Just to see how it worked, I engraved the Tek Circuit Computer scales on scrap CDs:

At first, I hadn’t correctly scaled the text paths, but the diffraction patterns caught my eye:

The illumination comes from two “daylight” T8 LED tubes in a shoplight fixture, running left-to-right, so it seems I held the camera rotated 1/4 turn in landscape mode. The pix look OK either way.
Bottom deck:

Middle deck:

Top deck, with the camera held portrait-style:

I’m a sucker for diffraction patterns …
The tiny engravings don’t photograph well, because they’re floating atop the transparent disc and the rainbow patterns from the data layer, but they still come out OK even when scaled to fit on a hard drive platter:

Looking good!
You could reverse-engrave them on the aluminum/label/top side and see how they look from the bottom/read/other side.
My one attempt with a pressed CD filled the shop with glitter as the friable lacquer shattered into a gazillion fragments. I should try a writeable CD / DVD to get, um, unicorns …