Hi Bojan,
Maybe you could try something like a watch face, that would be close to that diameter, you just need to ensure that if you need it for optical properties that you stay away from its edges where the radius will tighten. I suspect that if you found a ~40mm face you should be OK to have a reasonably constant radius for the 31mm zone you need. Where = Of course try eBay or an old toy watch or something?
Good Luck
EDIT..... As an example try this in increments of various diameters from 30 to 38....
https://www.ebay.com.au/itm/1pc-30-3...sAAOSwLVFbogvH
Or find a circa 200mm diameter acrylic sphere and start cutting
Best
JA