There was thread awhile back about drum screens where Bart mentioned that making your own is really easy and less expensive that buying one of the pre made ones. Well, I have researched it a little and I definitely agree with him on all points. Plexiglass/polycarbonate sheet is not that hard to work with and can easily be machined.

Has anyone made their own screen? How did you do it? What materials did you use?

In particular, I'm interested in what type of sound absorbing materials, if any, you used? I know acoustic foam is made just for this, but I am on a limited budget and was wondering if anyone has used any common materials-  like carpet padding or that cheap bed mattress foam - anybody used anything cheap that worked well?

The foam is a great idea, if you are in studio or live.  But how would you make it look nice if you were putting it on clear Plexiglass?  I mean, the sight of heave duty adhesive on the back of foam doesn't sound as if it would look very nice.  Naturally I'm talking about in a live situation, I could give a crap what things look like in the studio.  

The only thing I wouldn't like about the plywood/foam combo is that you are getting into some heavy stuff there, and I like as little weight as possible when loading in and out (especially out).  Maybe paint the front of the plexiglass to hide the foam and just glue the foam directly to the plexiglass?

(the other advantage of painting the inside of the screen is that carting won't scratch the paint off)

...you should rough up (course sanding) the plexiglass before painting, and use a good primer in the color you want to show because adhesion would be better with a primer, especially if you're gluing a layer of foam over it.

Do you know the difference between sound absorbtion and sound barrier?  You asked for sound absorbtion on your sound barrier.  Plexiglass is a sound barrier.  I know of no transparent sound absorbing materials (foam, carpet, whatever).

You are looking for a sound barrier.  Acoustics First sells a clear sound barrier sheet at around $5.00 /sq. foot.

I would stick with the plexiglass and have some foam type of absorbtion behind you...then you can see your church buddies as they are doing the "quake" and then you can keep your drum noise down.  Check out auralex.com for those barrier type absorbers (sunburst)arrays.  They also have isolation type/booth-panel deals.

But I like my idea the best/plexiglass in front with foam absorbtion behind you.  You can pay me later for my consultation fee.