Some thoughts on high etendue telescopes, HET as Mel Bartel calls them.
As a fan of rich field/wide angle astronomy viewing, and visually observing low contrast DSOs, and a tinkerer, I am interested in exploring the different possibilities with these. Additionally, havin taken up night vision image intensifier viewing, it brings in considerations that imagers have about fast optics to best illuminate their sensors.
There is no standard unit for measuring etendue, various systems of units are used depending on the application. Mel Bartel has a computation which I will call a "Bartel etendue figure of merit" which can be used to roughly compare different telescope confiugrations.
BEFOM = aperture^2 * TFOV^2
A "proportionality" symbol instead of an equality symbol might be better here since this is not geometrically accurate, omitting the Pi/4 factor for round optics. It also ignores the aperture loss from the central obstruction in Newtonians (which are the telescopes Mel is applying them to), though that would not be greatly different between the scopes likely to be compared for this.
Formulated this way, for a visual observer, the eyepiece is an integral part of the calculation since it determines the true field of view with the telescope focal length modified by the coma corrector.
Taking that into account the BEFOM of a system is determined by:
BEFOM = (Field Stop)^2/(Focal Ratio)^2
The coma correction factor can be applied to either the field stop (as Mel recommends) to decrease it or to the focal ratio, to increase it, as people more commonly do, with the same effect.
Now the aperture does not appear at all in the equation. It shows that HET potential is unrelated to aperture (relative CO being held constant).
What larger aperture does is provide the same etendue at higher magnification for the same field stop, which should always be as large as possible.
The additional constraint on this is that the exit pupil should be very close to the maximum pupil size of the observer, to get the benefit of the HET system. Much smaller, or larger, then the maximum potential of light capture in viewing is not obtained.
BTW - using the hex key method of measurement my exit pupil (age 62) is greater than 5.5 mm but less than or equal to 6 mm. Maybe it is 6 mm, but I suspect that might be a trifle optimistic and at any rate it is not going improve, so in planning a system I will want to use for the next 20 years I use 6 mm as a hard upper limit, and aim to be just below that. But effective BEFOM-wise though, going slightly larger has the same effect of going slightly smaller, if you take the "wasted light" into consideration.
Exit Pupil = (EP Focal Length)/(Focal Ratio)
Again with the coma correction factor applied to either value as you please.
There are only a few eyepieces on the market (or even optically feasible) that are candidates for maximizing BEFOM for any particular primary diameter and focal length and coma corrector combination, and there are only three suitable coma correctors on the market, each with a different magnification factor (1.15, 1.10, 1.06).
In optimizing telescope configurations then, this is a type of integer optimization problem (for those of you in to operations research, or algorithms) where there are only a few discrete choices to be made among available eye pieces that are close to what is optimal for a particular diameter and focal length. Or to look it a little differently, there are only a few EP/CC options on the market that can be matched to a feasible primary to optimize BEFOM.
On Mel's site he discusses the use only of Televue optics, the 21 mm Ethos and the Paracorr family,
Since Mel started writing on this subject Explore Scientific has come out with an eyepiece and a coma corrector that achieves equivalent BEFOM with an F/4 mirror, which are much more readily available.
I have built one such myself, using a 6" F/4 (well, 152mm F/3.92) mirror from GSO.
Looking toward a larger project, an 8" or a 10", I am wondering if I am missing something in using this combination instead of the F/3 Paracorr 20/21 mm 100 degree EP solution.
One argument might be that the overall optical quality of the ES 100 25mm, and the HRCC, is not quite as good as the Televue. And I will agree that Televue sets the standard. But if I find them acceptable (and I have thus far not found cause for complaint), is there anything else?
One advantage of using F/4 mirrors is that they are available at very reasonable prices. From GSO an 8" is $230 and and 10" is $480. I use one for a build AND drop in a replacement later, from Zambuto say, at a cost of $1475 and $2150, respectively. F/3 mirrors would run higher than that.
An advantage of the F/3 mirror is simply that it makes a more compact telescope. But in the 8-10" range this is not that big a factor, since even a 10" F/4 is all that long.
I am planning on building a 10" HET, and seeing if anyone can make the case for going with an F/3 mirror. I would sort of like to be convinced, but haven't been able to convince myself.
Attached are the optimum HET configurations of the telescopes under discussion. The lower field stop value is the calculated value for the ES 100 20 mm (which I have) and the higher is for the ES 100 25 mm (ditto).
P.S. Just after posting this it occurred to me another possible advantage of the F/4 mirror -- using if without the CC for an extended object like Andromeda or Barnard's Loop. You could do this with an F/3 also, but the comatic effect would likely be much less noticeable with the F/4. It would be interesting to compare the views though for a definitive judgement.
Edited by careysub, 10 April 2020 - 12:15 AM.