The Rich Field Telescope or Richest Field Telescope or RFT has an honorable history. Basically, the game is "how low of a power can I profitably use with a given objective". The old Amateur Telescope Making series (Ingalls, editor) had many articles on the RFT.
There are many uses for an RFT or an approximation. One use is just what the name suggests: wide-field views that are rich with stars. The Pleiades with a six-inch scope at 22x is an impressive sight. Another use is to maximize the brightness of extended objects: this is especially important when using narrow-band nebula filters, which I do much of the time. I discuss the observations that I make with my two RFT refractors in a companion article at this site.
An interesting question is "How rich can a rich-field telescope be?" What are the limits on either maximizing the number of stars visible in the field (the main concern of Amateur Telescope Making) or of maximizing the aparent surface brightness of an extended object like the Veil Nebula.
Although conceptually a RFT can be of any aperture, in normal usage, an RFT is relatively small. There is a "lowest" power for a 30-inch telescope (about 110x) but such a telescope, with a field-width of less than a degree, is not normally considered a RFT.
I have recently built two Rich Field Telescopes: a six inch folded refractor and a eight-inch or four-inch folded refractor with flip-mirror switching.
For a somewhat different view of the Rich Field Telescope than this one, see Mel Bartels RFT page.
The goal of an RFT is the lowest power for the widest field, and the lowest power for the brightest view of non-point sources.
What produces a lower limit on the power? The exit pupil. The exit pupil is the bundle of light that leaves the eyepiece, headed for your eye. If it does not get into your eye, through the pupil, light is wasted. Thus your pupil determines the lower limit on magnification. The standard nominal value for pupil diameter in the dark is 7mm. It decreases a bit with age; I measured 6.5mm at age sixty. When your eye-doctor dilates your eyes, your pupils can get to 9mm or even 10mm diameter -- but this isn't useful, because your lens isn't that big.
All that a too-big exit pupil does is waste light. If you have a four-inch aperture 20-inch focal length objective and you use a two-inch focal length eyepiece, you will get 10 power and a 10mm exit pupil. What bad is happening? If your pupils are only 7mm, then you are only using the inner 7/10 part of the light. You could get the same result with a 2.8-inch diameter objective. Thus you are wasting some of your four-inch telescopes light-gathering. This may be OK -- maybe you really want 10x and don't have a smaller telescope. But you wouldn't plan for this, because bigger aperture is a major cost.
Along with wanting to fill your pupil, you want to use all of the pupil. Your pupil is a circular disc. You not only want to match the diameter, but the shape. Fortunately, most telescope apertures are round. Unfortunately, many have holes in the middle: secondary obstruction. From the viewpoint of filling your pupil, the "hole in the middle" is a pure waste that cannot be recovered. (Further, the center of your pupil has the best acuity, so you are also losing eye resolution.)
Thus if you want to max-out the RFT, you need an exit-pupil that matches your eye and does not have a hole in it. This could be a refractor or an off-axis reflector. We will later see that we would like a short focal-ratio, on the order of f/6 or so. That makes an off-axis reflector exceedingly expensive.
The above discussion is the critical one: decide what field of view you want or what objective aperture you can afford, and then create a system that gives you a 7mm (or your measured pupil-size) exit pupil: exit pupil diameter = objective diameter / power. or alternatively exit pupil diameter = eyepiece focal length / primary f-ratio
The reader might think "Come-on, we are only talking about a small donut hole in the exit pupil here. How much does it really affect the throughput?"
Indeed the design of the optimal RFT might be considered a bit of "overkill". But the remarks above are real. Let me expand them a bit:
The central obstruction of a reflector, as I noted, is not something that can be recovered. It is a pure loss. How big a loss? Well, reflectors certainly exist with a central obstruction of about 0.25 linear, or 1/16th of the area. But remember we are talking about a short focal ratio and wide field telescope. That changes the story about a central obstruction: both the wide field and the shorter f-ratio require a larger secondary. We would like a f/6 system with room for nebula filters and coverage of the field-stop of a two-inch eyepiece without vignetting. (And a wide enough tube to minimize visible tube-currents.) If you perform a required-diagonal calculation (or ray-trace) for such a short Newtonian, you will see that a central obstruction of about 0.4 is required. That is a 16% light loss: not trivial.
Also, a reflector will have at least two reflecting surfaces. Reflecting surfaces are less efficient, today, than multi-coated transmissive surfaces. So the reflections will be an additional loss. This can be ameliorated with special coatings like "enhanced silver" -- but such a coating is expensive (and fragile) on a primary mirror.
So a refractor will be 12-16% more efficient, overall, than a reflector. And remember, one cannot say "Well, I can make that up by increasing the aperture a bit" because you are limited by the eye-pupil diameter.
The alert reader will note that my two RFTs are both "folded", indicating I have been willing to trade some efficiency for a good observing position. All true. In defence, I will only note that the folding mirror is well protected inside a closed tube, and is of moderate size, so it is resonable for it to feature an "enhanced" high reflectivity coating.
Long ago I designed an interesting folded reflector: a 0.36 meter system with a 0.18m folding flat and the focus at the Naysmith location: it could either be a f/4 folded Newtonian or a f/16 folded Cassegrain via mirror-rearrangement. I bought the optics, but never built the telescope. This was partly due to construction difficulties -- the mirror-rearrangement mechanism had to fit within the shadow of the folding flat -- and partly because a system with a 25% light loss due to the folding flat, plus three reflectons (five as a Cass) was never going to be a good low-power instrument.
One final facet of a reflector with a central obstruction is that the obstruction seems to makes it more difficult to keep the exit pupil aligned with your eye's pupil -- the "I am off center" visual feedback seems weakened. This is especially the case if you are using a super-wide-field eyepiece where you cannot see the field-stop.
The above is really the only crucial calculation: Use all your pupil. But there are other practical concerns.
One is eyepieces and focussers. Recall the second formulation about exit pupil: exit pupil = eyepiece focal length / objective f-ratio.
Thus if you have a f/15 refractor and you want a 7mm exit pupil, you need to use an eyepiece of 105mm focal length. Such an eyepiece is not practical. For it to have a decent apparent field of view, it would have to be at least four inches in diameter. We are talking bulk, weight, cost.
We see that if we would like the 68 degree apparent field of a TeleVue Panoptic, the longest focal length available is 41mm, due to the limitations of a two-inch barrel: for a 7mm exit pupil this means we need an f-ratio of six or under.
The Mel Bartels RFT page, mentioned earlier, notes the benefits of a super-wide eyepiece. Indeed if the goal is maximum nomber of stars visible in the apparent field, then an increased field (at the same exit pupil) is a clear win, since the "extra" field is just replacing blackness: this is assuming apparent field that you have to turn to see fully is valuable. The downside of the extra wide field is that for a 100-degree apparent-field eyepiece that fits in a two-inch focusser, the maximum possible focal length is about 27mm and the maximum for sale focal length is 21mm; with a 21mm Ethos eyepiece you need a primary f-ratio of three or under to get a 7mm exit pupil.
It is difficult to create a refractor with a short focal ratio that has acceptable optical quality. Fortunately, in our RFT we are going to be using the lowest feasible powers, so we are not stressing the image-forming capabilities of our objective.
In the preceeding section we discussed how our RFT goals interact with real-world considerations about eyepieces and eyepiece size.
Related to eyepiece size is the other elements of the path from objective to eyepiece -- in particular the diagonal.
We noted that for a 68 degree apparent field Panoptic, the longest focal length available is 41mm, because a longer focal length would require a field lens that would not fit in a two-inch barrel.
We can extend that geometric discussion to the rest of the system and in particular to the diagonal. Suppose we have a f/6 system with a 41mm Panoptic eyepiece, giving us a nice 7mm exit pupil. If we ray-trace from the objective to the eyepiece, we see that the photons fill a frustrum of a cone, with one end at the objective and the other end at the eyepiece. That cone gets wider as it goes from eyepiece to objective. If we have an eight-inch f/6 objective, then three inches from the eyepiece field-lens, it will have expanded by (8-2)/(3/48) inch. That is 3/8 of an inch, or 9mm. How big is your star-diagonal? The obtical path through a two-inch diagonal is about three inches. So the aperture of your diagonal needs to be 19mm larger than that of the eyepiece. If it is a two-inch diagonal, it is not: the diagonal will produce vignetting.
It is easy to draw a simple sketch of the converging beam, from objective to eyepiece, and see how big a diagonal you would need. Or, turning it around, how much a two-inch diagonal limits the illuminated field at the eyepiece and hence the eyepiece's focal length and apparent field of view.
We have narrowed our space of "ultimate" RFT systems to refractors of f/6 or shorter.
Since the shorter the refractor the more expensive and the harder it is to control aberrations, that effectively means a refractor between f/5 and f/6.
Our aperture should be greater than 50mm (below that we can easily use binoculars). We are limited at about 200mm at the high end due to unavailability.
Thus our ultimate RFT will be a refractor of between 80 and 200mm aperture, f/4 to f/6, with the appropriate eyepiece to create a 7mm or 6.5mm exit pupil.
If we do not want to vignette the outer part of the field due to a two-inch star-diagonal, we will need to keep the focal ratioo at f/5 or under.
Given the above, you might expect that my RFT refractors would fit the constraints listed above. Indeed they do. They are a six inch f/5 and a flip-mirror switching RFT that is both a eight inch f/6 and a four inch f/6.
One way you can beat the "size of your pupil" limitation is to realize that you have two of them.
Hence the appeal of large binoculars and binocular-telescopes.
How much you gain by using two eyes varies from person to person. Experiment before you go this expensive route. It is easy to experiment: just use astronomical binoculars and compare your observations using both eyes to your observations with one eye shut or one objective capped.
This is different from using a beam-splitter binocular eyepiece holder on a telescope. The latter cuts the overall brightness at each eye in half (really worse, considering losses) and so does not offer the improvement of binoculars.
I would be happy to correspond about telescope design with interested individuals.
I can be reached via email as "bob" at this dot-org domain. Or at astroayers@gmail.com