Automatic differentiation approach for acoustic holograms: Performance and potential applications

Acoustic holography underpins the number of modern acoustics applications. The usage of multi-focal acoustic holograms with phased array transducers (PATs) in ultrasonic tactile displays and acoustic levitation are increasing, and achieving a high-quality hologram are of significant interest. Inspired by the latest optical hologram optimizer, we developed a novel acoustic hologram optimizer for PATs called Diff-PAT [T. Fushimi, K. Yamamoto, and Y. Ochiai, “Acoustic hologram optimisation using automatic differentiation”]. Diff-PAT is based on a gradient-descent algorithm and automatic differentiation. The performance of Diff-PAT was numerically evaluated using three array configurations and it achieved superior accuracy over the conventional optimizers. For example, when two focal points are generated with 196 ultrasonic (40 kHz) transducers; the state of art optimizer (with phase and amplitude modulation) based on Eigensolver has an average error of 4.07 % where Diff-PAT (with only phase modulation) achieve average error of 0.0174%. These results show that amplitude and phase modulation may not be necessary for PATs to be successful. Furthermore, we demonstrate the versatility of Diff-PAT by applying it to binary acoustic holograms, simultaneous modulation of acoustic amplitude and phase at the target plane, and phase plates. [Work supported by Pixie Dust Technologies, Inc., Diff-PAT is patent pending (JP2020-167367A).]