OptiTrap: Optimal Trap Trajectories for Acoustic Levitation Displays

Abstract

Acoustic levitation has recently demonstrated the ability to create volumetric content by trapping and quickly moving particles along reference paths to reveal shapes in mid-air. However, the problem of specifying physically feasible trap trajectories to display desired shapes remains unsolved. Even if only the final shape is of interest to the content creator, the trap trajectories need to determine where and when the traps need to be, for the particle to reveal the intended shape. We propose OptiTrap , the first structured numerical approach to compute trap trajectories for acoustic levitation displays. Our approach generates trap trajectories that are physically feasible and nearly time-optimal, and reveal generic mid-air shapes, given only a reference path (i.e., a shape with no time information). We provide a multi-dimensional model of the acoustic forces around a trap to model the trap-particle system dynamics and compute optimal trap trajectories by formulating and solving a non-linear path following problem. We formulate our approach and evaluate it, demonstrating how OptiTrap consistently produces feasible and nearly optimal paths, with increases in size, frequency, and accuracy of the shapes rendered, allowing us to demonstrate larger and more complex shapes than ever shown to date.

High-speed acoustic holography with arbitrary scattering objects

“…We now show how our SIMPLIFIED levitation solver performs on multipoint levitation [i.e., number of traps J = (1,2,4,8,16)] in the presence of the four scattering objects used in the previous evaluations (see fig. S3).…”

“…Here, we compare these three solvers to demonstrate that only the SIMPLIFIED solver provides both high computational speed and trap quality. Similar to the previous evaluation, we used 1000 random combinations of trap positions per condition [i.e., four scattering objects with the different numbers of traps J = (1,2,4,8,16)]. The numbers of transducers (N = 256) and iterations (K = 100) were fixed.…”

“…Acoustic levitation (1), a technique that used mechanical energy of sound to levitate and manipulate materials, has been notably advanced over the past decade through the introduction of two fundamental techniques: phased arrays of transducers (PATs) (2,3) and acoustic holography (4)(5)(6). PATs allow dynamic control of dense arrays of sound sources (e.g., 16 × 16 ultrasound transducers), while holography, a wavefront-handling technique originally developed in optics, enabled PATs to accurately control sound fields in threedimensional (3D) space. Thanks to its capability of levitating almost any type of materials, acoustic holography using PATs has many potential applications in laboratory-on-chip (7), biology (8), computational fabrication (9), and midair displays (6,(10)(11)(12)(13)(14)(15)(16).…”

“…PATs allow dynamic control of dense arrays of sound sources (e.g., 16 × 16 ultrasound transducers), while holography, a wavefront-handling technique originally developed in optics, enabled PATs to accurately control sound fields in threedimensional (3D) space. Thanks to its capability of levitating almost any type of materials, acoustic holography using PATs has many potential applications in laboratory-on-chip (7), biology (8), computational fabrication (9), and midair displays (6,(10)(11)(12)(13)(14)(15)(16). Acoustic levitation is also emerging as a strong candidate for creating mixed-reality (MR) interfaces that can seamlessly blend the digital and physical worlds, as envisioned in the Ultimate Display of Ivan Sutherland (17).…”

A digital twin approach for experimental acoustic hologram optimization

“…While these numerical approaches use simulated values to optimize acoustic fields, a number of experimental results suggest that the acoustic field in reality is offset from the numerically simulated field 3 , 8 , 21 – 23 . These offsets could emerge from simple uncertainties in the transducer position, power, and phase, or could emerge from non-linearity, inhomogeneity, or the existence of other scatterers in the field.…”