Ray Acoustic Model Research Articles

A composite spread spectrum sequence for underwater acoustic signal acquisition

AbstractSpread spectrum technology has been widely employed for positioning and communicating with autonomous underwater vehicles (AUVs), but conventional spread spectrum sequences lack confidentiality and reliability in UWA channel. Considering the limitations of conventional sequences and the characteristics of underwater acoustic (UWA) channel, a composite chaotic orthogonal sequence (CCOS) based on the UWA channel is proposed. The confidentiality of the CCOS is superior to that of the m‐sequence, while the autocorrelation performance of the CCOS is superior to that of the orthogonal sequence. Moreover, the CCOS can compensate for the imbalance of logistic chaotic sequence when assigned certain initial values. Acquisition is a crucial component of accessing the spread spectrum signal; therefore, the acquisition performance indicates the applicability of the CCOS. The source–target model is established to simulate communication with an underwater moving target. To simulate the acquisition process, a parallel algorithm based on fast Fourier transform is adopted, and the entire simulation process is completed based on the BELLHOP ray acoustic model. Through data processing, the Doppler shift error is less than half of the frequency‐search element. Furthermore, the acquisition probabilities of the CCOS with different numbers of bits are over 90%, which demonstrates the reliability of the CCOS.

Simulation-corrected focusing to the vertebral canal

Phased arrays have long been used to deliver focused ultrasound to the brain, but applications in the spinal cord remain comparatively unexplored. This is largely due to the aberrating effect of vertebral bone on the incoming wavefront, where variable density and complex geometry distort the pressure field in the canal. For controlled focusing, phase and amplitude corrections must therefore be calculated in advance. Here, we validate a previously-developed ray acoustics model for transvertebral focusing with a bilateral spine-specific array. Benchtop trials were conducted with ex vivo human vertebrae and ray acoustics beamforming was compared to a geometric baseline and hydrophone-corrected gold standard. Planar shift in the 90% contour was evaluated via raster scans of the sagittal and coronal planes. Ray acoustics correction reduced mean sagittal shift from 1.76 ± 0.79 mm to 1.63 ± 0.86 mm and reduced mean coronal shift from 0.99 ± 0.54 mm to 0.76 ± 0.63 mm, while hydrophone correction produced mean sagittal and coronal shifts of 1.40 ± 0.83 mm and 0.53 ± 0.47 mm, respectively. Large variance in simulation-corrected results is hypothesized to stem from nonuniform attenuation and intervertebral acoustic windows, a possibility that will be explored in future in silico and benchtop work.

Calculation for Acoustic Radiation Force from Rectangular Weakly Focusing Transducer Using the Ray Acoustic Model

Calculation for Acoustic Radiation Force from Rectangular Weakly Focusing Transducer Using the Ray Acoustic Model

Improvement of Seafloor Positioning Through Correction of Sound Speed Profile Temporal Variation

Dear Editor, This letter proposes a high-precision seafloor transponder positioning method based on the correction of sound speed profile (SSP) temporal variation. In the proposed method, the ocean sound speed error is modeled as the temporal variation of a background SSP, and the linearized expression of the acoustic travel time with respect to the sound speed coefficient is derived based on the ray acoustic model. Moreover, the proposed method introduces the constraint of acoustic ranging observations between seafloor transponders and determines the weights of travel time and ranging observations using Akaike's Bayesian information criterion (ABIC) to reduce the positioning error caused by the correlation between sound speed and position parameters. The experimental results in the South China Sea show that the proposed method performs better than the global navigation satellite system-acoustic ranging combined positioning solver (GARPOS) [1], in terms of rigid distance errors and long baseline positioning accuracy.

Establishing density-dependent longitudinal sound speed in the vertebral lamina.

Focused ultrasound treatments of the spinal cord may be facilitated using a phased array transducer and beamforming to correct spine-induced focal aberrations. Simulations can non-invasively calculate aberration corrections using x-ray computed tomography (CT) data that are correlated to density (ρ) and longitudinal sound speed (cL). We aimed to optimize vertebral lamina-specific cL(ρ) functions at a physiological temperature (37 °C) to maximize time domain simulation accuracy. Odd-numbered ex vivo human thoracic vertebrae were imaged with a clinical CT-scanner (0.511 × 0.511 × 0.5 mm), then sonicated with a transducer (514 kHz) focused on the canal via the vertebral lamina. Vertebra-induced signal time shifts were extracted from pressure waveforms recorded within the canals. Measurements were repeated 5× per vertebra, with 2.5 mm vertical vertebra shifts between measurements. Linear functions relating cL with CT-derived density were optimized. The optimized function was cL(ρ)=0.35(ρ-ρw)+ cL,w m/s, where w denotes water, giving the tested laminae a mean bulk density of 1600 ± 30 kg/m3 and a mean bulk cL of 1670 ± 60 m/s. The optimized lamina cL(ρ) function was accurate to λ/16 when implemented in a multi-layered ray acoustics model. This modelling accuracy will improve trans-spine ultrasound beamforming.

Simulating transvertebral ultrasound propagation with a multi-layered ray acoustics model

The simulation accuracy of transvertebral ultrasound propagation using a multi-layered ray acoustics model based on CT-derived vertebral geometry was investigated through comparison with experimental measurements of pressure fields in ex vivo human vertebral foramen. A spherically focused transducer (5 cm diameter, f-number 1.2, 514 kHz) was geometrically focused to the centre of individual thoracic vertebral foramen, through the posterior bony elements. Transducer propagation paths through the laminae and the spinous processes were tested. Simulation transducer-vertebra configurations were registered to experiment transducer-vertebra configurations, and simulation accuracy of the simulation model was evaluated for predicting maximum transmitted pressure to the canal, voxel pressure in the canal, and focal distortion. Accuracy in predicting maximum transmitted pressure was calculated by vertebra, and it is shown that simulation predicts maximum pressure with a greater degree of accuracy than a vertebra-specific insertion loss. Simulation error in voxel pressure was evaluated using root-mean-square error and cross-correlation, and found to be similar to the water-only case. Simulation accuracy in predicting focal distortion was evaluated by comparing experiment and simulation maximum pressure location and weighted >50% focal volume location. Average simulation error across all measurements and simulations in maximum pressure location and weighted >50% focal volume location were 2.3 mm and 1.5 mm, respectively. These errors are small relative to the dimensions of the transducer focus (4.9 mm full width half maximum), the spinal cord (10 mm diameter), and vertebral canal diameter (15–20 mm diameter). These results suggest that ray acoustics can be applied to simulating transvertebral ultrasound propagation.

A Ray Acoustics Model for the Propagation of Aircraft Noise through the Atmosphere

A ray-tracing tool, called RAYTRAC, has been developed to compute the propagation of aircraft noise through a stratified atmosphere. The mathematical model on which RAYTRAC is based is derived from first principles, i.e. the linearized Euler equations for a non-uniform atmosphere. The main result of the model consists of two equations:one for the location of the rays and one for the change in amplitude along each ray. An analysis of these equations is given with respect to their possible solutions under various atmospheric circumstances. Also an efficient iteration procedure is presented that finds the ray connecting the source and a specific observer point. It is shown how multiple rays can be added, with incorporation of a reflecting surface. Finally, the tool is demonstrated by application to two examples that are representative for an aircraft emitting sound to an observer on the ground.

Transcranial passive acoustic mapping with hemispherical sparse arrays using CT-based skull-specific aberration corrections: a simulation study

The feasibility of transcranial passive acoustic mapping with hemispherical sparse arrays (30 cm diameter, 16 to 1372 elements, 2.48 mm receiver diameter) using CT-based aberration corrections was investigated via numerical simulations. A multi-layered ray acoustic transcranial ultrasound propagation model based on CT-derived skull morphology was developed. By incorporating skull-specific aberration corrections into a conventional passive beamforming algorithm (Norton and Won 2000 IEEE Trans. Geosci. Remote Sens. 38 1337–43), simulated acoustic source fields representing the emissions from acoustically-stimulated microbubbles were spatially mapped through three digitized human skulls, with the transskull reconstructions closely matching the water-path control images. Image quality was quantified based on main lobe beamwidths, peak sidelobe ratio, and image signal-to-noise ratio. The effects on the resulting image quality of the source’s emission frequency and location within the skull cavity, the array sparsity and element configuration, the receiver element sensitivity, and the specific skull morphology were all investigated. The system’s resolution capabilities were also estimated for various degrees of array sparsity. Passive imaging of acoustic sources through an intact skull was shown possible with sparse hemispherical imaging arrays. This technique may be useful for the monitoring and control of transcranial focused ultrasound (FUS) treatments, particularly non-thermal, cavitation-mediated applications such as FUS-induced blood–brain barrier disruption or sonothrombolysis, for which no real-time monitoring techniques currently exist.

Numerical analysis for transverse microbead trapping using 30 MHz focused ultrasound in ray acoustics regime

Numerical analysis for transverse microbead trapping using 30 MHz focused ultrasound in ray acoustics regime

Simulations of transcranial passive acoustic mapping with hemispherical sparse arrays using computed tomography-based aberration corrections

Passive acoustic mapping (PAM) is receiving increasing interest as a method for monitoring focused ultrasound (FUS) therapy. PAM would be beneficial during transcranial cavitation-enhanced FUS treatments, particularly non-thermal, cavitation-mediated applications such as FUS-induced blood–brain barrier disruption or sonothrombolysis, for which no real-time monitoring technique currently exists. However, the use of PAM in the brain is complicated by the presence of the skull bone. If not properly accounted for, skull-induced aberrations of propagating cavitation emissions will lead to image distortion and artifacts upon reconstruction. Through the use of numerical simulations, this study investigated the feasibility of transcranial PAM via hemispherical sparse hydrophone arrays. A multi-layered ray acoustic transcranial ultrasound propagation model based on computed tomography-derived skull morphology was developed. By incorporating skull-specific aberration corrections into a conventional passive beamforming algorithm [Norton and Won, IEEE Trans. Geosci. Remote Sens. 38, 1337–1343 (2000)], simulated acoustic source fields were spatially mapped through digitized human skulls. The effects of array sparsity and receiver element configuration on the formation of passive acoustic maps were examined. Multiple source locations were simulated to determine the imageable volume within the skull cavity. Finally, the reconstruction algorithm's sensitivity to noise was explored.

Radiation force calculation and acoustic power measurement for a cylindrical concave transducer based on the ray acoustic model

New relationships between the radiation force and the acoustic power for a cylindrical concave transducer were derived based on the ray acoustic model. The performance of this model is compared with that of the far-field integration model. The numerical results showed excellent agreement. Thus, these two models can be applied in the correction of measured results. Moreover, the formula based on the ray acoustic model can be applied more widely in practice because of its simplicity. The experimental results demonstrated further the reliability of the relationships between the radiation force and the acoustic power in theory, and the feasibility of using cylindrical concave transducers based on the ray acoustic model in practice.

A ray model of sound focusing with a balloon lens: An experiment for high school students

A weather balloon filled with carbon dioxide gas is used as a positive spherical acoustic lens. High frequency but audible sound from a circular loudspeaker ensonifies the balloon and produces increased sound pressure levels in a region along the principal axis according to a ray acoustics model. This enhancement was measured experimentally and was found to agree with theory. The possibility that interference from reflected sound off walls or the floor could mask or mimic the expected focusing was countered by calculating and measuring within a "shadow zone" in which only direct rays or rays refracted by the balloon exist by the method of Fresnel volumes. The experiment described in this paper would be a suitable learning experience for junior high and high school students showing how rays and Snell's law apply to sound as well as light and giving them a measurable predicted focal region for enhanced sound pressure levels.

Calibration of sound forces in acoustic traps

A two-dimensional or transverse acoustic trapping and its capability to noninvasively manipulate micrometersized particles with focused sound beams were experimentally demonstrated in our previous work. To apply this technique, as in optical tweezers, for studying mechanical properties of and interactions among biological particles such as cells, the trapping forces must be calibrated against known forces, i.e., viscous drag forces exerted by fluid flows. The trapping forces and the trap stiffness were measured under various conditions and the results were reported in this paper. In the current experimental arrangement, because the trapped particles were positioned against an acoustically transparent mylar membrane, the ultrasound beam intensity distribution near the membrane must be carefully considered. The total intensity field (the sum of incident and scattering intensity fields) around the droplet was thus computed by finite element analysis (FEA) with the membrane included, and it was then used in the ray acoustics model to calculate the trapping forces. The membrane effect on trapping forces was discussed by comparing effective beam widths with and without the membrane. The FEA results found that the broader beam width, caused by the scattered beams from the neighboring membrane and the droplet, resulted in the lower intensity, or smaller force, on the droplet. The experimental results showed that the measured forces were as high as 64 nN. The trap stiffness, approximated as a linear spring, was estimated by linear regressions and found to be 1.3 to 4.4 nN/μm, which was on a larger scale than that of optical trapping estimated for red blood cells, a few tenths of piconewtons/nanometer. The experimental and theoretical results were in good agreement.

Ray identification theory in ocean acoustic tomography

The identification problem in multipath ocean acoustic tomography is not only one of the more crucial but also one of the more difficult signal processing problems to solve for further inverse studies. It is only recently that a tool, based on the Bayesian decision theory and close to the data association problem in RADAR, has been proposed by Mauuary and Moura. It fundamentally uses prior information ocean variability which transits through the ray acoustic model. It also statistically solves the ray identification problem with a Bayesian strategy. Despite the inherent complexity of resulting algorithms, a first successful attempt has been made on a French tomographic set of data (GASTOM). Some simplifications and further experimental use are now being investigated on the Mediteranean set of data (THETIS). With another approach given by Send, those are the only practical tools, but, they are sufficiently general to solve the identification problem in the most difficult conditions given by unresolved and unstable data. Both solutions are very close to the generalized Kalman filter theory and joint use of these algorithms in data assimilation models can be expected.

Approximate ray synthesis of the surface fields of a submerged elastic cylindrical shell with hemispherical endcaps

Combining the available ray acoustic algorithms descriptive of submerged cylindrical and spherical shells, this paper formulates the pressure and velocity distributions on a hemispherically capped cylindrical shell which is immersed in an acoustic fluid and insonified by an obliquely incident plane wave. As the first ray acoustic model for a noncanonical (nonseparable) shell geometry of considerable current interest, it neglects wave coupling and diffraction due to curvature discontinuities at the junctures as well as contributions from the leaky waves excited through the endcaps. Nevertheless, by matching the surface wave vectors along the joints, due account is taken of leaky wave propagation on, and radiation from, the hemispheres. The total pressure or velocity on the cylinder—their ray constituents are related to each other by appropriate impedances—is then synthesized by a modified geometrical acoustics field, as developed recently, and a supersonic membrane wave field. The latter is contributed by the surface leaky rays successively traveling to the observer along helical trajectories and great circles on the cylinder and hemispheres; such rays are excited through phase matching by a series of incident rays, which are in turn identified by reciprocal ray tracing so as to quantify the leaky wave contribution. Numerical implementation is also performed here. The results are compared with the reference solution generated at the Naval Research Laboratory (NRL) by boundary element/finite element codes.

Near-field ray acoustic response of submerged elastic spherical shells

The presence of conspicuous penumbra regions in near-field wave scattering renders asymptotic treatment of ray integrals—by Fock’s theory, for instance—extremely involved, especially for elastic shell–fluid boundary conditions. A modified ray acoustic model that avoids these intricacies as well as those associated with reflected-leaky wave transition regions has recently been proposed, and proved very accurate at moderate and high frequencies for the thin cylindrical shell prototype [J. M. Ho, J. Acoust. Soc. Am. 96, 515–524 (1994)]. Following this approach, this paper discusses the ray synthesis of the on- and off-surface acoustic response of a submerged empty thin spherical shell insonified by an acoustic plane wave. In particular, the two spectral integrals that would yield the incident and reflected ray fields by saddle point reductions are combined into a single integral representing the modified geometrical acoustics field, which may be so rearranged that it is merely the continuum form of the discrete (normal mode series) solution for the total field, thereby facilitating its numerical implementation. The complementary leaky compressional wave fields are described by spectral integrals characterizing multiple guided wave circumnavigations around the shell and are evaluated by residue calculus as usual. It is shown through extensive numerical results that, for the thin spherical shell, the modified ray algorithm also accurately reconstructs the acoustic near field in the entire latitudinal domain provided ka≥1 or so (where k is the fluid acoustic wave number and a is the shell mean radius).

Frequency and time domain Bragg-modulated ray acoustics for truncated periodic arrays

Many scenarios in underwater acoustics involve radiation from, or scattering by, configurations with periodic or quasiperiodic features. Depending on the operating conditions, the acoustic field generated by these processes carries the gross imprint of periodicity or quasiperiodicity, without or with effects of truncation, regardless of the detailed structure in each unit cell. To understand and quantify the phenomenology under time harmonic and pulsed excitation, especially in the mid- to high-frequency regime where the width of each cell can cover many wavelengths, it is instructive to explore alternative parametrizations that emphasize, respectively, the nondispersive direct radiation from each cell and the dispersive collective treatment of strict or weakly perturbed periodicity, without and with truncations. The prototype configuration for this two-dimensional study is a finite periodic array of linearly phased parallel filamentary elements. The formulation makes use of Poisson summation and subsequent asymptotics applied to the finite array, and is parametrized in the configuration-spectrum phase space; it highlights the connection between local and global phenomena in both the space-time and wave-number-frequency domains, with a view toward phase-space data processing. Formal aspects and general principles are presented in this paper and are applied to infinite and truncated periodic arrays to illustrate how known results obtained by other methods are recovered with the Poisson-based algorithm. The outcome is a new frequency and time domain Bragg-modulated ray acoustic model that generalizes the nonuniform and uniform ray fields of the geometrical theory of diffraction, so as to include effects of periodic dispersion, with truncations. Under transient conditions, such dispersion gives rise to new time domain Bragg modes.

Ray acoustic modeling of the surface fields of a submerged elastic cylindrical shell with hemispherical endcaps

Combining the available ray acoustic algorithms descriptive of submerged thin cylindrical and spherical shells, this paper formulates the pressure and velocity distributions on a hemispherically capped cylindrical shell insonified by an obliquely incident acoustic plane wave. As the first ray acoustic model for a noncanonical shell geometry of considerable current interest, it neglects wave coupling and diffraction due to curvature discontinuities at the junctures as well as contributions from the leaky waves excited through the endcaps. This might be justifiable, because the junctions are not sharp edges (i.e., the normals are continuous) and because the cylinder under consideration is very long compared to the radius. By matching the surface wave vector along the joints, however, due account is taken of leaky wave propagation on, and radiation from, the hemispheres. The total pressure or velocity—their ray constituents are related to each other by appropriate impedances—on the cylinder is then synthesiz...

Geometrical ray acoustic model in the case of a linear sound‐speed profile for outdoor sound propagation

To estimate the effects of temperature, wind, and atmospheric turbulence on the outdoor sound propagation, a heuristic model based on the geometrical acoustic approximation has been developed. This model assumes a constant linear sound‐speed gradient, which allows an analytical determination of the direct and reflected curved ray paths and of all the possible additional rays that may appear between a source and a receiver over the ground in presence of a positive sound‐speed gradient. The total sound pressure at the receiver is computed by summing the contribution of all the partially coherent rays. In presence of a negative sound‐speed gradient, the receiver may be located in the shadow zone. In that case, the sound‐pressure level at the receiver is evaluated with the diffraction solution proposed by Berry and Daigle [J. Acoust. Soc. Am. 83, 2042–2058 (1988)]. Experimental results found in the literature for wind speed gradient and experimental results obtained during summer 1990 for temperature gradient will be presented and compared with the model.

Pulse propagation at long ranges in an underwater surface duct

In a previous communication, we have presented a hybrid‐ray‐mode theory for coping with convergence difficulties occurring near the source depth in the ray acoustic model of long range propagation in a surface duct. The hybrid formulation replaces the problematic acoustic ray fields with a uniquely defined group of surface ducted modes, while retaining the legitimate ray fields intact. Detailed numerical calculations for a high frequency Gaussian pulse propagating in a model environment with exponential velocity profile in depth have now revealed the inherent features of the hybrid scheme. With a solution obtained by modal summation as a reference, the hybrid form is found to be accurate and numerically efficient. It is also capable of explaining in cogent physical terms the features of the received signal by blending automatically and self‐consistently the ray arrivals dominant at early times with mode arrivals dominant at later times. The interpretations follow from separate examination of ray fields and mode fields, with clear indications of ray field failure in the transition region noted above. [Work supported by ONR Underwater Acoustics.]