Re: My office "showroom" build-out.
Logo transfer to foam board:
Print out an outline image on paper
Place image on foam board and affix with tape
Use pointed object like nail, needle or pin to poke holes along the outline of your image, into the foam
Remove the paper to reveal a dotted outline on the foam
Use a scalpel blade (x-acto, utility knife, etc.) to cut the shape following the outline - a thin blade on a jigsaw could also work
For my specific example I transferred the image onto the back side of the foam and also cut from the back side. This was so that the back would be a very tight and clean outline but the front could be chipped and ragged. Since the foam was over an inch thick, the side opposite your cut will never be as precise.
The texture was accomplished through carving and paint application. First I lightly drew some feature lines on the foam and then started on it with the blade removing large chunks. Then smaller chunks. Anything that was smooth I also scored lightly with the blade and then scraped to give it a rough texture. For paint I used black, blue, white and grey, plus some sponge application with various of the paints mixed with clear acrylic gloss medium. The base coat was solid black first of course. I also had to do a lot of touch-up with brush to get a bunch of little pink bits that were still showing through. If it's available to you, use blue foam instead.
Lighting up a logo.
What I didn't do:
I was originally planning to use plexiglass (acrylic) for this effect but decided to go a different route simply to avoid going out to buy a piece of plexi. Basically you put a piece of plexiglass behind your cut-out and edge-light it. The light will shine through wherever there is an angular disturbance in the face of the plexi. So that means you scuff it, cut it, etc. to create marks that will light up. In this particular case I was going to use two sheets of plexi, each lit with a different color and scratched up in different areas to try and create a fiery look.
What I did:
Create a bumpy texture with a little bit of papier-mâché pulp on a sheet of 1/8 hardboard.
I just shaped it with my hands, very low relief.
When it was nearly dry I made adjustments to the texture with my hands and a scraper.
Get yourself a large square of tinfoil and crumple it up, then stretch it back out again - it should be all creased up.
When the texture was completely dry I glued the piece of tin foil to it and shaped the tin foil so it would follow all the contours of the texture I'd created, pressing it into all the nooks and crannies.
When the glue dried I applied black acrylic paint to the foil with a brush and let that start to dry. Don't worry about being ruff and leaving exposed areas.
Before the paint dried I rubbed a cloth over top of the foil removing some of the paint and exposing the foil in many places.
The exposed foil will reflect the most light, so the balance of exposed to black is really going to affect what the final piece looks like lit.
The lighting is provided with LED ribbon light - RGB 5050 LEDs in my case. The ribbon segment is sandwiched between the original foam and this hardboard/foil background texture. The lights shine inward toward the center of the logo. The images below show the testing phase when I was using plain white (smaller) LEDs.
Back to your piece of foam - flip it around so you're working on the back with the clean logo outline
Make an outline in marker around the cut-out, at least 1/2" outside of it.
Score this new outline with a blade - you're making a channel to support the LED ribbon light.
Now start inserting the ribbon light into this channel you've cut, making sure not to insert it so deep that you cover the LEDs - just the edge of the strip needs to be inserted.
Remove the adhesive backing on the ribbon first and that will help hold it in place.
Optionally add glue around the ribbon when you're done to permanently affix it.
Now grab your textured foil background and lay it over the LED and onto the bad of the foam creating your sandwich.
I just used metalized duct tape tape to hold it down and block any possible light leakage.
Done.
I've updated the image in the previous post to show the properly secured backdrop.
How did you manage to get this texture and what did you use to cut out the Bat Logo? Is it easy to do? 
"Resistance is Futile"
