Elec. Eng. Dept., Amirkabir Univ., Hafez St., Tehran, Iran
Ultrasonic nondiffracting beams are of interest for use in pulse-echo systems because they have long depth of field and small beamwidth. Recently, a new class of nondiffracting beams, termed the x waves, has been discovered and its properties in lossless media have been reported. In some pulse-echo applications, however, propagation media are dissipative. It can be shown that x waves diffract in such media, i.e., the beam spreads and its amplitude decays with distance. In order to limit beam spread within a reasonable range, attenuation of the media must be taken into account while designing the transducer and the excitation signal. Also, amplitude decay of the echoes must be compensated for at the receiver by using a proper time gain compensation curve. In this paper, conditions for designing an x wave pulse-echo system for use in dissipative media are described. Given the attenuation coefficient and maximum allowable beamwidth, proper values for transducer parameters, such as diameter, axicon angle, beam concentration parameter in lossless media, and the bandwidth of the interrogating pulse are discussed and determined. Also, variations of the beamwidth are investigated. It is shown that for wideband x waves, the beam spreads linearly with depth. Furthermore, analytical expressions for the time gain compensation curve are obtained. In contrast to the conventional exponential gain function, the gain function for the wideband x wave approaches a linear function of time.