I would approach this problem through the use of compositing. In other words, you shoot a shot of the screen, and you shoot a shot of what’s behind it, and then you use the Sequence Editor (or iMovie or Final Cut or whatever) to blend the two together to your liking.
(Terminology: I’m going to refer to each of these images that you are compositing as strips.)
The simple benefit of this is that you can easily tweak it. You’ve got the finished strips, and you don’t have to spend any more time re-creating them. 2D video effects are very cheap and fast to do. Don’t like what you see? Well, just tweak something and in a few seconds you’re looking at the new results.
If you want to make the “stuff behind the screen” seem blurry, as well it would be, you once again use a 2D blur-filter in your compositing. The (sharp, crisp, clear) background strip is fed through a blurring filter, then composited behind the Japanese-screen strip, to produce the final image.
To vary the translucency of the screen, you vary the Alpha value of various pixels on this strip. You can do this while generating the strip, or you can create what’s called an Alpha mask based on the contents of the strip, and use this to modify the Alpha of the various pixels on that strip during compositing. Masks like these are usually gray-scale images, where darker areas indicate “more Alpha” and lighter areas “less” (or vice-versa). The same masking-technique can be used to achieve the illusion of depth-of-field (“depth maps”), to control specularity, to add lens-flare, and so-on.
In movie-land these things are called post-production, and directors who’ve gotten themselves into a tight spot are known to mutter, “Oh, we’ll fix it in ‘post.’” (While nearby technicians who know they’ll actually have to pull-off that miracle go … :o … and … :< …)
In Blender’s Sequence-Editor, all of these effects on strips are achieved through filters, which take one or more strips as input and produce a combined output. Other compositing tools basically do it the same way.