A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then Summing their response. A fast calculation is obtained by using the far-field approximation. Examples of the accuracy of the approach and actual calculation times are given. >

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Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers

Femtosecond filamentation in transparent media

Time reversal of ultrasonic fields represents a way to focus through an inhomogeneous medium. This may be accomplished by a time-reversal mirror (TRM) made from an array of transmit-receive transducers that respond linearly and allow the incident acoustic pressure to be sampled. The pressure field is then time-reversed and re-emitted. This process can be used to focus through inhomogeneous media on a reflective target that behaves as an acoustic source after being insonified. The time-reversal approach is introduced in a discussion of the classical techniques used for focusing pulsed waves through inhomogeneous media (adaptive time-delay techniques). Pulsed wave time-reversal focusing is shown using reciprocity valid in inhomogeneous medium to be optimal in the sense that it realizes the spatial-temporal matched filter to the inhomogeneous propagation transfer function between the array and the target. The research on time-reversed wave fields has also led to the development of new concepts that are described: time-reversal cavity that extends the concept of the TRM, and iterative time-reversal processing for automatic sorting of targets according to their reflectivity and resonating of extended targets. >

Time reversal of ultrasonic fields. I. Basic principles

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.

A new method for estimation of velocity vectors

An approach is presented to compute the near‐ and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integrals. A simple expression is developed for an impulse response function, which is the time‐dependent velocity potential at a spatial point resulting from an impulse velocity of a piston of any shape. The time‐dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the appropriate impulse response. The response of an array may be computed using superposition. Several examples illustrating the usefulness of the approach are presented. The farfield time‐dependent radiation from a rectangular piston is discussed for both continuous and pulsed velocity conditions. For a pulsed velocity of time duration T it is shown that the pressure at several of the field points can consist of two separate pulses of the same duration, when T is less than the travel time across the piston.

Transient Radiation from Pistons in an Infinite Planar Baffle

The forward and backward propagation of harmonic acoustic fields using Fourier transform methods is presented. In particular, the forward propagation of a velocity distribution to obtain a pressure field and the backward propagation of a pressure field to obtain a velocity distribution are addressed. Numerical examples are presented to illustrate the nearfield behavior of the pressure field from complex planar vibrators, e.g,—an ultrasonic transducer or plate, with nonuniform velocity distributions. The numerical results, which were obtained via the use of FFT algorithms, are presented for vibrators which are operating above and below coincidence. These results illustrate the acoustic nearfield as a function of distance from the vibrator. Numerical results are also presented to illustrate the backward projection method. The pressure field of a 3×3 focused array is back projected to obtain the velocity distribution for several cases of interest. These results illustrate the utility of the transform method and the effect of spatial windows or filters in its implementation using FFT algorithms.

Forward and backward projection of acoustic fields using FFT methods

A model and approach to evaluate the transmit/receive response of pulsed ultrasonic thickness expander transducers is presented. The approach is based on utilizing the Mason model to account for the transducer’s dynamic response and an impulse response method to account for wideband acoustic nearfield and farfield phenomena. An overall transmit/receive impulse response which relates the electrical input and output of the transducer, including the effects of transducer dynamics and acoustic diffraction, is developed via a block diagram and Fourier transform method. Numerical results are presented for typical piezoelectric transducers. The results illustrate the effects of matching and acoustic diffraction on the receive response of typical transducers. Since the effects on the pulse response of matching and backing the piezoceramic element and/or changing the shape of the radiating surface are readily investigated, the model and approach may be used for design purposes. Furthermore, the model may also be readily combined with various types of signal processors to improve spatial resolution in pulse echo systems via the utilization of coded pulses and/or advanced processing methods.

Pulsed transmit/receive response of ultrasonic piezoelectric transducers

An approach is presented to evaluate the pressure field and vibratory response of a finite fluid‐loaded cylindrical shell with infinite rigid extensions which are connected to the shell. The approach combines a generalized Fourier series or in vacuo eigenfunction expansion of the velocity field of the shell with a Green’s function and integral equation representation of the acoustic loading on the shell. Although modes with different circumferential wavenumbers are decoupled, all modes with identical circumferential wavenumbers are coupled via the fluid. The algebraic equations which account for this coupling include both shell impedances and acoustic impedances which are mode dependent. General integral expressions are presented for the acoustic impedances which include both self radiation and interaction impedances. In order to illustrate the general characteristics of these acoustic impedances, the impedances are investigated for a particular set of eigenfunctions. Low‐frequency and asymptotic expressi...

Modal coupling in the vibration of fluid‐loaded cylindrical shells

A wave vector, time‐domain (k−t) method of forward projecting time‐dependent pressure fields from complex vibrators is developed using space‐time Fourier transform methods. Axisymmetric fields are included as a special case of the general formulation in which a pressure field at one plane can be forward projected to other planes. In brief, a wave vector, time‐domain representation of the field at one plane is forward projected via a temporal convolution with a wave vector, time‐domain impulse response that is dependent on the projection distance. The projected field is then obtained via the use of an inverse spatial Fourier transform. A numerical study of the method illustrates the accuracy of the approach when implemented using fast Fourier transform (FFT) algorithms. The forward projections of simulated pressure fields from a planar ultrasonic transducer are shown to be in excellent agreement with corresponding results from the use of a time‐domain impulse response method.

Peter R. Stepanishen

Papers

Transient Radiation from Pistons in an Infinite Planar Baffle

Forward and backward projection of acoustic fields using FFT methods

Pulsed transmit/receive response of ultrasonic piezoelectric transducers

Modal coupling in the vibration of fluid‐loaded cylindrical shells

A wave vector, time‐domain method of forward projecting time‐dependent pressure fields