Acoustic Field of Plane or Spherical Transducers

Author： Cathignol Dominique Faure Philippe Chavrier Françoise

ISSN： 1610-1928

Source： Acta Acustica united with Acustica, Vol.83, Iss.3, 1997-05, pp. : 410-418

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Abstract

The authors derive a method for calculating the time-dependent Rayleigh integral in the case of plane and spherically focused ultrasonic transducers with uniform distribution of amplitude. The method (line integral method) involves the decomposition of the radiated field into a geometrical wave (either plane or spherical) and a diffracted edge wave. The method has two main advantages. First, it can deal with possibly complex transducer shapes for which an analytical calculation of the diffraction impulse response h(M,t) is not tractable and second, it is considerably faster than the Rayleigh integral method. Comparisons between the transient pressure time waveform obtained with the line integral method and those obtained with conventional methods show an excellent agreement in the two cases of a shell and a spherical sector. In the case of the shell, the computation times of the impulse response with the line integral method are approximately 3 times and 50 times faster than those obtained with the impulse diffraction and the Rayleigh integral methods respectively. In the case of the semi-spherical shell, no analytical expression of h(M,t) exists and the computation time of the impulse response is approximately 15 times faster than with the Rayleigh integral method.