After looking for a "nice" 360degree projection of the night sky, I realised none look like. What you will actually see in real life, as the distortions at the Poles or Equator region is too severe, depending on the projection of your choice.
The nearest is a EquiRectangluar Spherical Projection (at least I know this from 360x180 panoramic photography.
I somehow feel in the Deep Sky Stacker method of AstroPhotography, Image distortion because of Lens is not being taken into account as much it is being taken in Panoramic Photography.
When I over lay a photograph of a Constellation on an IAU constellation map, and match the FoV/size of both the map and the photo, the stars at the edges are "way off" the Map marker, ultimately I use a "wrap" in photoshop to make them fit "better".
In wrap, I find it better to start at the corner stars and move the edges to try to get as many inner- stars align with the map, do this for all corners and try to get a. "better fit" but as you move one edge it will effect the entire image, so once u do a basic corner correction warp, move to the Center and start to better fit the star-photo to the Star Map.
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