Propagation Transfer Function Research Articles

Time-reversed ultrasound

Time-reversal invariance is a very powerful concept in classical and quantum mechanics. However, simple experimental evidence of this concept is difficult to obtain. In the field of acoustic waves, where time reversal invariance also occurs, time-reversal experiments may be achieved simply with large ultrasonic piezoelectric transducer arrays. Time-reversal mirrors (TRMs) are made of such reversible acoustic retina, allowing an incident acoustic field to be sampled, recorded, time-reversed, and re-emitted. Time reversal of acoustic fields allows an optimal approach to focus pulsed ultrasonic waves through inhomogeneous media in the sense that it realizes the matched filter in both the spatial and temporal dimensions to the inhomogeneous propagation transfer function. In the field of acoustics, the ability to work directly in the time domain, with piezoelectric retina, allows pulse echo mode processing in an iterative mode. In multitarget media, such an iterative process converges on the most reflective target. In the case of an extended elastic target, automatic resonances of vibration modes can be achieved. TRMs are also innovative tools in the field of fundamental physics. They may be used to study inverse scattering problems, multiple scattering processes, chaotic scattering as well as scattering by turbulent media. Several experiments illustrating these areas will be presented. Applications of TRMs will also be described and include medical applications (kidney stone destruction and hyperthermia) as well as nondestructive testing of solid media. Experimental results illustrating these applications will be presented.

The effect of surface variability on the short‐range propagation of tire/road interaction noise.

The object of this work was to identify the origin of differences between sound levels measured on two track types used for standardized motor vehicle passby noise tests: i.e., the ISO and SAE surfaces. The measured differences could result either from the effect of the road surface on tire/road interaction noise generation, or from surface sound absorption differences. Near‐field intensity data measured at the tire/road interface on vehicles in motion were first examined to establish the correlation between surface type and source spectrum and level. Source levels were approximately 1 dB higher at SAE sites than at ISO sites. Two‐microphone methods were then used to estimate the acoustic impedance of both the ISO and SAE surfaces. The surface impedances were used together with measured tire source spectra and sound propagation theories to calculate the passby level variability that could be attributed to variations in test site acoustic impedance. It was found that differences in propagation transfer functions for the ISO and SAE surfaces were on the order of only 0.3 dB. Thus it was concluded that the differences in passby levels measured at ISO and SAE sites resulted primarily from differences in tire/road interaction noise generation.

Focusing in transmit–receive mode through inhomogeneous media: The time reversal matched filter approach

For a few years, adaptive time delay focusing techniques have been extensively studied in order to focus through inhomogeneous media. However, these techniques can only correct the effects of a thin aberrator located near the array. Time reversal of ultrasonic fields allows another approach to focus in the transmit mode through inhomogeneous media. Compared to the adaptive time delay focusing technique, time reversal requires the transmission of different waveforms from each individual element of an array. Focusing via time reversal is shown to be optimal in comparison with time delay focusing since it realizes the spatio-temporally matched filter to the inhomogeneous propagation transfer function between the array and the focal point. In previous papers [Fink et al., Proc. IEEE Ultrasonics Symposium, Montreal (1989)], focusing by time reversal has been described in the transmit mode only. A complete focusing in inhomogeneous medium requires the extension of this technique in the receive mode. This paper describes the extension of the matched filter approach in the receive mode and it is shown that optimal focusing in this mode can be achieved using adaptive convolution beamforming techniques instead of simple time delay lines. Theoretical and experimental results are presented to show the efficiency of this technique compared to adaptive delay line focusing.

Focalisation en émission-réception en milieu inhomogène : le concept de filtre adapté

Time reversal of ultrasonic fields is a mean to focus through inhomogeneous media on a reflective target. In previous papers, we have shown that in contrast to time delay focusing techniques, that can only correct distortions produced by a thin aberrator located close to the transducer array, TRM focusing is able to compensate for distortion independently of the aberrator position. We have also shown that the TRM focusing is optimal as it realizes the spatial-temporal matched filter to the propagation transfer function through inhomogeneous media. It is a self-adaptive technique that compensates for any geometrical distortions of the array structure as well as for distortions due to the propagation through inhomogeneous media. However, TRM focusing has only been described in the transmit mode. The extension of this matched filter focusing technique in the receive mode is presented in this paper. This new focusing technique can be achieved using adaptive convolution techniques instead of delay line techniques. Theoretical and experimental results will be presented

Time reversal of ultrasonic fields. I. Basic principles

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.

Effect of dispersion on a plane ultrasonic pulse

Propagation through typical biological media involves dispersion as well as attenuation, since the attenuation coefficient varies with frequency more slowly than f2 in the ultrasonic range. Dispersion effects are explored for plane pulses in a homogeneous medium. The smoothing of an initially steplike pulse as it propagates through different attenuating media is illustrated numerically. Pulse waveforms are compared with and without allowance for dispersion, using a family of model α(f) curves. The associated dispersion in each case is obtained from the Kramers‐Kronig relations, which ensure that the propagation transfer function is causal.

On a simple derivation of the Fresnel diffraction formula and a transfer function approach to wave propagation

The Fresnel diffraction formula is straightforwardly obtained by solving a partial differential equation (PDE) for envelope propagation using Fourier transform techniques. The PDE, in turn, can be derived from the dispersion relation of a linear medium by employing a simple operator formalism. The transfer function and impulse response of propagation follows as a spin-off and is used to solve illustrative problems. Huygens’ principle is visualized as a consequence of the convolution property of linear systems.

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.

Image reconstruction and range distance estimation for planar holographic systems using symmetry properties

In a recent paper by Narasimhan et al. [J. Acoust. Soc. Am. 79, 382–385 (1986)] a method is proposed for the determination of object range distance for planar holographic systems by phase unwrapping the spectral distribution along the major axes. In this letter, an alternative approach is introduced to improve the range distance estimation process. This technique simplifies the procedure by utilizing the Fourier transformation symmetry properties associated with the real object distribution and propagation transfer function. The computation complexity can be significantly reduced because of the elimination of the complicated computing and phase unwrapping steps. In addition, the accuracy of the distance estimation is improved by using the complete two-dimensional spectral distribution instead of only the variation along the axes.

A transfer function approach to transient propagation in media with a quadratic frequency dependence of attenuation coefficient

The propagation of short acoustical pulses in lossy media is presented as a time‐varying transfer function (or spatial filter) that acts on the spatial spectrum of the source excitation. The source is a planar source of arbitrary (but separable) spatial and temporal dependence mounted in a rigid baffle. The homogeneous medium obeys Stokes' equation, resulting in a quadratic dependence of the plane‐wave attenuation coefficient. Using distribution theory, an integral expression for the field is derived in terms of the normal velocity of the source, the Green's function, and its normal derivative on the boundary. This expression leads to an approximate solution for a point source in the source plane, which in turn produces a spatial transform that is the propagation transfer function. This transfer function is simply related to the transfer function of lossless propagation. Computer simulations of fields as well as a discussion of some casuality problems introduced by the use of the Stokes' equation are pres...