Background partly shows up in the outline

http://www.pasteall.org/blend/42757
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When I press shift z, the background doesn’t show up through the outline, but when I render the image with F12, you can see part of the background show up between the outline and the sphere itself. The outline is made from the solidify backfacing method while the color of the sphere itself is a shadeless placeholder. Any help or explanation is appreciated.

If you can afford the increased render time, full-sample antialiasing should take care of this problem.

Thank you, that fixed the problem.