Target acoustic field and transducer state optimization using Diff-PAT

Abstract

Phased array transducers (PATs) are used in many applications, from airborne ultrasonic tactile displays to acoustic levitation. Acoustic holograms play a significant role in determining the performance of these applications. Many PATs and optimizers have been developed; however, only the following have been demonstrated in the literature: “phase” and “phase and amplitude” control of transducers and “phase” and “amplitude” only control at target points. Thus, most of the combinations of transducer state and target acoustic field conditions are yet to be explored. Here, we explore such combinations using Diff-PAT, one of the latest acoustic hologram optimizers. Diff-PAT is based on automatic differentiation and stochastic gradient descent. This optimizer achieves higher accuracy than conventional optimizers. We formulated multiple loss functions and wave propagators to enable each combination of the operation mode and quantitatively assessed the performance of each combination. The developed optimizers will offer new opportunities in the field and could allow further simplifications in PAT applications.

A digital twin approach for experimental acoustic hologram optimization

“…A number of acoustic hologram optimization techniques have been proposed, including Gerchberg-Saxton 12 – 14 , Eigensolver and Tikhonov-regularization 2 , machine learning methods 15 , 16 , direct solvers 17 , and greedy-type solvers 18 . In 2021, we demonstrated an automatic differentiation approach to acoustic hologram optimization 19 , 20 and exhibited good accuracy with the application of automatic differentiation and the Adam optimizer in simulation.…”

“…We use PAT as described in the “Methods” section, and it takes phase-only acoustic holograms (operates in phase-only A mode hologram). As in Fushimi et al 20 , we begin by defining a suitable loss function for the phase-only (A:i), amplitude-only (A:ii), and phase and amplitude (A:iii) optimization: where A c and ϕ c are the target pressure amplitude and phase, and and are the substituted pressure amplitude and phase, respectively. The substituted pressure amplitude allows the automatic differentiation package (in this case TensorFlow) to track the gradient of the function, whereas the inside of function G () is untracked by the package (achieved by e.g.…”

“…We note that this process does not act as mathematical operators, and only serves a functional purpose to introduce foreign variables to the computational graph of TensorFlow. As in Fushimi et al 20 , A c = 1 was set for A:i and ϕ c = 0 was set for A:ii.…”