Acoustic holography is the process in which sound waves are recorded and arranged into a visual pattern using a computer. The sound field can be modeled to reconstruct its structure using three-dimensional (3D) images.
Parametric speakers are sort of like a laser beam with the sound focused at high
intensity into a relatively small area. The result is that two people can be standing only a few feet apart from each other yet only one of them will hear the directional audio waves emanating from the parametric audio source.
I wonder if these might not be combined with a bit of geometry to create a basic hologram made of sound.
Initial sound waves are sent through an acoustic splitter so that parts of each sound wave are redirected 90 degrees from the target object, and then both the redirected and the original wave are then reflected from slight parabolas towards an array of microphones.
By playing the interference patterns on a continuous loop in reverse, and reflecting them off of the same surfaces, the re-convergence pattern of sound waves should create standing wave nodes in the shape of the original object.
I've done a sketch of how I think it might work. [link]
The effect would be an invisible three dimensional shape until mist or very fine particles were released, which would then remain suspended within the standing wave nodes to act as a screen for projection.
If this projection came from underneath the audiologram the result would be a Real three dimensional hologram rather than just the illusion of one.