Background : a solution to reduce file size or 3D calculating

Hello everybody

I tried to create a 360 space background (editing style; photo mapped sphere; photo mapped cylinder).
When I launch the animation the program cuts shapes and show inside. That works fine (no section planes) without the background.

How can I create a 360 background without increase 3D calculating ?

Thanks for all your advice.

Some photos to explain my problem that appears too when shadows mode is on.

Shadows off :

Shadows on

What do you think about my problem ?