The first case is for uniform harmonic excitation and the second is for uniform excitation by a short modulated Gaussian pulse. The axial pressure distribution for a piston transducer radiating into a dissipative medium (assuming that the dispersion can be ignored) is calculated analytically with the help of two methods-the well-known impulse response method and the modified diffraction integral. Evidence for the validity of this integral is provided by considering two classical problems. For a finite aperture, solutions characterizing the field are calculated numerically using a dissipative form of the Rayleigh–Sommerfeld diffraction integral. Non-diffraction solutions to this equation that are a generalization of previously obtained X-waves are obtained as particular cases. A general solution in the time domain is obtained with the help of the method of Donnelly and Ziolkowski for an infinite aperture. Recently derived dispersion relations for media with ultrasonic attenuation obeying a frequency power law are used to build a causal wave equation in a frequency domain. Percent than the difference between theoretical X-wave and rectangular That the new approach improve the precise of the approximation, theĭifference between theoretical X-wave and the new approach is lower 10 The goodĪgreement of the driving pulse and the result resulting fieldĭistributions, with those obtained from the classical X-wave excitationsĬan be justified by the filtering effects induced by the transducerĮlements in frequency domain. Of implementation of classical 0-order X-wave and the precision ofĪpproximation with the simple pulsed electrical driving. X-wave signals and driving pulses, related to their excitation effects,Īre minimized by L2 curve criterion. Castellanos's methodīy calculating the approximation driving pulse not only from rectangularīut also triangular driving pulse.
Which could be implemented with a moderate cost in analogicalĮlectronics. Limited-diffraction waves with relatively simple driving waveforms, The results suggested the possibility of achieving Castellanos proposedĪn approach to approximate the X-wave excitations with rectangular Order to simplify the X-wave generating process, L. Specific voltage for the excitations for each distinct array element. Ultrasonic fields is a complex technology which involves precise and In practice, the generation of real time X-wave Potential applications in the enlargement of the field depth in acoustic X-wave is a particular case of limited diffracting waves which has great These results suggest the possibility of achieving limited-diffraction waves with relatively simple driving waveforms, which can be implemented with a moderate cost in analogical electronics. The good agreement of the source vibration signals and resulting field distributions, provided by the drastic simplification presented here, with those obtained from the classical X-wave excitations, can be justified by the filtering effects induced by the transducer elements in frequency domain. The differences between theoretical X-wave signals and approximate driving pulses, related to their excitation effects, were minimized by using the time widths and amplitudes of the rectangular pulses as fitting parameters. In order to optimize these driving signals in each array annulus, the L2 curve criterion is applied. The main idea is to approximate the theoretical X-wave electrical excitations by means of simple driving rectangular pulses. In this work, an approach for simplifying the experimental arrangement, needed to generate limited diffracting waves, is proposed.
The main interest of using limited diffracting waves is motivated by their potential applications in the enlargement of the field depth in acoustic imaging systems, under collimated conditions.
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