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GS-PAT and IBP are both modified versions of the Gerchberg-Saxton algorithm 32. Marzo & Drinkwater proposed the iterative back propagation (IBP) method in 2018 14, and Plasencia et al. proposed Eigensolver and Tikhonov based regularisation in 2014 13.
Multiple control points are becoming a necessary part of PAT applications, and low-quality acoustic hologram can lead to poor performances during practical use in applications. Generating an acoustic hologram for a single control point in space using PATs is trivial however, it has been a significant challenge to generate a hologram that can create more than one control point in space. demonstrated that the control points can be converted into levitation points by adding a twin-trap hologram in acoustic levitation 14, 15. The control point is modulated at low frequencies to create haptic sensations that are sensible by human hands in an AUTD 12, 13. In all of these applications, acoustic holograms must generate a pressure control/focal point at a specified position. Acoustic levitation in particular is used for digital fabrication 18, 19, display applications 20, 21, 22, 23, 24, 25 and sample holding in medicine 26, 27, physics 28, 29 and chemistry 30. Recent advancement of airborne phased array transducers (PATs) have enabled new applications such as airborne ultrasound tactile display (AUTD) 12, 13 and acoustic levitation 14, 15, 16, 17. Thus, developing an acoustic hologram optimiser that can generate holograms with accurate field reconstruction is of significant interest of the field. The reconstruction accuracy of the acoustic field from the hologram plays a significant role in determining the performance of the system. In addition, we applied Diff-PAT to a phase plate and achieved an increase of > 8 dB in the peak noise-to-signal ratio of the acoustic hologram.Īcoustic hologram is becoming an imperative part of a wide range of acoustics applications such as in the fields of medicine 1, 2, 3, biology 4, 5, 6, 7, 8, and engineering 9, 10, 11. This optimisation platform for acoustic hologram can be used in a wide range of applications of PATs without introducing any changes to existing systems that control the PATs.
The performance of Diff-PAT was evaluated by randomly generating 1000 sets of up to 32 control points for single-sided arrays and single-axis arrays. We show that in the most fundamental case of optimizing the output amplitude to match the target amplitude our method with only phase modulation achieves better performance than conventional algorithm with both amplitude and phase modulation. In this paper, we present Diff-PAT, an acoustic hologram optimisation platform with automatic differentiation. Optimisation methods that control only the phase of an acoustic wave are considered inferior to methods that control both the amplitude and phase of the wave. They encode three-dimensional acoustic fields in two dimensions, and their quality determines the performance of acoustic systems. Acoustic holograms are the keystone of modern acoustics.