Why "alignment is not perfect"? It seems quite good for me.
It is not perfect in the sense that it is not computed as the exact projection, that could be awaited from a modeled scene.
I used the perspective tool of the Gimp to go from the rendered image to the phantogram image, by placing the grid manually over the square.
This results in small inaccuracies, such as the plane not being exactly at zero parallax for example. But the difference with ideal is indeed small, except perhaps in terms of resolution.