Radiation pattern of a focused transducer: A numerically convergent solution

Abstract

The radiation pattern of a focused transducer is reexamined. The radiation field is divided into an illuminated zone and a shadow zone. A numerically convergent solution of the pressure distribution in terms summations of Bessel functions is provided. This solution is computationally more advantageous than earlier results where a double or single integral in the complex plane is required. The pressure amplitude differs from earlier reports slightly for off-axis locations at low frequency. This difference may have significance for backscatter coefficient determination where scatterers are assumed present over a time-gated volume. The solution for a flat disk radiator is obtained as a limiting case.

Active echolocation beam focusing in the false killer whale, Pseudorca crassidens

“…Because the MLDB complex is located just dorsal and anterior to these structures, it is possible that the skull and air sacs reflect the pulse and the collective structures may function like a spherically concave focusing radiator (O'Neil, 1949). Many devices, such as ultrasound transducers, use spherically concave radiators to create a highly focused beam (Chen et al, 1993). Such a system results in a focused beam so long as the diameter of the radiator is much larger than the wavelength of the emitted signal.…”

“…Although there are no published data on the curvature of the Pseudorca skull, it is clearly concave (Fig.6). Thus, assuming that the skull and air sacs reflect the pulses generated in the MLDB complex, the morphology of a false killer whale's sound-generating apparatus might be modeled as a focused radiator that creates a region of very narrow beamwidth at a certain distance from the source (O'Neil, 1949;Chen et al, 1993). Of course, such a simplified model assumes a homogenous volume within the concavity and does not account for the muscles, tissue and acoustic fats that comprise the odontocete forehead and may further modify the echolocation beam.…”

Sound concentration caused by curved surfaces

“…This method is used in acoustic microscopy. The pressure field generated by these radiators have been studied extensively (see e.g., [O'Neil49], [Lucas82], and [Chen93]). …”

Sound concentration caused by curved surfaces

“…The approximation and solution technique used here will follow the strategy used in [Chen93]. Additionally the incident sound will be incorporated (in [Chen93] only the in-phase radiation from a piezoelectric element is considered) and larger aperture angles will be considered.…”

“…Additionally the incident sound will be incorporated (in [Chen93] only the in-phase radiation from a piezoelectric element is considered) and larger aperture angles will be considered. The first step is to approximate the distances s and u from source and receiver respectively to surface element dS, as a function of the angles θ and φ .…”