u/RedOctober54

I am a mechanical engineer thrust into quality to help relieve some pressure. We have a fowler (aberlink) cmm.
We are being asked to measure some small gear teeth to a .02mm profile.
I do not think we have the right tools for the job, I could be wrong. But looking at vision systems, I am not even sure they are the right tool. Just looking for input from real quality personnel. If you tell me that tolerance is wild that is good information too!

Edit: It is a type of hirth coupling not a traditional gear (thanks to u/involutes)