Validation of a three-dimensional model for improving the design of multiple-backscattering ultrasonic sensors

Ultrasonic sensors based on backscattering principles have been developed for various applications involving arbitrary or random scatterer distributions. Although the theory of multiple scattering of waves is well-established, it has not been thoroughly explored in these applications. This work presents a feasible and simplified three-dimensional scattering model to predict the transient response generated by a set of rods positioned in the near field of a 1 MHz water-coupled ultrasonic transducer. The developed algorithm accurately reproduced the received waveform for seven different configurations of scatterers. Additionally, this model was used as the core of a parametric optimization routine to determine the optimal distribution of five rods that maximizes the acoustic energy of the echo signal. The theoretical signals were compared with experimental data, demonstrating good agreement and indicating the feasibility of the method as a design tool for the backscattering sensor.