Multi focus acoustic field generation using Dammann gratings for phased array transducers

Phased array transducers can shape acoustic fields for versatile manipulation; however, generating multiple focal points typically involves complex optimization. This study demonstrates that Dammann gratings – binary phase gratings originally used in optics to generate equal-intensity spot arrays – can be adapted for acoustics to create multiple equal-strength focal points with a phased array transducer. The transducer elements were assigned phases of 0 or $\pi$, based on a Dammann grating defined by its transition points. Simulations show that simple gratings with two transition points can generate fields with up to 12 focal points of nearly equal acoustic pressures. Compared to conventional multi-focus phase optimization techniques, the Dammann grating approach offers computational efficiency and facile reconfiguration of the focal pattern by adjusting the grating hologram. We tested this approach in numerical simulations with a hypothetical high-resolution array, achieving up to 12 focal points, and validated the efficacy of the Dammann grating in a conventional 16x16 transducer array through both simulations and experiments. This comparison highlights that while Dammann gratings effectively generate multi-focus fields, the recreation ability of these gratings in a conventional array shows a lower resolution than the hypothetical array. This study underlines the potential of adapting binary phase functions from photonics to enhance ultrasound-based acoustic manipulation for tasks requiring parallel actuation at multiple points.