Posted 08 February 2013 - 02:33 PM
First, your analysis is correct that an 82 degree eyepiece does indeed see further off axis than a 68 degree AFOV eyepeice of the same focal lenght.
But magnification is what allows you to actually resolve small angular detail. The comatic blur of a star will basically not be resolved as long as it remains smaller than about 2 arc minutes of apparent field. The dark adapted human eye is far less capable of resolving small details than the scotopic eye.
Let's use the example you mention above. I have a Panoptic with a one degree field, and a Nagler that shows a slightly larger true field.
A star at the field stop of the Panoptic would fall inside the field stop of the Nagler by 7 degrees of the apparent field.
Ah, but it would be magnified by a lower amount and this is the key. The role of the eyepeice is to magnify the view, and the Nagler basically makes the comatic blur larger angularly than it is in the Panoptic.
And the smaller it is, the harder it is for the eye to see it as a comatic blur.
So, anywere in the field of the Panoptic, stars will appear slightly sharper simply because the blur is slightly smaller. In terms of angular size on the focal plane, it is identical (it never chances of course), but in terms of the magnification, while I am seeing a point exactly the same distance from the center of the field in the Panoptic, it is being magnified less, so the abberations is simply harder to see. After all, that is what magnification does. It expands the angular size of a detail to the point that the eye can resolve it (about 2 to 3 arc minutes of apparent field for scotopic eye).
Does that make sense?
For the second part of your question, it is more complicated, but you can think about it like that if you like, though it is more about how the energy is concentrated (per linear millimeter) at the focal plane.
In a 3" f/6 telescope, the energy is contained in an area 1/4th the size as it is in a 12" f/6 telescope.
If I use a 10mm eyepeice in both scopes, they both produce an image just as bright but this is because in the smaller scopes, fewer rods are receving more light than in the larger scope. I see the image as just as bright, but smaller.
If I put in an eyepeice with 1/4th the focal lenght in the 3" scope, the energy from the focal plane is now spread out over an area equal in size to the 12" scope, but now the rods are all getting 1/4th of the light that they would receive in the 12" scope. You see the image now at the same mangification as the 12" scope, but because the light is spread over such a much larger area, it appears dimmer to you.
Here is another example. I have Pairs of 24mm 68 AFOV degree eyepeices, 32mm 52 degree AFOV eyepieces, and 40mm 43 degree AFOV eyepieces that I use in my Binoviewer.
All give about the same true field of view (limited by the field stop) but of course all three give different magnifications.
I use the 40s when I want to see Nebula and Galaxies show up with as much brightness as possible.
The 24s give a beautiful wide field, but at kind of small exit pupil. The Orion Nebula fills up the field.
When I put in the 32mm or 40m Plossls, the Orion Nebula still fills the field, but the field is much narrower. But the light is not more concentrated into fewer rod, so the nebula appears smaller, but brighter.
Same scope, same true field, but three different eyepieces that show the Nebula three different ways. One extreme gives a good view of the structure, but it looks dimmer. The other shows the Nebula much brighter. And the 32s are in between.
I went to the 40s in the Binoviewers because binoviwers cut the light into half and each eye is now only getting the light from a telescope that has 50% less light gathering (though binocular summation increases this to the equilivent of a telescope with 70% of the aperture).
This dimming bothered me, so in order to restore some of the brigtness, I knew I could just make the exit pupil larger and turn it back from a C11 to a C14 (brightness wise).
Anyway, it is the exit pupil that determines how bright an object looks and any two scopes using the same exit pupil will produce an image that is about the same brightness, and it is because of the way the incoming light is spread over more or fewer rods in the eye (or pixels in a CCD chip... I can put a 4x barlow in front of the camera on an 80mm ED and get the same image scale as the 12" scope, but I will now have turned my f/6 refractor into an f/24 camera lens!).
Again, I don't know if I have explained it well enough.
Anyway, a bigger exit pupil for a given scope will produce a brighter image, so a longer focal lenght Panoptic will produce a brighter (but smaller) image than a Nagler or Ethos with the same size true field...
If Galaxies and Nebula are important targets for you, then you can trade a little magnification to gain a bit of image brightness.
One caveat... Under light polluted skies, many people prefer to go to a smaller exit pupil for deep sky becuase it has the effect of suppressing sky glow. There is likely some truth to this because I think somone explained that it increases the signal to noise ratio or something.
If I want to see it as bright as possible though, I tend to use my lowest power eyepecies regardless of sky conditions. But that is just me. I feel like it gives the best result.