Bandwidth enhancement : correcting magnitude and phase distortion in wideband piezoelectric transducer systems

Acoustic ultrasonic measurements are widespread and commonly use transducers exhibiting resonant behaviour due to the piezoelectric nature of their active elements, being designed to give maximum sensitivity in the bandwidth of interest. We present a characterisation of such transducers that provides both magnitude and phase information describing the way in which the receiver responds to a surface displacement over its frequency range. Consequently, these devices work efficiently and linearly over only a very narrow band of their overall frequency range. In turn, this causes phase and magnitude distortion of linear signals. To correct for this distortion, we introduce a software technique, which considers only the input and the final output signals of the whole systemwhich is therefore generally applicable to any acoustic system. By correcting for the distortion of the magnitude and phase responses, we have ensured the signal seen at the receiver replicates the desired signal. We demonstrate a bandwidth extension on the received signal from 60-130 kHz at -6dB to 40-200 kHz at -1dB in a test system. The linear chirp signal we used to demonstrate this method showed the received signal to be almost identical to the desired linear chirp. Such systemcharacterisation will improve ultrasonic techniques when investigating material properties by maximising the accuracy of magnitude and phase estimations

Time-reversal methods for acousto-elastic equations and applications

Time reversal (TR) is a subject of very active research. The principle is to take advantage of the reversibility of wave propagation phenomena, for example in acous- tics, elastic or electromagnetism in an unknown medium, to back-propagate signals to the sources that emitted them. In a previous paper [1], we introduced a time-reversed method for acoustic equation. In this paper, our aim is to extend this approach to elastodynam- ics equations. As the application we have in mind are concerned with ultrasound-based elasticity imaging methods, we consider both elastic and acousto-elastic systems of equa- tions. We stress that our method does not rely on any a priori knowledge of the physical properties of the inclusion

Numerical validation of probabilistic laws to evaluate finite element error estimates

We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements $P_k$ and $P_m, (k<m)$. In particular, we show practical cases where finite element $P_{k}$ gives more accurate results than finite element $P_{m}$. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.Comment: 15 pages, 11 figure

A new asymptotic approximate model for the Vlasov-Maxwell equations

AbstractIn this paper, we derive a new asymptotic approximation of the Vlasov-Maxwell equations. This formulation follows the beam in a speed-of-light frame. It is fourth order accurate in the small characteristic velocity of the beam. The formulation is simpler than standard particle-in-cell methods in the lab frame or in the beam frame. It promises to be very powerful in its ability to get an accurate, but fast and easy to implement algorithm