The topic of these occasionally seen tight rings around stars has come up several times. Here is a Hubble example:
There have been a few proposed explanations but nothing made sense to me, mainly because the rings hold intensity well and they don't die off quickly. In the Airy pattern they die off very quickly - but these rings show even in linear images with no stretch.
The rings are also fairly narrow and they get tighter as you go out.
For me they are correlated with good guiding and good seeing - and very small stars.
I think they are a form of Tolansky fringes, described in this early paper and seen in Fabry Perot interferometry:
What I think happens is the star image is formed mostly on a single pixel and the microlens reflection acts like a point source. The sensor coverslip then acts like an etalon and allows the fringes to form. The key thing is that the number of bounces within the window isn't increasing as you go away from the star - that is why the fringes remain bright. Only the effective path length is increasing - not the number of bounces. If the number of bounces increased as you go out - they would die off very quickly.
To view it properly you need to forget about the light coming from the star itself through the OTA and instead view the pixel itself as the local point source. So you have a point source next to an etalon and you get fringes.
If you have less good guiding then the fringes from nearby pixels will overlap and blur out the pattern - so a key factor is that most of the light is concentrated on a single pixel so it acts like a point source.
And nothing to do with filters or bounces off elements in the OTA. But it does depend on the AR coatings of the coverslip. No connection to f/number except in ending up with a very small star spot mostly landing on one pixel.