Holographic planetarium Discussing the possibility of building a planetary with some colleagues, we started wondering about the theoretical idea of a planetarium dome based on a multichannel CGH able to show the sky of different latitudes depending on the distance of the observer to the center of the room. The flat Earth joke arose, but the theoretical exercise continued. Its clear that, just to begin:


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*The objects at the horizon (and at low right ascension if the CGH has a finite angular resolution) would necessarily be the same for every observer in the ground. Maybe a high skyline could mask this.

*If the distance hologram-observer is not cosmic... the perceived sky will also depend on his/her height, messing up the idea of a true floor-point --  effective-latitude mapping.


Both are consequences of the hologram multiplexing their channels according to angles, as two observers share their line of sight when looking to an object in the horizon, and the angle also depends on their height.
What would be other practical or geometrical limitations for this hologram? For example, regarding the complex setup for reference beams...
 A: What you propose could be done, in principle.  
In the drawing below, the circle represents the planetarium dome.  The blue lines represent rays from a single star, incident from infinity and propagating diagonally downward to the left.  Your hologram would be made using a reference beam containing a collimated light source for each star.  The object beam could be pretty much anything, but in the drawing the black radial lines represent a reference beam propagating outward from the center of the dome.  

The resulting hologram, formed in a medium (e.g., photopolymer) on the dome, will be a reflection hologram that can be illuminated from the center of the dome.  The hologram will reconstruct all of the components of the object beam, as if the collimated light from each star were propagating into the dome.  Everyone inside the dome would see the same sky.  Simply rotating the dome would correspond to changing the observer's latitude and/or longitude.
Making such a hologram would be a monumental project, but it could be done.  Most likely each small portion of the hologram would be recorded separately.  Designing the apparatus to record it would be straightforward.  The individual pieces of the hologram could be flat.
This isn't quite the "flat earth" hologram you envisioned, but it's close.  The "flat earth" hologram would also be possible, but would be more complicated to design.
