You won't get a proper global Mercator map through light projection (a so called geometric projection) from a sphere, the relation is purely mathematical.
A central cylindrical projection is what you get when you put a light in the center of a sphere and project that on a cylinder
A central cylindrical projection is what you get when you put a light in the center of a sphere and project that on a cylinder
http://www.progonos.com/furuti/MapProj/Normal/ProjCyl/ProjCE...
https://en.wikipedia.org/?title=User:Peter_Mercator/Draft_fo...
You could get pretty close with Braun type stereographical for non-global uses with a fixed light source.
http://www.progonos.com/furuti/MapProj/Normal/CartHow/HowBra...