Volumetric acoustic holography and its application to self-positioning by single channel measurement

We generated dense mid-air volumetric acoustic holography using a newly developed computation algorithm and experimentally verified its utility for three-dimensional self-positioning via monaural amplitude measurements. We computed the holography by solving an inverse problem where complex amplitudes of ultrasound emissions are to be determined so that the given acoustic amplitude field at a finite set of control points in the workspace could be generated as faithfully as possible. With a one-directional gradient pattern of a 40 kHz ultrasonic field that stretched uniformly toward the depth direction, numerical simulations showed that positioning with an average error less than 3 mm is ideally possible in a 100 mm-sided cubic workspace. We experimentally verified that this error was approximately 8 mm with our custom-made phased array. Our work shows the first example of information systems, where a position-dependent information field is embedded in the environment as a form of holographic wave field that can be sensed by standalone mobile devices.