Step 5: Pad it out...
You need this fluffy layer to act as the photon transport matrix to spread the light. I guess you could design something similar to a thin LCD panel. More discussion here www.instructables.com/id/Light-Tablet/. If you really want find out about how light really moves, just ask our resident particle geek, www.instructables.com/member/kelseymh/ .
You may want to experiment with your light source to see how thick your padding layer should be. Trim to fit coming to about 1/2 inch short of the edges.
Use duct tape or clear packaging tape to close in the back of this layer. The free edge of the sewn cutout gives you a place to anchor the tape at the edges.