An analytical study of spatial resolution enhancement for a dual-frequency acoustic beamformer

In this paper, we address an acoustic directed-self-assembly (DSA) problem for aiming to pattern particles based on creating an appropriate acoustic field by the fine adjustment of transducer operating parameters. The proposed idea is to incorporate the DSA problem with multi-frequency beamforming techniques. First, the boundary element method (BEM) is implemented for the direct modeling of the proposed DSA problem. Then, it is integrated with the concept of dual-frequency beamforming. In this study, the influence of changing excitation frequency is investigated on the spatial resolution enhancement of the pressure field. Also, the optimal frequency difference is calculated theoretically to produce two adjacent pressure traps with maximum separability and, therefore, maximum spatial resolution in a two-frequency acoustic beamformer without any restriction on the chamber shape. The performance of the proposed Dual-Frequency Beamforming (DFB) method is evaluated by simulations based on the finite element method (FEM) and compared with conventional Delay-And-Sum (DAS), Eigen Vector-Based (EigVec-based), and Bessel Beam techniques. Several evaluation metrics such as Full Width at Half Maximum (FWHM), Peak Side-lobe Level (PSL), Contrast Ratio (CR), Positioning Accuracy (PA), and processing time are considered for comparisons. Simulation results indicate the superiority of the proposed DFB method over the mentioned methods in separability and focusing precision when the two pressure traps are close to each other.