Time-frequency analysis based on the scalogram technique of the 0-order ultrasonic X-waves assessing their viability as a detection tool in medical diagnosis

In medical diagnosis by ultrasonic imaging, it is of vital importance to be able of collimating the emitted ultrasonic beams along all the patient field under analysis, if a good and maintained spatial resolution is desired, for instance for echographic purposes in tissues. An interesting future alternative, to the classical dynamic electronic focusing of ultrasonic beams, in large arrays, for scanning the patient field under study, would be the application in annular radiators of a recently proposed type of limited diffraction waves (LDW), the X-waves. The main objective of this paper is to analyze the time-frequency composition of some limited diffraction wave profiles obtained by means of performing a high-frequency ultrasonic transducer implementation of the 0-order solution of the ultrasonic X-waves. The well-know scalogram technique was employed in this work for achieving this analytical aim. The analysis was performed for four radial positions of the radiating ultrasonic transducer. Furthermore, the corresponding acoustic field, evaluated in dBs levels, is analyzed in detail. New X-wave characteristics are compared with the diffracted field at a fixed point, and over the same radial positions. The results obtained here show that the diffraction phenomenon reduces the wave content in high-frequencies, and modifies the phase of the wave, causing a delay in the diffracted 0-order X wave.