Studley is right... bigger the file, better the BG result.

You can get this done at any sign print shop that will accomodate you.

You need it printed in REVERSE onto clear vinyl.. make sure that the print is double strike or it will wash out as soon as light hits it.
Apply this to your sheet of acrylic or glass using the WET method... say 1/2 ltre water to 4 drops wahing up liquid in a garden spray... liberally wet the glass.. apply print, align and squeedgy out from centre to edge.
Leave this to dry overnight.

Now you need some white transluscent vinyl ( is a light dispersor)... apply this on top of print once again usinf WET method.. all edges trimmed with new scapel blade.

At this point you can add any blockout on the back... GAME OVER letters can be inserted etc

Once this is done, a spray of clear to seal it all.

Once dried place over a light source and cut out score windows.

Flip glass over and you have yourself a very good looking backglass