This is absolutely not possible. I have four patents in autosteroscopic imaging, and I'm quite familiar with the available technology. The closest thing available today is a video projection onto a falling curtain of stage fog, as seen in the Disney Pirates of the Caribbean ride. The equipment for it is bulky, and wholly impractical for this purpose. Such technology may exist in a decade or two, but the development of it is outside the scope of Quirky's design team. I cannot fathom how this made it through evaluation. Sorry :(
I'm sorry to be another buzzkill, but this cannot possibly work.