and tissues. The method results in single integral expressions for uniform transducer excitation that can easily be altered for nonuniform surface excitation (apodization) or focused ring transducers. Procedures for verifying the accuracy of the derived equations are demonstrated. It is shown that beam diffraction errors are larger the higher the fluid or tissue attenuation. An experimental procedure is presented for measuring the effective focal length and effective aperture size of a spherically focused transducer with a single experimental measurement in a fluid with known acoustic velocity. Procedures are suggested for reducing the errors caused by beam diffraction in fluid attenuation measurements, avoiding them entirely or estimating their magnitude when they cannot be avoided.

Progress in medical ultrasound exposimetry

Biomedical applications of ultrasound have experienced tremendous growth over the past 50 years. Early work in thermal therapy and surgery soon was followed by diagnostic imaging and Doppler. Because patient safety was an important issue from the beginning, the study of methods for measuring exposure levels, and their relationship to possible biological effects, paralleled the growth of the various therapeutic and diagnostic techniques. The diverse conditions of use have presented a range of exposure measurement challenges, and the sensors and techniques used to evaluate ultrasound fields have had to evolve as new or expanded clinical applications have emerged. In this paper some of the more notable of these developments are presented and discussed. Topics covered include devices and techniques, methods of calibration, progress in standardization, and current problem areas, including the effects of nonlinear propagation. Some early methods are described, but emphasis is given to more recent work applicable to present and future uses of ultrasound in medicine and biology.

Steady state unfocused circular aperture beam patterns in nonattenuating and attenuating fluids

Single integral approximate formulas have been derived for the axial and lateral pressure magnitudes in the beam pattern of steady state unfocused circular flat piston sources radiating into nonattenuating and attenuating fluids. The nonattenuating formulas are shown to be highly accurate at shallow beam depths if a normalized form of the beam pattern is utilized. The axial depth of the beginning of the nonattenuated beam pattern far field is found to be at 6.41Y0. It is demonstrated that the nonattenuated lateral beam profile is represented at this and deeper depths by a Jinc function directivity term. Values of alpha and z are found that permit the attenuated axial pressure to be represented by a plane wave multiplicative attenuation factor. This knowledge should aid in the experimental design of high accuracy attenuation measurements. The shifts in depth of the principal axial pressure maxima and minima due to fluid attenuation are derived. Single integral approximate equations for the attenuated full beam pattern pressure are presented using complex Bessel functions.

Modeling of anomalies due to hydrophones in continuous-wave ultrasound fields

Needle and spot-poled membrane hydrophones using polyvinylidene fluoride (PVDF) sensors are widely used for characterization of biomedical ultrasound fields. It is known that, in measurements of continuous-wave (CW) fields, standing waves may be generated between the transducer and the hydrophone, distorting the field and possibly alternating the signal of the hydrophone. This study uses a three-dimensional, full-wave method to computationally simulate the distortion in the CW field caused by needle and membrane hydrophones. The physical model used in simulations is based on the linear time-harmonic wave equation, which therefore neglects the effects of nonlinear wave propagation. The significance of the distortion is examined by comparing fields emitted by 0.5-5.0 MHz planar circular transducers in the absence and presence of the hydrophones. In addition, the effect of the field distortions on the signal of the hydrophones is studied with simulated measurements. The simulations showed an observable standing wave pattern between the source and the needle hydrophone if the diameter of the needle was larger than a half of the wavelength. However, the standing waves had no clear effect on the signal of the hydrophone. The presence of membrane hydrophone in the CW field generated notable standing waves. Furthermore, the standing waves caused a periodic distortion to the signal of the membrane hydrophone.

Spatial averaging in the beam of a piston transducer

This paper presents a theoretical analysis of the spatially averaged free-field responses of phase-sensitive and phase-insensitive receivers centered in the beam of a harmonically excited piston transmitter. The responses of unfocused circular plane piston receivers are analyzed, and both unfocused and spherically focused piston transmitters are considered. A set of closed-form expressions figures prominently in the analysis. The expressions are based on the Lommel diffraction formulation which is, in turn, based on the Fresnel approximation. Although approximate, the expressions allow for quick and easy estimation of phase-sensitive or phase-insensitive unfocused piston receiver responses. It is shown that the spatial averaging effects associated with phase-sensitive and phase-insensitive receivers are virtually identical when gamma < or = 0.1, where gamma = b/a is the ratio of receiver radius b to transmitter radius a. In addition, numerical results obtained from the closed-form expressions are compared with previously reported results. The comparisons indicate that the approximate results are valid from the m = 3 maxima forward under the assumption of linear propagation when ka > 58, where k is the circular wave number. Finally, it is pointed out that the closed-form expressions may prove useful in the estimation of the potential for bioeffects associated with diagnostic ultrasound.

Experimental validation for the diffraction effect in the ultrasonic field of piston transducers and its influence on absorption and dispersion measurements

The aim of this work was to study the diffraction effects in the ultrasonic field of piston source transducers and their importance for accurate measurements of attenuation and dispersion in viscoelastic materials. In laboratory measurements, the diffraction phenomena are mainly due to the beam spread of the ultrasonic wave propagating in viscoelastic materials. This effect is essentially related to the estimated attenuation and dispersion in the material. In this work, a frequency domain system identification approach, using the maximum likelihood estimator (MLE), was applied to the measured data in order to determine a function for correcting the diffraction losses in both normal and oblique incidences for a large frequency band (300 kHz to 3 MHz). The effective radius of the used transmitter was determined by the inverse problem when ultrasonic beam propagation was investigated in a water medium. Using the estimated radius, the propagation through viscoelastic materials was established, and the acoustic parameters of these materials were estimated. Attention was paid to the determination of the attenuation and dispersion in the materials. These quantities were compared to those obtained without diffraction correction in order to see the influence of introducing the diffraction correction into the propagation model.

Wideband spherically focused PVDF acoustic sources for calibration of ultrasound hydrophone probes

Several broadband sources have been developed for the purpose of calibrating hydrophones. The specific configuration described is intended for the calibration of hydrophones In a frequency range of 1 to 40 MHz. All devices used 25 /spl mu/m film of PVDF bonded to a matched backing. Two had radii of curvatures (ROC) of 25.4 and 127 mm with f numbers of 3.8 and 19, respectively. Their active element diameter was 0.28 in (6.60 mm). The active diameter of the third source used was 25 mm, and it had an ROC of 254 mm and an f number of 10. The use of a focused element minimized frequency-dependent diffraction effects, resulting in a smooth variation of acoustic pressure at the focus from 1 to 40 MHz. Also, using a focused PVDF source permitted calibrations above 20 MHz without resorting to harmonic generation via nonlinear propagation.