Daniel Guyomar

Boundary effects on transient radiation fields from vibrating surfaces

The transient radiation or diffraction from a planar source imbedded in an infinite baffle is analyzed for three different baffle conditions (rigid, free‐space, and soft). For an excitation separable in time and space, it is shown that the field is related to the normal derivative of the input field only. A method is also given for computing the transient fields based on a wave decomposition in the spatial frequency domain. This method is a time generalization of the angular spectrum theory that presents transient wave propagation as a time‐varying spatial filter, allowing a linear systems interpretation of the diffraction. The formalism is shown to easily include the effects of a finite receiving aperture. The method is amenable to computing the field from an arbitrary time excitation and an arbitrary spatial distribution. The method is valid for arbitrary distances to the observation point and uses computationally efficient FFT calculations.

Time deconvolution of diffraction effects—Application to calibration and prediction of transducer waveforms

The concept of a radiation coupling function is used to write a transducer response that includes the diffraction losses. This concept leads to easy interpretations of experimental observations. In a second part a method is proposed for removing the diffraction effects from the observed transducer response. A linear system approach is taken to define the transducer output signal in terms of successive convolutions. The proposed method, based on a numerical deconvolution of the radiation filter, leads to an absolute calibration of the transducer impulse response. Deconvolved waveforms are presented for circular and annular arrays. Once the intrinsic transducer response is known, a direct convolution enables the prediction of the output signal for any distance transducer/reflector. Comparisons between predicted and observed transient waveforms are given for circular and annular arrays.

Transient fields radiated by curved surfaces—Application to focusing

A theoretical model is presented for computing the transient radiated field (potential or pressure) resulting from a curved surface having an arbitrary velocity distribution. The method is a generalization of the angular spectrum theory giving the time impulse response for a given shaped surface. The technique leads to a systems theory interpretation of the radiation and diffraction effects. General expressions for arbitrary surfaces are given but important simplifications occur for radially symmetric geometries. For this case, simple expressions for the wave location may be obtained without requiring solution of the wave. Numerical simulations for common focused waves are given using computationally efficient FFT algorithms.

A Fourier approach to diffraction of pulsed ultrasonic waves in lossless media

A method based on a Fourier domain approach is presented for computing the diffraction of a pulsed ultrasound wave from a rigidly baffled source in lossless media. The propagation from a planar source is dependent on the total impulse response which is just the Green’s function. Computing the spatial transform of the point spread function gives the propagation transfer function which multiplies the spatial spectrum of the spatial excitation to produce the spatial spectrum of the propagated wave. The propagation transfer function can then be considered to be a time‐varying spatial filter. The results are valid for separable arbitrary time excitation and planar spatial distributions of the source. The solution is amenable to including the effects of a finite receiver. Results of different simulations using this method are included.

Computation of the impulse diffraction of any obstacle by impulse ray modeling—Prediction of the signal distortions

In this article, a numerical method of modeling the output signal of a transducer after reflection of the pulsed radiated wave on a reflector of arbitrary geometry is presented. This method, based on impulse ray modeling, corresponds to a discrete approach of the Kirchhoff‐radiation integral: It leads to a numerical evaluation of the diffraction effects. The overall response can be written as a time convolution of the transducer impulse response with the radiation coupling function related to the reflector geometry. This linear system approach permits an easy explanation of the signal distortion due to the reflector geometry. After a presentation of the basic principles of the method and their justification, the model is applied to several geometrical configurations: tilted plane, cylindrical, and spherical reflectors of infinite acoustical impedance. The method is extended to model a focused transducer and a solid layer reflector of finite acoustical impedance.

Propagation of Transient Acoustic Waves in Lossy and Lossless Media

This paper presents a computationally efficient technique for calculating the transient wave from a planar source within a medium. The spatial and temporal excitation are known at the input plane. The technique is applicable to lossless media, to media with a loss coefficient that is linear in frequency, and to media with a loss coefficient that is quadratic in frequency. The technique is computationally efficient in that it relies on FFT algorithms for the calculation rather than integral solutions requiring geometrical interpretation. In this method, we find the Green’s function that solves the applicable wave equation and that meets the required boundary conditions in the source plane. This Green’s function is then used in a form of the Kirchhoff integral that applies to transient wave propagation and we find the response to a time-domain impulse excitation. The solution is then expressed in the spatial frequency domain where a linear systems interpretation provides a physically intuitive interpretation of the results. The propagation is seen to be represent a time-varying spatial filter that increasingly attenuates the higher spatial frequencies as time goes on. Unlike the continuous wave case, the filter is neither band-limited nor a pure phase filter. The particular form of the spatial filter depends on the medium assumed and on the baffle conditions. The solutions for the impedance-matched baffle and the resilient baffle can be expressed in terms of the solution for the rigid baffle case. Several examples of calculated fields will be given.

Reflection of an impulse spherical wave at a plane interface separating two fluids

In this paper, the reflection of an impulse spherical wave by an infinite plane interface separating two fluids is studied. Since both propagation media have a finite acoustical impedance, the boundary conditions at the interface show that the reflected field is distorted and does not show a spherical wave front. Under some particular conditions according to the velocity ratio between the two fluids, it is possible to observe the generation of head waves and/or tail waves. A numerical method is proposed to compute the reflected field based on Fourier transforms over temporal and spatial variables. It will be shown how the reflected field can be reduced to a single integral transform, and how a closed form solution can be obtained in some particular cases. Computations of the reflected field are presented for different values of densities and velocities, illustrating the generation of head waves and tail waves in addition to the expected spherical wave front. Finally, these results are compared to those ob...

Transient radiation from axially symmetric sources

A method is presented for the efficient calculation of radiated acoustic fields from a radially symmetric source in a rigid baffle excited by an arbitrary time excitation. The technique is a modal analysis based on the series expansion of the source velocity excitation in terms of either of two basis functions. Each mode is propagated by the technique with rapid convergence of the solution evident in 30 or less terms, allowing rapid and efficient computer‐based solutions to be obtained. Several numerical field simulations are given.

Self and mutual time‐dependent interaction forces between ultrasonic transducers—Application to the computation of radiation impedances

In this paper, diffraction theory is used to describe the self and mutual time‐dependent interaction forces between ultrasonic transducers. This concept is interesting since it is equivalent, up to a temporal Fourier transform, to the radiation impedance. The formalism allows a description of self and mutual radiation impedances in terms of the aperture functions of the emitter and the receiver, and this description does not suppose that the transducers work in the piston mode. Then, the formalism is used to retrieve the well‐known results about the radiation impedance of a circular piston. Finally, the mutual radiation impedance between two transducers is analyzed, and the particular case of small transducers compared to the wavelength is discussed. The results are similar to those obtained by Stepanishen and Pritchard [R. L. Pritchard, J. Acoust. Soc. Am. 32, 730–737 (1960); P. R. Stepanishen, ibid. 49, 283–292, 841–849 (1971)], except that the results here exhibit a correction term that increases the v...

A Transfer Function Model For Propagation In Homogeneous Media

Diffraction effects are important in acoustic imaging and tissue characterization because of the relatively large wavelengths used and the fact that applications are frequently used in the near-field of the source. It is difficult to intuitively anticipate the shape of the field there, yet the description of the fields spatial acoustic potential or pressure distribution is necessary. This problem is more complicated when focused transdu-cers or phased arrays are used. Using the spatial frequency, domain it is possible to model propagation in lossless and lossy media as a transfer function. The sources are represented as planar sources with separable arbitrary time excitation and arbitrary spatial excitation. Transfer functions can be obtained for lossless media, media with a linear frequency dependence of attenuation coefficient, and media with a quadratic dependence of attenuation co-efficient. The transfer functions are shown to be simply related to the two-dimensional spatial transform of the Greens function of the wave equation for propagation in the medium of interest with the assumed boundary conditions. The transfer functions of the lossy and lossless propagation models are shown to be interdependent. For any given observation plane, these transfer functions are time-varying spatial filters that attenuate higher spatial frequencies with increasing effectiveness as time proceeds. The effects of source excitation and apodization, source boundary conditions, assumed media properties, and receiver aperture effects are easily incorporated in this model. Several numerical simulations of computed acoustic potentials and pressure distributions are shown.