I have recently noticed during my own tournament games that I am not infrequently closing my eyes, or at least looking away from the board, when engaged in in-depth calculation (or what counts as in-depth for me). This isn't deliberate on my part; it's just something I've naturally started doing more often. I know that some well-known players do this quite a lot, e.g. Ivanchuk has a reputation of very often staring up at the ceiling when calculating, and I think it actually makes a good deal of sense:
Having an image of the current position in front of you can be helpful if you're apt to lose track of it. But that's not a problem for someone like Ivanchuk, and so that "plus" is inconsequential. On the other hand, having the full current position right in your visual field might actually interfere (for some folks) with the process of fixing projected future positions in your mind's eye, thus sometimes leading one to look away.
With that in mind, it seems not unreasonable to me that a lesser light than Ivanchuk might possibly benefit from the middle ground of staring at a blank chessboard while calculating like this. The current piece positions aren't there to interfere, while one still gets the image of the chessboard to serve as a potentially useful "frame" for the successful mental imaging of positions. I don't think that I'd actually find it very useful, and perhaps nobody would, but that's neither here nor there as far as my question is concerned.
While one obviously can't use an analysis board when playing tournament chess, do the rules (e.g. FIDE or USCF) actually preclude having an empty chessboard nearby at which to stare while calculating?
Many scorebooks already have scoresheets that look something like this:
Thus many tournament players already have a small empty board available to use exactly as I've described, if they so desired. So, is it technically permissible for them to place an empty board nearby before the game, and stare at it if they like? (If nothing else, I suppose one could make custom scoresheets featuring quite large empty diagrams ...)