Various details are at http://www.instructables.com/id/Making-Your-Mini-Laser-Engraver-Safer-and-Better/
I used 1/8" thick for the panels, but got ones that are almost completely opaque -- which is why the little circular window. Now, I think I'd recommend simply using any opaque material, not bothering with a window, and simply using a webcam for viewing. The particular webcam I used for this isn't widely available now, but it's less than $10 to buy a USB endoscope camera that is tiny (so easy to mount inside) and has some surprisingly bright LEDs built-in that help light the part being worked on. The endoscopes can plug into either a cell phone or a computer. Still a good idea to put a little filter material over the camera lens, but it is usable without it.