Transparent High Density Foam

I posted a thread in the Chemical and Material Science section and got some good feedback. What I'm learning is that this may be a new technology. And with some more clarity in the concept, perhaps viewers in this section could be of assistance.

What we are looking to do is create a product that has nearly all the same properties of high density foam. It needs to be more dense than packing foam. The best example is an archery target. Plus, the foam must be able to maintain form when punctured without tearing. Here is the kicker - it needs to be transparent. Not clear enough to read through, but enough to be able to see objects suspended in the material as deep as 2-3 feet. Does that make sense? Is it possible? Thanks for your feedback.