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Good question. Definitely would be better to use thicker stuff. I had to press down around the edges of the chamber to ensure it was flat, had to be extra careful. 1/4" plexi/lexan might be ideal as it is inflexible (at least for small distances). Before CDs, I used 1/8" plexi because I had some ready to hand.

Also best to use a very thin layer of grease, as it has to be pushed flat so the measurement is not affected. This is where the CD case material flex came into play, the grease thickness was causing it to flex a bit instead of just pushing the grease down. Pushing and rotating the plastic worked well.