Acoustic Wavefront Research Articles

Full correction for spatially distributed speed-of-sound in echo ultrasound based on measuring aberration delays via transmit beam steering

Aberrations of the acoustic wave front, caused by spatial variations of the speed-of-sound, are a main limiting factor to the diagnostic power of medical ultrasound imaging. If not accounted for, aberrations result in low resolution and increased side lobe level, over all reducing contrast in deep tissue imaging. Various techniques have been proposed for quantifying aberrations by analysing the arrival time of coherent echoes from so-called guide stars or beacons. In situations where a guide star is missing, aperture-based techniques may give ambiguous results. Moreover, they are conceptually focused on aberrators that can be approximated as a phase screen in front of the probe. We propose a novel technique, where the effect of aberration is detected in the reconstructed image as opposed to the aperture data. The varying local echo phase when changing the transmit beam steering angle directly reflects the varying arrival time of the transmit wave front. This allows sensing the angle-dependent aberration delay in a spatially resolved way, and thus aberration correction for a spatially distributed volume aberrator. In phantoms containing a cylindrical aberrator, we achieved location-independent diffraction-limited resolution as well as accurate display of echo location based on reconstructing the speed-of-sound spatially resolved. First successful volunteer results confirm the clinical potential of the proposed technique.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam’s path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque.

Impact of defectiveness on the parameters of the acoustoelectric transformations in heterogeneous non-metallic materials

The article studies acoustoelectric transformations of concrete with a crack. The research presents three-dimensional modeling and 3D visualization of wave processes in a concrete sample with a surface crack. The parameters of the electrical response are found to reflect the processes of interaction between the acoustic wave front and the defect and boundaries of the sample.

A numerical study of effects on detection height of a radio acoustic sounding system influenced by atmospheric wind and temperature

Radio acoustic sounding system (RASS) is a detection technique using the interaction between radio wave and acoustic wave to remotely measure vertical profiles of the atmospheric temperature, and usually composed of a Doppler radar with fixed beam (monostatic or bistatic) and an acoustic source with high power. By combining acoustic propagation equation and radio wave propagation equation in a disturbance medium and using a finite-difference time-domain method, a numerical model describing the interaction between acoustic wave and electric wave is constructed, and the model is used to analyze the effects of wind and temperature on detection height of RASS. In the atmospheric temperature background, the propagations of a single frequency acoustic wave packet under different wind conditions are simulated, and the scattering propagation of electric wave packets corresponding to the acoustic scatterer are analyzed and compared. Besides, the entire physical process are described from the angle of energy density. The numerical simulation results show that the propagation trajectories of both acoustic wave and radio wave backscattering echo are changed due to the existence of wind field and temperature profile. The presence of wind field results in an offset of acoustic wave front, reducing the strength and changing the trajectory of radio wave backscattering echo, so that the detection height is limited due to the reduction of receiving data. The simulation results of the acoustic wave reveal that the temperature profile mainly affects the propagation velocity of acoustic wave, while the presence of wind field may result in shifts of propagation trajectory and acoustic wave front, and the greater the wind speed, the more the horizontal shift of acoustic wave front is. The numerical analyses of scattering propagations of radio wave with the acoustic scatterer at the same height under different background atmospheric conditions manifest that the stronger the wind speed, the more the deviation of electric wave echo from the receive antenna is, and the smaller the echo intensity is when the scattering echo propagates to the same position. The theoretical calculations with the acoustic wave scatterer at different heights under the same atmospheric wind field (strong wind) background demonstrate that if the height of scattering point is reduced, the offset of the scattering echo “bunching point” at the same altitude will be greatly improved and the intensity will be enhanced, but it also means the decline of detection height. In order to improve the detection height under the background of wind field, some methods are adopted, such as using a bistatic radar antenna or increasing the reception antenna area.

Novel optoacoustic source for arbitrarily shaped acoustic wavefronts

We present a novel approach to generate arbitrary acoustic wavefronts using the optoacoustic effect on custom designed PDMS substrates. PDMS blocks are casted into the desired shape with a 3D-printed mold and coated with a layer of an optical absorber. Acoustic wavefront corresponding to the geometry of coated surface is generated by exposing this structure to nanosecond laser pulse (Nd:YAG, λ = 532 nm). For a spherical shell design, pressure pulses of amplitude up to 6.1 bar peak to peak and frequency >30 MHz could be generated. By utilizing other geometries, we focus the acoustic waves from different sections of the transmitter onto a single focal point at different time delay, thus permitting generation of double-peak acoustic pulse from a single laser pulse. Further modification of the structure permits designing of multi-foci, multi-peak acoustic pulses from a single optical pulse.

Simulation of Propagating Acoustic Wavefronts with Random Sound Speed

AbstractA method for simulating acoustic wavefronts propagating under random sound speed conditions is presented. The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase, instead of tracing rays. The Lagrangian nature often makes full-field ray solutions difficult to reconstruct. The level set method captures multiple-valued solutions on a fixed grid. It is straightforward to represent other sources of uncertainty in the input data using this model, which has an advantage over Monte Carlo approaches in that it yields an expression for the solution as a function of random variables.

Estimating waveguide parameters using horizontal and vertical arrays in the vicinity of horizontal Lloyd’s mirror in shallow water

When shallow water internal waves approach a source-receiver track, the interference between the direct and horizontally refracted acoustic paths from a broadband acoustic source was previously shown to form Horizontal Lloyd’s mirror (Badiey et al. J. Acoust. Soc. Am. 128(4), EL141–EL147, 2011). While the modal interference structure in the vertical plane may reveal arrival time for the out of plane refracted acoustic wave front, analysis of moving interference pattern along the horizontal array allows measurement of the angle of horizontal refraction and the speed of the nonlinear internal wave (NIW) in the horizontal plane. In this paper we present a full account of the movement of NIW towards a source-receive track and how we can use the received acoustic signal on an L-shaped array to estimate basic parameters of the waveguide and obtain related temporal and spatial coherence functions particularly in the vicinity of the formation of the horizontal Lloyd mirror. Numerical results using Vertical Modes and Horizontal Rays as well as 3D PE calculations are carried out to explain the experimental observations. [Work supported by ONR 322OA.]

Gigahertz Modulation of Femtosecond Time-Resolved Surface Sum-Frequency Generation Due to Acoustic Strain Pulses

We study the properties of aqueous solution/air interfaces with time-resolved surface sum-frequency generation (SFG) spectroscopy. Using this technique, we monitor the change in SFG signal following the excitation of the water hydroxyl stretch vibrations with a strong ultrashort infrared pump pulse. We observe that, in addition to the excitation-induced changes in the signal resulting from vibrational excitation and relaxation on a time scale of picoseconds, the infrared excitation also induces a modulation of the SFG signal with a period of ∼180 ps. This modulation is caused by the interference between the SFG field directly radiated away from the air/liquid interface and the SFG field reflected or generated at the acoustic strain wavefront that is created by the infrared excitation pulse. The modulation is observed to be much stronger for aqueous salt solutions than for pure water, and the phase of the oscillations depends on the nature of the dissolved salt. This dependence of the phase can be explained from the differences in surface propensities of the ions of the different salts, giving rise to different net orientation of the interfacial water species.

Tracing Three-Dimensional Acoustic Wavefronts in Inhomogeneous, Moving Media

We present a numerical implementation of an alternative formulation of the geometrical, or ray, acoustics, where wavefronts rather than rays are the primary objects. Rays are recovered as a by-product of wavefront tracing. The alternative formulation of the geometrical acoustics is motivated, first, by the observation that wavefronts are often more stable than rays at long-range sound propagation, and, second, by a need for computationally efficient modeling of high-frequency acoustic fields in three-dimensionally inhomogeneous, moving or motionless fluids. Wavefronts are found as a finite-difference solution to a system of partial differential equations, which is equivalent to the eikonal equation and is a direct implementation of the intuitive Huygens' wavefront construction. The finite-difference algorithm is an extension of the approach originally developed in the framework of an open source Madagascar project. Benchmark problems, which admit exact, analytic solutions of the eikonal equation, are formulated and utilized to verify the finite-difference wavefront tracing algorithm. Huygens' wavefront tracing (HWT) is applied to modeling sound propagation in three-dimensionally inhomogeneous ocean and atmosphere.

On the damping effect of gas rarefaction on propagation of acoustic waves in a microchannel

We consider the response of a gas in a microchannel to instantaneous (small-amplitude) non-periodic motion of its boundaries in the normal direction. The problem is formulated for an ideal monatomic gas using the Bhatnagar, Gross, and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers. Analysis combines analytical (collisionless and continuum-limit) solutions with numerical (low-variance Monte Carlo and linearized BGK) calculations. Gas flow, driven by motion of the boundaries, consists of a sequence of propagating and reflected pressure waves, decaying in time towards a final equilibrium state. Gas rarefaction is shown to have a “damping effect” on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. The effect of having two moving boundaries, compared to only one considered in previous studies of time-periodic systems, is investigated. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuum-limit solution, however, should be considered with care at early times near the location of acoustic wavefronts, where relatively sharp flow-field variations result in effective increase in the value of local Knudsen number.

Broadband field rotator based on acoustic metamaterials

We have theoretically designed and experimentally realized a metamaterial-based acoustic field rotator that can be tailored to rotate the acoustic wavefront by a certain angle. For airborne sound, the designed field rotator simply comprises an array of identical plastic plates. The rotation effect and the broadband functionality of the resulting device have been demonstrated both numerically and experimentally. Excellent agreement is observed between the numerical simulation and experimental results. The realization of acoustic field rotator has offered possibility of acoustic manipulation and may have potential application in situations in need of special controls of acoustic wave.

Manipulating Acoustic Wavefront by Inhomogeneous Impedance and Steerable Extraordinary Reflection

We unveil the connection between the acoustic impedance along a flat surface and the reflected acoustic wavefront, in order to empower a wide wariety of novel applications in acoustic community. Our designed flat surface can generate double reflections: the ordinary reflection and the extraordinary one whose wavefront is manipulated by the proposed impedance-governed generalized Snell's law of reflection (IGSL). IGSL is based on Green's function and integral equation, instead of Fermat's principle for optical wavefront manipulation. Remarkably, via the adjustment of the designed specific acoustic impedance, extraordinary reflection can be steered for unprecedented acoustic wavefront while that ordinary reflection can be surprisingly switched on or off. The realization of the complex discontinuity of the impedance surface has been proposed using Helmholtz resonators.

Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces

The introduction of metasurfaces has renewed the Snell's law and opened up new degrees of freedom to tailor the optical wavefront at will. Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces. The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space. By careful selection of the phase profiles in the transverse direction of the metasurfaces, some fascinating wavefront engineering phenomena are demonstrated, such as anomalous reflections, conversion of propagating waves into surface waves, planar aberration-free lens and nondiffracting Bessel beam generated by planar acoustic axicon. Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

Investigation of the Velocity Profiles in a Ninety-Degree Curved Standing Wave Resonator with Particle Image Velocimetry

Travelling wave thermoacoustic heat engines have been reported to have a higher efficiency than the standing wave ones. The former are generally large systems which consist of toroidal shape resonators. While standing wave heat engines are inherently smaller, a reduction in size could be considered which may involve curvatures as compared to the straight tube conventional systems. However, as with the streaming losses in the travelling wave resonators, losses due to the curvature may be generated. This study involves preliminary experimental measurements using the Particle Image Velocimetry (PIV) method to analyze the velocity profiles in a standing wave resonator before and after a ninety degree curvature. This design can reduce the space generally occupied by the straight standing wave resonator. The overall length of the resonator fits a quarter wavelength wave based on the straight closed-end tube type. The working gas is air at 1 atmospheric pressure. Results have shown that the velocity profiles after the stack but before the curvature exhibit clear straight paths up just as reported elsewhere. Signs of disordered motion could be observed just before the bend and the pattern continues until after the curvature. The results are obtained before one periodic cycle and before the acoustic wave front hit the tube end. The trend is expected to affect the overall thermoacoustic performance of the engine as returning gas particles interact with the oncoming particles that pass by the curvature.

Turbulent boundary-layer noise: direct radiation at Mach number 0.5

AbstractBoundary layers constitute a fundamental source of aerodynamic noise. A turbulent boundary layer over a plane wall can provide an indirect contribution to the noise by exciting the structure and a direct noise contribution. The latter part can play a significant role even if its intensity is very low, explaining why it is difficult to measure. In the present study, the aerodynamic noise generated by a spatially developing turbulent boundary layer is computed directly by solving the compressible Navier–Stokes equations. This numerical experiment aims at giving some insight into the noise radiation characteristics. The acoustic wavefronts have a large wavelength and are oriented in the direction opposite to the flow. Their amplitude is only 0.7 % of the aerodynamic pressure for a flat-plate flow at Mach 0.5. The particular directivity is mainly explained by convection effects by the mean flow, giving an indication about the compactness of the sources. These vortical events correspond to low frequencies and thus have a large lifetime. They cannot be directly associated with the main structures populating the boundary layer such as hairpin or horseshoe vortices. The analysis of the wall pressure can provide a picture of the flow in the wavenumber–frequency space. The main features of wall pressure beneath a turbulent boundary layer as described in the literature are well reproduced. The acoustic domain, corresponding to supersonic wavenumbers, is detectable but can hardly be separated from the convective ridge at this relatively high speed. This is also due to the low frequencies of sound emission as noted previously.

Speed‐of‐sound compensated photoacoustic tomography for accurate imaging

In most photoacoustic (PA) tomographic reconstructions, variations in speed-of-sound (SOS) of the subject are neglected under the assumption of acoustic homogeneity. Biological tissue with spatially heterogeneous SOS cannot be accurately reconstructed under this assumption. The authors present experimental and image reconstruction methods with which 2D SOS distributions can be accurately acquired and reconstructed, and with which the SOS map can be used subsequently to reconstruct highly accurate PA tomograms. The authors begin with a 2D iterative reconstruction approach in an ultrasound transmission tomography setting, which uses ray refracted paths instead of straight ray paths to recover accurate SOS images of the subject. Subsequently, they use the SOS distribution in a new 2D iterative PA reconstruction approach, where refraction of rays originating from PA sources is accounted for in accurately retrieving the distribution of these sources. Both the SOS reconstruction and SOS-compensated PA reconstruction methods utilize the Eikonal equation to model acoustic wavefront propagation. The equation is solved using a high accuracy fast marching method. The authors validated the new reconstruction algorithms using numerical phantoms. For experiments they utilized the recently introduced PER-PACT method which can be used to simultaneously acquire SOS and PA data from subjects. It is first confirmed that it is important to take SOS inhomogeneities into account in high resolution PA tomography. The iterative reconstruction algorithms, that model acoustic refractive effects, in reconstructing SOS distributions, and subsequently using these distributions to correct PA tomograms, yield artifact-free highly accurate images. The approach of using the hybrid measurement method and the new reconstruction algorithms is successful in substantially improving the quality of PA images with a minimization of blurring and artifacts.

An Application of the Level Set Method to Underwater Acoustic Propagation

An algorithm for computing wavefronts, based on the high frequency approximation to the wave equation, is presented. This technique applies the level set method to underwater acoustic wavefront propagation in the time domain. The level set method allows for computation of the acoustic phase function using established numerical techniques to solve a first order transport equation to a desired order of accuracy. Traditional methods for solving the eikonal equation directly on a fixed grid limit one to only the first arrivals, so these approaches are not useful when multi-path propagation is present. Applying the level set model to the problem allows for the time domain computation of the phase function on a fixed grid, without having to restrict to first arrival times. The implementation presented has no restrictions on range dependence or direction of travel, and offers improved efficiency over solving the full wave equation which under the high frequency assumption requires a large number of grid points to resolve the highly oscillatory solutions. Boundary conditions are discussed, and an approach is suggested for producing good results in the presence of boundary reflections. An efficient method to compute the amplitude from the level set method solutions is also presented. Comparisons to analytical solutions are presented where available, and numerical results are validated by comparing results with exact solutions where available, a full wave equation solver, and with wavefronts extracted from ray tracing software.

Numerical Study of Mach Number and Thermal Effects on Sound Radiation by a Mixing Layer

Mach number and thermal effects on the mechanisms of sound generation and propagation are investigated in spatially evolving two-dimensional isothermal and non-isothermal mixing layers at Mach number ranging from 0.2 to 0.4 and Reynolds number of 400. A characteristic-based formulation is used to solve by direct numerical simulation the compressible Navier-Stokes equations using high-order schemes. The radiated sound is directly computed in a domain that includes both the near-field aerodynamic source region and the far-field sound propagation. In the isothermal mixing layer, Mach number effects may be identified in the acoustic field through an increase of the directivity associated with the non-compactness of the acoustic sources. Baroclinic instability effects may be recognized in the non-isothermal mixing layer, as the presence of counter-rotating vorticity layers, the resulting acoustic sources being found less efficient. An analysis based on the acoustic analogy shows that the directivity increase with the Mach number can be associated with the emergence of density fluctuations of weak amplitude but very efficient in terms of noise generation at shallow angle. This influence, combined with convection and refraction effects, is found to shape the acoustic wavefront pattern depending on the Mach number.

Theory of the sound field fluctuations in the presence of internal waves due to adiabatic mechanism of interaction

In the presence of moving nonlinear internal waves character of interaction between sound field and internal waves depends on angle between direction of an acoustic track and wave front of internal waves (mode coupling, horizontal refraction or adiabatic regime) [JASA, vol. (122), pp. 747-760, 2007]. In particular, if this angle is about 15-20 degrees there should be adiabatic mechanism. Adiabatic regime of propagation means that variations of the sound field follow variations of the sound speed profile. In this paper similar situation is considered when wave front of the train of internal waves crosses the acoustic track at the angle about 15 degrees. Theoretical modeling shows specific features of adiabatic fluctuations: variations of shape of waveguide modes, fluctuations of amplitudes (excitation coefficients) of the corresponding modes and phase fluctuations. These fluctuations can be separated in time on dependence on position of the train. Results of modeling are compared with experimental data [shown in accompanying paper, Badiey et al.] and are in good agreement. This work was supported by ONR and RFBR.

Observation of sound fluctuations in presence of internal waves: Difference between refractive and adiabatic regimes

Angular dependence of sound field on the internal solitary wave propagation in shallow water has been previously shown [JASA, vol.122, p747-760, 2007]. In the presence of moving nonlinear internal waves, the interaction between sound field and internal waves can vary from refractive, to adiabatic, and mode coupling regimes. The mechanism is largely dependent on the angle between the direction of an acoustic track and wave front of internal waves. For small angles, refraction of horizontal field (focusing and de-focusing) can occur. However, for larger angles, the characteristics of the interaction between the acoustic field and internal waves is very different. For example for angle of about 15-20 degrees, the variations of the sound field follow variations of the sound speed profile while for the angle of about 5 degrees, focusing is observed. In this paper experimental observations and the corresponding modeling results showing the difference between the sound field for the small and larger angles are presented. This observation has prompted theoretical investigation [shown in an accompanying paper, Katsnelson, Badiey, et al.] showing the analytical aspect of the problem. Good agreement between the model and the experimental data is shown. [Work was supported by ONR.]