Strange shadow artifact

Hello there!

So I was experimenting on some curtain-like material, and I found something close enough to what I’d like to achieve, simply with subsurface shading model.
The result I’m trying to achieve is the following: a plane on wich meshes project shadows. Those shadows can be seen on both faces of the plane, because the light going through the material would allow us to see the shadow from the other side.
But I want the plane itself to cast a complete shadow (see picture below).

And as I said, I managed to do that with a subsurface shading model.

The thing is, when I’m under my plane, I have a weird artifact, where a shadow appears out of nowhere, masking the tree’s shadow.

And when I move the camera, the intruder shadow moves with it, and sometimes makes artifacts like if two planes were clipping (which is not the case)

348042-ueshadow4.jpg

Is there a way to have the same result on the two faces of the plane? I tried turning it around just out of curiosity, and it’s always the face facing the ground that has this issue.