I was with you until this part. I think it is important to share the manufacturers AR claims on the window itself. They are 98.5% or 1.5% whichever way you want to slice it -- which based on previous comments you have shared -- is not very good. Now the testing on the refractor showed a net zero effect of the window. The refractors also had the lowest probability to show any of the conditions in question at all. In fact I suspected the window would show little to no difference based on the surfacing of the issue on those lenses to be very small or close to zero.
The type of telescope has been very relevant in the surfacing of this issue. So again I disagree with your assumptions. The data we have on hand in this thread shows otherwise. The same battery of tests needs to be done with a larger telescope, more prone to produce these conditions in question.
In the abscence of that, here is a frame to look at:
This is the worst case scenario for this problem we are working though. 12.5" Corrected DK Telescope (Cassegrain design), with a Sony IMX455, Chroma 5nm HA filter, and a 20 minute exposure on a Mag 4 star. None of the issues outlined here surfaced. No halo, no ((o)), and no grid.
I do appreciate your contributions to the thread though and hope that you continue to engage with this.
In the image you shared I indeed can see a grid, or better called mottling in this case since the spots are almost overlapping, just very closely spaced near the star in the surrounding (normal) halo. The grid here is possibly from the coverslip to microlens which might be less than 1 mm distance and at f/8 (?) the spots remain small.
In any case what are the differences the OTA can impart on the light cone received by the filter wheel/camera?
-Angle of cone, determined by f/ratio.
-Spectral content: mostly determined by the source star, with refactors losing more in the extreme violet due to absorption in the glass. (BTW a corrected reflector has much the same properties here as a refractor since the lenses are made of glass
-Polarization: not measurable by our sensors, and nearly always perfectly random from the source anyways.
-Transverse intensity distribution: here a small difference is the hole in obstructed telescopes pupil pattern. Can we think of any reasons why this would matter?
-Type and amount of diffraction: Refractors have much less of this for sure, and no spikes due to spider vanes or cables, but how does this affect haloes which are reflections?
-Intensity or amount of photons: aperture and exposure time determine this.
IMHO the problem you are trying to address is multiple reflection out of focus artefact, the type of OTA does not have great leverage here.
BTW you can estimate the transmission product of the non-perfect contributing surfaces. Image a star, but do not saturate, record total integrated ADU in the seeing disk (e.g. aperture tool in Maxim). Now record long exposure to recover the unwanted halo. Find average adu level per pixel from the halo (above background) and halo diameter in pixels. Multiply avg adu by halo area, this is the halo power. Divide halo power by the star power times the integration time ratio. This number is R1*R2, where R1 and R2 are the reflection coefficients of the surfaces involved.
A formula might be clearer:
R1R2 = (avg halo count * halo area) / (star signal * LongTime/ShortTime)
Typical 'good' R would be 0.5% which is 0.005, so 0.005 squared is 25E-6, not much! So for a 1,000,000 adu star (way saturated!), 25 adu's of signal will be spread over the entire halo (1E6 * 25E-6).
For the halos to register I feel the star must be saturated in the order of 40E6 adu, those anti-blooming gates are just too good!