How to make a spherical projection mapping

Hello everyone!
I try to make a projection of the sphere with a diameter of 0.7 meters.
I use two projectors Panasonic DX100 XGA (10,000 lumens).

I was faced with information projectors. Projector diverge on each side of the sphere. Video sample and patch investments in the post.

Has anyone tried to do it, or who have an understanding of how to resolve this problem?

spherical mapping patch (11.5 MB)