Reconstructing mid-air acoustic holograms using PMUT arrays: a simulation study

Abstract

Mid-air acoustic holographic techniques allow the tempo-spatial reconstruction of the desired wave profile (in amplitude and/or phase), driving novel applications such as particle trapping and haptics in air. Piezoelectric micro-machined ultrasound transducer (pMUT) remains promising for these applications due to its potential to build up high density, cost effective phase arrays compatible with drive electronics. For this purpose, we characterized in-house fabricated discrete pMUT devices and assumed each element of pMUT phase array performs the same in this paper. Using these parameters as input of $25 \times 25$ pMUT arrays, we mainly demonstrated three different acoustic projection methodologies for reconstructing mid-air acoustic holograms 1 cm distant from the aperture by simulations: pure pseudo-inverse (PINV) algorithm, PINV algorithms together with iterative weighting, PINV methods integrated with Tikhonov regularization. The resulting drive performance of pMUT array, calculated as transducer drive efficiency for variant acoustic holograms, was increased by 3-6 times when adding iterative weighting or Tikhonov regularization. The trade-off was the side lobes distributed across the final pressure field compared to the reference of PINV but Tikhonov regularization outperformed iterative weighting especially in the central region.