An Analytical Method to Guide mm-Sized Ultrasonic Transducer Design by Demarcating Regimes of Beam-Spreading and Attenuation

In this paper, we present a novel approach that aids in the sizing of micron to mm-sized ultrasonic transducers for enhanced resolution and denser integration. This seeks to optimize penetration-depth which is an important metric of a transducer’s efficacy in different acoustic media. It is generally accepted that in conventional transducers used in clinical imaging, penetration depth is greater for lower driving frequencies which suffer lessened attenuation. However, in acoustic characterization studies, the drops in axial pressure by beam-spreading and attenuation haven’t been individually quantified and their relative effects are poorly understood. We, therefore, undertake a closer investigation of factors that shape the axial pressure profile of a generalized transducer element in a weakly attenuating medium like water and in a highly attenuating medium like tissue. We have found that it is critical to quantify the
relative
contributions of beam-spreading and attenuation in a medium. We introduce a new parameter called ‘transition distance’ (
${d}_{\textit {Trans}}$
) to graphically demarcate the regimes in beam-spreading and attenuation dominate to explain how a low frequency (2 MHz) or a high frequency (5 MHz) gives greater penetration depth in different media.