As described on Theta's Details page, Wah put in that communicator a radically different kind of moiré effect that came from two stacked samples of a thin multi-prismatic sheet found in the Edmund Scientific "Experimenter's Moiré Kit with Booklet":

These translucent plastic sheets, with tiny parabolic lenses on one side, are no longer available, but the same manufacturer Rowlux still makes a very similar product called "Clear Colorless Moiré Illusion Film," item #PC-13-001, that has the two layers pre-bonded to create a rippled pattern intended for larger-scale applications:

Small sample sheets like what's shown above can be purchased through retail distributors ePlastic and CanalPlastics.  With it, you can then re-create the 1960s product to near perfection for your replica prop.  This is done by sanding off the tiny lenses from one side and polishing back up that surface.  The results are spectacular, but in order to bring the two lenses close enough to properly interact, you must reduce the thickness of the sheet by half, from 0.015" down to around 0.0075".  The complete process to do this is below.  Figure it's about an hour of focused labor to do a sheet good enough for at least four circles, or two sets.

All the tools needed are pictured here.  Get the 400 grit sandpaper as dry/wet, since it clogs less with the powdered plastic when kept wet.  And it pays to keep your hands and workspace as clean as possible throughout:

On a smooth, hard, exceptionally flat surface, lay down (at least) four strips of 1/2" wide (or 3/4" from Rite Aid) double-sided office tape, placed as edge-to-edge as you can without any overlapping.  Shoot for 6" long by 2 to 3" wide - much bigger and it's hard to get uniform end results in your sheet.  It's critical to remove any bits of raised dirt that may have ended up on or under the tape, as even the tiniest bump will affect (spoil) the sanding of the sheet there:

Adhere down the plastic sheet, cut to the dimensions of your taped surface. 

Minor note: it doesn't really matter where you cut your sample piece out from the purchased large sheet, but be aware that the ripples you see in the product may or may not get completely sanded out.  It seems the prismatic lenses on one side are perfectly geometrically aligned, whereas the other has slight distortions that then create those ripples.  Thus depending on what side you remove, the mild distortions are either gone or they remain.  And it's impossible to know in advance which side is which before you start sanding.  If the ripples do remain, it simply means the moiré patterns the sheets eventually produce will have some interesting curves in them.  An example of this is pictured further below.

And since you may in the end have a preference for either the geometrically-precise or the mild distortion patterns (our is the "precise"), you'll want to keep track from the beginning (with, say, colored markers) of which side of the master sheet your cut sample is being worked on.  This way when you see if you've removed (or not) the ripples, you'll later be able to duplicate (or change) your results as you see fit with the next sheet sample you work on.

Now comes the grunt part - the sanding.  Start with 150 grit to remove the bulk of the excess thickness.  If you don't remember from shop class, always sand with any one grit in the same direction (never swirl), then for the next finer grit, sand at 90 degrees to the last one.  This lets you easily see the older scratch marks you still need to remove.  Occasionally measure your thickness progress using the micrometer by gently lifting the sheet in a few spots from the tape.  Aim with this first grit to get down to about 0.008".  Be mindful not to speed the work by pressing down harder, as that will leave excessively deep scratches.  Once you've reached that target thickness with the 150, sand with the 320 grit in the opposite direction until the 150 scratches are gone.  After, switch directions with the 400 until the 320 scratches are gone:

Continue this process until you're using the 2000 and just some mild scuffing is seen (you don't have to be perfect here).  Note your corners and edges will take a beating, but there's still plenty of good sheet left.  Also be aware that as your sheet gets thinner it also becomes more flimsy and fragile.  Thus be slow and careful when lifting up and measuring the thickness so as to not dent the material with the micrometer:

At this point you should be at about 0.0075 to 0.0070" thickness, and all that's left is to bring the surface to a dull shine, either with a burnisher or by vigorous rubbing with a firm paper towel (7th Generation brown recycled is good).  Don't go overboard with the polishing as it won't matter in the end product.

Here's at last what you get, compared to the original material:

The re-creation looks blank, but that's only because the sheets end up too thin and lightweight to lay flat and tight against each other, so the pattern effects don't appear.  But when we press the layers together under a piece of glass:

Now we're talking!  Note how in fact the newer sheet (if you sand off the distorted side) is more geometrically unform than the vintage product.  But it gets better.  When we simulate in both products the two layers being glued together (this with a drop of water, substituting for a clear adhesive)... 

... the effects really stand out, with the re-created sheets even surpassing in clarity and sparkle the original!  Now given that our guess of Wah's actual pattern in Theta is tenuous at best, you have full license to choose any pattern you favor from your finished layers and still proudly declare your moiré insert to be completely screen-accurate.  Picking your one final pattern may sound easy, but so numerous are good ones that you'll want to leave yourself time here to make the decision.

To glue the two layers together, we'd avoid clear epoxies and solvent-based glues that, if they smear out and get on the outer surface, will instantly ruin your work, since you'll never be able to clean the gunk out of the microprisms.  Rather, consider using water-based (i.e. easily removable) transparent craft glues, as the bonding strength actually needed here is minimal.

One last tip is how and when to cut your sheets into disks.  The upshot is you'll want to trim your disk after you've selected your pattern and glued the two layers together.  Here's how... first draw two circles (carefully sized to fit inside your bezel ring) on the prism side of the sheet with a mechanical pencil (for its sharp lead tip).  Cut out the circles with sissors - but do so first in squares slightly larger than the circles.  This extra material outside the lines will help you in manipulating the sheets into position, plus allows extra room to prevent any excess glue squishing out beyond the circles from leaking onto your prisms.  Wash off the drawn circle from one of the squares so you're left with only one circle to guide your eventual trimming.  Temporarily mount one square, smooth side up, onto a black, flat surface using a bit of tape at the sample's corners, add in the middle a tiny drop of water (to simulate the glue), place on top the second square (smooth side down) and rotate it until you find your desired pattern.  Mark with tape or a pencil the alignment of the top layer, then remove it and dry both surfaces.  Now add a drop of your clear glue on the bottom sheet and lay down the top (IMPORTANT - be sure you're putting together here the two smooth sides and not any of the prism sides).  Position the top to your previously-marked alignment (to create your chosen pattern) and press down as flat as possible, pushing any air bubbles in the glue to outside the circle.  Only then, once the glue has set, do you trim your disk with scissors. [Note - no images of this step are provided as it was figured out too late].

So here are two re-created disk assemblies; the left one constructed with sheets that have the precision geometry and the right with the mild ripple distortions, both next to the original product - and all set to about the same pattern (as per our tiny pointer guide):

And this is what you get when you stick with it... the most dazzling, true static moiré effect you could ever wish for (this one is the above "precise" re-creation):

p.s.  We asked Rowlux if they could produce from their machinery a small sample of half-thick film with the prisms on only one side.  Their answer was unfortunately a no.

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