Accurately positioning a camera from a plane

Hi all,

I’m trying to figure out how to position a camera so that I can precisely capture a plane that is displaying a 1080p texture. Displaying the texture in the UI rather than a 3d plane gives great results but I want to be able to have 3d objects in front of the screen. I’m trying to avoid using green screen etc as I lose the ability to have certain lighting effects and translucent materials etc. I have positioned the screen manually but as you would guess it loses some clarity as the pixels are not perfectly aligned. Is there a tool for this or a good way of calculating the ideal distance based on the lens settings etc?

Thanks for your help!