I wonder, is it possible to create 2D holograms? That is, a sprite, or a hologram that looks the same no matter the angle?
My usecase would be a set of parentheses (as in XKCD #297 "These are your father's parentheses, elegant weapons for a more... civilized age"), or perhaps even dragon balls (the star formation are supposed to look the same no matter the viewing angle).
But I suspect that the interference pattern would in that case interfere with itself down to nothing.
In the general case, you can make a hologram that looks like anything from any angle (like play a movie as you walk past) - given a particular viewing distance, because at a different viewing distances you will see mixtures of different "frames" due to parallax.
I can't offhand reason out what "viewing distance distortion" would do in the specific case of making a 2d image "follow" you (might even cancel out!), but in any case it's not a big deal if the viewing distance is much larger than the hologram size.
Interestingly, there's a traditional optical solution to this problem as well: beer pump logos, which are often displayed behind a very convex lens which partially corrects for parallax distortion.
(Edit: you will not, however, be able to correct for rotation. The hologram can't possibly "know" what orientation your head is in, only where it is.)
Depending on the way the hologram is printed or created, the hologram recreates the full wavefront, so the hologram replays the image without needing to know how your head is oriented.
Will need to look up beer pump logos. Interesting.
A traditional analog hologram of a real plane, like a table, would simply recreate the image of that object exactly. It would have parallax just like the real thing.
To engineer a hologram that makes some attempt at "following" you, you would either need an extremely elaborate multi-exposure analog setup with rails and shutters and god knows what, or a digital holographic printer, which is another (fascinating) kind of beast entirely. In the latter case you generate what you want the hologram to look like from every possible angle, which is your case is simply the same image with perspective (un)distortion.
My usecase would be a set of parentheses (as in XKCD #297 "These are your father's parentheses, elegant weapons for a more... civilized age"), or perhaps even dragon balls (the star formation are supposed to look the same no matter the viewing angle).
But I suspect that the interference pattern would in that case interfere with itself down to nothing.