https://www.youtube.com/watch?v=BtMqx5P74n4In this video, Les' Lab makes an integrating sphere. His channel does a lot of optical stuff, mostly laser related. Therefore the integrating sphere he makes is very small, but he does reveal some excellent information.
Commercially, integrating spheres are internally coated with a special coating of mostly PTFE called Spectralon. Not very accessible, and even if you were able to buy it you would still be spending a heck of a lot of cash for it. But a coating made of PVA glue and barium sulfate apparently is a reasonable alternative. The paper that he cites claims a 95% reflectivity of the coating (as opposed to the >99% reflectivity of Spectralon). Barium sulfate is also apparently sufficiently non-fluorescent so it isn't gonna mess up spectrometer measurements. Obviously this is not quite as good as Spectralon, but with my non-existent optical expertise I conclude that it is
probably good enough.
So far all of these things are easily accessible. The only remaining problem I see here is selecting a spherical container large enough for HID lamps. In the video he used a cannonball mold, but unsurprisingly they don't make them big enough for our purposes. All we need are two spun sheet metal hemispheres. You would think this would be easy but apparently not. So far I found these stainless hemispheres for decorating:
https://www.amazon.com/dp/B09ST7PY3HYou can find them bigger than 12" but they get really expensive, and 12" really isn't that big. Obviously not as expensive as an actual integrating sphere, but that isn't saying a lot. Anybody else have other ideas for enclosures?