Ultrasound fields in attenuating media

For medical ultrasonic imaging and for nondestructive testing, the attenuation of pressure waves and the resulting shift in wave velocity are important features in commonly used transmission media such as biological tissue. An algorithm for the numerical evaluation of pressure field distributions generated by ultrasonic transducers is presented. The attenuation and dispersion of the sound transmission medium are taken into consideration. The sound fields are computed numerically for continuous wave as well as pulse excitation. The transducer has plane or gently curved geometry and is embedded in a plane rigid baffle. The numerically determined pressure fields are presented as 3D plots, as gray-scale images for a fixed time stamp (like a snapshot), or as isobars regarding the maximum values over time for each local point in the area under investigation. The algorithm described here can be utilized as a tool for design of ultrasound transducers, especially array antennas.     

超声检测用压电换能器瞬态特性可控可调

超声检测用压电换能器瞬态特性主要包括瞬态空间响应和瞬态时间响应。本文通过调整控制换能器和激励源,实现瞬态空间响应和瞬态时间响应的某些特性的可控可调。其中包括在空间响应方面消除边缘波以获得平行声束和消除平面波以获得聚焦绳声束;在时间响应方面,调整换能器的背衬阻抗以获得可调首次波幅比和调整换能器结构和激励电信号以获得任意检测信号等。     

The influence of progressive light diffraction in Debye-Sears phenomena

Two previous theories of Debye-Sears diffraction of light by plane ultrasonic waves are summarized. The theories assume that significant modulation of the light wave occurs in both phase and amplitude. In our own approach account is taken of both curvature of the light rays inside the ultrasonic beam and diffraction of the system alone at the exit plane, neglecting any diffraction effect in the liquid itself. In the Hargrove's method progressive diffraction in the medium is considered. Results from these theories are compared with experimental data obtained at a frequency of 5 MHz with ultrasonic waves having large amplitude and beamwidth (50 mm).     

Simulation of 3-D radiation beam patterns propagated through a planar interface from ultrasonic phased array transducers

Phased array transducers are quite often mounted on solid wedges with specific angles in many practical ultrasonic inspections of thin plates <10 mm in their thickness or welded joints with convex crowns. For the reliable application of phased array techniques with testing set-up, it is essential to have thorough understanding on the characteristics of radiation beam pattern produced in the interrogated medium. To address such a need, this paper proposes a systematic way to calculate full 3-D radiation beam patterns produced in the interrogated solid medium by phased array transducers mounted on a solid wedge. In order to investigate the characteristics of radiation beam patterns in steel, simulation is carried out for 7.5 MHz array transducers mounted on an acrylic wedge with the angle of 15.45 degrees with various of steering angles and/or focal planes.     

一维超声光子晶体禁带结构分析

超声波在介质中传播时可以引起介质的折射率发生周期变化,当光波垂直于超声波的传播方向时,这种介质可以被用来作为光栅使用,称为超声光栅。当光波沿超声波的传播方向通过这种介质时,它还可以用作一维光子晶体,并称其为一维超声光子晶体(1D-USPC)。利用平面波法证明了一维超声光子晶体具有一般一维周期层叠结构光子晶体的禁带特征。同时这种光子禁带是可以通过超声波的波长和振幅来改变的,这就为控制光的行为方面提供另一种新的方法。     

Wave guide imaging through Time Domain Topological Energy

Time Domain Topological Energy (TDTE), uses the reflected ultrasonic field recorded by an array of transducers placed on the boundary of the inspected medium. Two numerical determinations (forward and adjoint problems) of the acoustical field inside a reference medium are necessary to compute an image. Topological Energy is defined as a variation of topological sensitivity or gradient and comes from the field of mathematical optimisation. Recent developments for Non-Destructive Testing have shown the analogy with Time Reversal concepts. Time Reversal mirrors have been employed for various applications in a wide number of situations including wave guides where very good re-focalization performances have been obtained with a reduced number of transducers instead of an array of transducers. Moreover recent works have enlightened that the reverberation properties of a wave guide allow to re-focalize using Time Reversal with only one transducer. For TDTE imaging a single transducer placed at one end of a wave guide has been modelled. The boundaries of the wave guide create virtual sources that can be understood as a virtual array of transducers. Numerical and experimental results are presented using TDTE and a single transducer in a wave guide for targets and conditions of increasing complexity.     

Beam profile measurements and simulations for ultrasonic transducers operating in air

This paper outlines a method that has been implemented to predict and measure the acoustic radiation generated by ultrasonic transducers operating into air in continuous wave mode. Commencing with both arbitrary surface displacement data and radiating aperture, the transmitted pressure beam profile is obtained and includes simulation of propagation channel attenuation and where necessary, the directional response of any ultrasonic receiver. The surface displacement data may be derived directly, from laser measurement of the vibrating surface, or indirectly, from finite element modeling of the transducer configuration. To validate the approach and to provide experimental measurement of transducer beam profiles, a vibration-free, draft-proof scanning system that has been installed within an environmentally controlled laboratory is described. A comparison of experimental and simulated results for piezoelectric composite, piezoelectric polymer, and electrostatic transducers is then presented to demonstrate some quite different airborne ultrasonic beam-profile characteristics. Good agreement between theory and experiment is obtained. The results are compared with those expected from a classical aperture diffraction approach and the reasons for any significant differences are explained.     

Heating of the phantom of a biological tissue by a phase conjugate ultrasonic beam

The local heating of an absorbing medium by an ultrasonic beam with a conjugate wave front has been experimentally demonstrated. Plastisol, which is a polymeric material close in acoustic properties to biological tissue, is used as the medium. An ultrasonic heating of 7.2°C has been obtained in a time of about 100 s when the sample equipped with a thermocouple is placed between a focused piezoelectric transducer emitting a “probe wave” with a frequency of 5.0 MHz and a system that reverses the ultrasonic wave front with amplification. The characteristic features of heating by ultrasonic beams with the conjugate front, as well as the prospects of applications of this effect in medicine and other fields, have been discussed.     

Characterization of measurement system effects in ultrasonic scattering experiments

A general model is developed to characterize the effect of an ultrasonic measurement system on the experimental determination of ultrasonic scattering as a function of angle and frequency. The model includes arbitrary emitter beams and detector apertures as angular spectra of plane waves. Arbitrary emitted pulses and detector time gates are incorporated through frequency spectra of temporal harmonics. A transformation of variables is employed to express the spectrum of the measured pressure as a product in wave space of a system function and the Fourier transform of the medium variations. The mean-square value of the measured pressure spectrum is similarly expressed as a product of the squared magnitude of the system function and the power spectrum of the medium variations. The measured quantities are shown to become scaled values of intrinsic scattering characteristics when the system function weight is concentrated relative to the medium characteristics in wave space. The assumption of an indefinitely long detector gate is used to represent the system function as a product in which one factor is a beam function dependent on spatial frequency and the other factors are dependent on temporal frequency. Beam-function calculations as well as calculations of second moments and overall beam weight are made for identical Gaussian-shaped emitter and detector apertures to illustrate the blurring and weighting effects of measurement system beam patterns as a function of scattering angle. The moment calculations are shown to identify circumstances when the medium variation function can be factored out from under the integral and the measurement represented as a simple product of the medium properties and a measurement system weight. The results may be used to design scattering experiments in which degradations due to system effects are within acceptable limits.     

Effect of deviation from plane wave conditions on the Doppler spectrum from an ultrasonic blood flow detector.

Deviation from plane wave conditions within the ultrasound beam of a Doppler blood flow detector leads to a non-linear relationship between the phase angle of the back-scattered signal and the scatterer position. This in turn leads to frequency modulation of the Doppler signal and an increase in the Doppler spectrum width. The relationship between the ultrasound beam and the observed signal spectrum has been investigated by employing a computer-based model of the ultrasound field which enabled the calculation of: 1, pressure (amplitude and phase angle) field distributions from plane disc and focused transducers with unapodized and apodized aperture field distributions; 2, the Doppler signal from a scatterer moving through the field; and 3, the spectrum of this signal. The increase in spectral width resulting from deviations from plane wave conditions was calculated by comparing this spectrum with that of the signal from which frequency modulation had been removed.     

Study on the multifrequency Langevin ultrasonic transducer

Langevin ultrasonic transducers are widely used in high-power ultrasonics and underwater sound. In ultrasonic cleaning, a matching metal horn rather than a metal cylinder is used as the radiator in order to enhance the radiating surface and improve the acoustic matching between the transducer and the processed medium. To raise the effect of ultrasonic cleaning, the standing wave in the cleaning tank should be eliminated. One method to eliminate the standing wave in the tank is to use the multifrequency ultrasonic transducer. In this paper, the Langevin ultrasonic horn transducer, with two resonance frequencies, is studied. The transducer consists of two groups of piezoelectric ceramic elements: the back metal cylinder, the middle metal cylinder and the front matching metal horn. The vibrational modes of the transducer are analysed, and resonance frequency equations of the transducer in the half-wave and the all-wave vibrational modes are derived. According to the resonance frequency equations, transducers with two resonance frequencies are designed and made. The resonance frequencies, the effective electromechanical coupling coefficients and the equivalent electric impedances of the transducers are measured. It is shown that the measured resonance frequencies are in good agreement with the computed results, and the transducer can be excited to vibrate at two resonance frequencies, which correspond to the half-wave and the all-wave vibrational modes of the transducer.     

The effect of wave reflection and refraction at soft tissue interfaces during ultrasound hyperthermia treatments.

An improved numerical model for calculating the ultrasonic power deposition in layered medium was developed and experimentally tested. The new model takes into account the ultrasound wave reflection and refraction at the tissue interfaces thereby providing improved accuracy in ultrasound hyperthermia treatment planning. The model was compared with a simplified model to evaluate when the tissue interfaces could be ignored in the hyperthermia treatment planning and evaluation. The effect of variations in water and tissue temperatures, the fat layer thicknesses, and the beam entrance angle were also investigated to establish guidelines for treatment execution. It was found that in most cases the effects of the soft tissue interfaces can be ignored. However, in some instances the acoustic focus may be shifted several millimeters off axis in layered medium. This is important when sharply focused transducers are used for ultrasound surgery or under the condition of pulsed, high-temperature hyperthermia treatments.     

Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers

A nonparaxial multi-Gaussian beam model is proposed in order to overcome the limitation that paraxial Gaussian beam models lose accuracy in simulating the beam steering behavior of phased array transducers. Using this nonparaxial multi-Gaussian beam model, the focusing and steering sound fields generated by an ultrasonic linear phased array transducer are calculated and compared with the corresponding results obtained by paraxial multi-Gaussian beam model and more exact Rayleigh-Sommerfeld integral model. In addition, with help of this novel nonparaxial method, an ultrasonic measurement model is provided to investigate the sensitivity of linear phased array transducers versus steering angles. Also the comparisons of model predictions with experimental results are presented to certify the accuracy of this provided measurement model.     

Detection limits for single small flaws and groups of flaws when using focussed ultrasonic transducers

The performance of ultrasonic imaging systems, using line-focussed transducers, was evaluated theoretically by employing a simple technique based on convolution. The analysis considered the response of single reflectors, which are mainly voids, and also multiple reflectors located both on a single plane and on multiple planes, which represent a porous layer or bond-line. The limits of detection for each of the above cases, in the presence of different levels of acoustic noise in the object under test were also calculated. The results presented are expressed as a function of a dimensionless flaw size, incorporating the ultrasonic frequency and beam F-number. The results can be used to identify the best match between ultrasonic equipment and a specific imaging problem. They can also serve to guide decisions regarding the most suitable detection method for use with the chosen equipment. If the inspection is properly designed, surprisingly small flaws could be reliably detected — even in objects where significant levels of incoherent acoustic noise are found. The method and results presented in this paper for line-focussed transducers fit qualitatively the case of spherically focussed transducers. The method is highly versatile and it can be extended to cover a range of problems, outside the scope of this paper, including, quantitatively, that of the spherically focussed transducer by employing a formulation which uses more computer time and memory.     

Harmonic generation of an obliquely incident ultrasonic wave in solid-solid contact interfaces

The conventional acoustic nonlinear technique to evaluate the contact acoustic nonlinearity (CAN) at solid-solid contact interfaces (e.g., closed cracks), which uses the through-transmission of normally incident bulk waves, is limited in that access to both the inner and outer surfaces of structures for attaching pulsing and receiving transducers is difficult. The angle beam incidence and reflection technique, where both the pulsing and receiving transducers are located on the same side of the target, may allow the above problem to be overcome. However, in the angle incidence technique, mode-conversion at the contact interfaces as well as the normal and tangential interface stiffness should be taken into account. Based on the linear and nonlinear contact stiffness, we propose a theoretical model for the reflection of an ultrasonic wave angularly incident on contact interfaces. In addition, the magnitude of the CAN-induced second harmonic wave in the reflected ultrasonic wave is predicted. Experimental results obtained for the contact interfaces of A16061-T6 alloy specimens at various loading pressures showed good agreement with theoretical predictions. Such agreement proves the validity of the suggested oblique incidence model.     

An ultrasonic method for dynamic monitoring of fatigue crack initiation and growth

Attached ultrasonic sensors can detect changes caused by crack initiation and growth if the wave path is directed through the area of critical crack formation. Dynamics of cracks opening and closing under load cause nonlinear modulation of received ultrasonic signals, enabling small cracks to be detected by stationary sensors. A methodology is presented based upon the behavior of ultrasonic signals versus applied load to detect and monitor formation and growth of cracks originating from fastener holes. Shear wave angle beam transducers operating in through transmission mode are mounted on either side of the hole such that the transmitted wave travels through the area of expected cracking. Time shift is linear with respect to load, and is well explained by path changes due to strain combined with wave speed changes due to acoustoelasticity. During subsequent in situ monitoring with unknown loads, the measured time of flight is used to estimate the load, and behavior of the received energy as a function of load is the basis for crack detection. Results are presented from low cycle fatigue tests of several aluminum specimens and illustrate the efficacy of the method in both determining the applied load and monitoring crack initiation and growth.     

The feasibility of constructing a cylindrical array with a plane rotating beam for interstitial thermal surgery

Thermal surgery has been shown to be a useful therapeutic option when external ultrasound applicators cannot be used as their beam will not reach the target site. If plane transducers are used, the ultrasound beam has to be rotated in order to generate a sufficiently large volume of necrosis. However, rotating deep-seated interstitial applicators and controlling their shooting direction presents major technical problems. The purpose of this study is to evaluate the feasibility of constructing a cylindrical array with a plane rotating beam for ablating esophageal tumors by interstitial hyperthermia. The feasibility of such an array has been initially evaluated using a plane array (which is easier to make from a technical point of view). This array was made with a new piezoelectric material because its mechanical properties make it ideal for the construction of a cylindrical array in the future. We showed that the beam of each array element is sufficiently divergent and that cross-coupling is small enough to generate a plane wave from a cylindrical array. In addition, power tests and electro-acoustic efficiency measurements demonstrated that the output was sufficient to induce tissue necrosis in the relevant conditions.     

Characterization of airborne transducers by optical tomography

This paper describes the application of an acousto-optic method to the measurement of airborne ultrasound. The method consists of a heterodyne interferometric probing of the pressure emitted by the transducer combined with a tomographic algorithm. The heterodyne interferometer measures the optical phase shift of the probe laser beam, proportional to the acoustic pressure integrated along the light path. A number of projections of the sound field, e.g. a set of ray integrals obtained along parallel paths, are made in moving the transducer to be tested. The main advantage of the method is its very high sensitivity in air (2 x 10(-4) Pa Hz-1/2), combined with a large bandwidth. Using the same principle as X-ray tomography the ultrasonic pressure in a plane perpendicular to the transducer axis can be reconstructed. Several ultrasonic fields emitted by wide-band home made electrostatic transducers, with operating frequencies between 200 and 700 kHz, have been measured. The sensitivities compared favorably with those of commercial airborne transducers.     

Determination of the threshold intensity of a laser beam for exciting stimulated Mandelstam-Brillouin scattering in the atmosphere

Stimulated Mandelstam-Brillouin scattering at small angles is considered in the case of a powerful laser beam propagating in the static mode in an unbounded medium. In contrast to the pulse mode, a hypersonic wave can be formed not only in the backward direction, but also in the forward direction at small angles. In this work, the latter case is considered as having the smallest value of the threshold intensity. It is shown that finite dimensions of the beam significantly change the excitation conditions for a scattered radiation owing to the mismatch of the wave triplet due to diffraction effects. Determination of the threshold intensity is shown to be possible using the well-known expressions for a plane wave only if the Fresnel number of the beam on the path the length of which is equal to the distance of the optical wave decay due to absorption in the medium is much larger than unity. Moreover, a large number of decay distances of the hypersonic wave must fall on the beam radius. When these conditions are not satisfied, the threshold intensity increases as compared to the plane wave.     

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array’s transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.