Re: (ATM) Newbie eyepiece question

[grant@aretha.llnl.gov (Chuck Grant)]

> From: pvg@eroch.mc.xerox.com (Paul Van Graafeiland)
...
> However, I haven't been able to find an answer to one question I have
> about eyepieces.  Does the focal ratio of an eyepiece make any
> difference?  I know that magnification is tied to an eyepiece's focal
> length, and that the eyepiece can only have so large of an outside
> diameter based upon the focuser it is used with, but will a 2"
> eyepiece give a "better" image than a 1.25 diameter eyepiece with
> everything else being equal?

I haven't seen anyone leap up with an answer to this one yet, so I
will take a shot.  This is a good question for a beginner to have.
I hope this clears things up.
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Does the focal ratio of an eyepiece make any difference?  Well, we
will have to define "the focal ratio of an eyepiece" as the answer
depends on the definition. Here are four answers.
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The telescope objective focuses the incoming, nearly parallel, light
into the shape of a cone.  The apex of the cone is in the focal
plane.  The focal ratio of the objective is roughly the length of the
cone (from objective to apex) divided by the diameter of the
objective.  (More exactly, it is twice the reciprocal of the slope of
the highest [closest to the edge of the objective] on-axis [parallel
to the optical axis before the objective] ray as it passes through
the image plane.

The width of the light cone shrinks as you move from the objective to
the image plane, and then spreads out after passing through the image
plane and moving towards the eyepiece. (With most, but not all,
eyepieces the image plane is located outside the lenses of the
eyepiece.)  The amount of the spreading of the light cone entering
the eyepiece is the same as the focal ratio of the objective.  Even
if the eyepiece could accept a wider light cone, the eyepiece always
operates at exactly the same focal ratio as the objective.

All other things being equal, including the field stop diameter, 
1.25" and 2" eyepieces will perform identically.  The extra size of
the 2" eyepiece will be completely wasted.

The field stop is an opaque surface with a round hole. It is a part
of the eyepiece and is located on the image plane (when the eyepiece
is properly focused).  The size of the field stop controls how wide
of an image can be seen with the eyepiece. It blocks the light from
the parts of the image plane which are too far off-axis.  The maximum
size of the field stop is the inside diameter of the eyepiece
body. It is usually much smaller than this because the eyepiece can
not focus these far off-axis rays very sharply.

2" eyepieces can have larger field stops than 1.25" eyepieces, thus a
2" eyepiece can have wider true field of view then any 1.25"
eyepiece.  (Clearly, you can put a bigger image in a 2" tube than in
a 1.25" tube.)

So in one sense, the focal ratio of the eyepiece is the same as the
focal ratio of the objective, and, within limits, is independent of
the eyepiece.

So the ratio of the eyepiece focal length to the eyepiece field lens
diameter doesn't make any difference.
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Now there is a maximum width light cone which a particular eyepiece
can accept and transmit completely through the eyepiece based on the
sizes of the lenses and stops within the eyepiece.  This might be
considered the non-vignetting focal ratio of the eyepiece.
(Vignetting means blocking part of the light)

An eyepiece with a smaller non-vignetting focal ratio can be used
with telescopes with smaller focal ratios (wider light cones) without
losing some of the light. This is not much of a consideration real
telescopes as the non-vignetting light cones of the eyepieces are
quite wide and more vignetting occurs in other parts of the
telescope.

Doesn't really make any difference.
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The optical performance (particulary the off-axis performance) of an
eyepiece, and just about any optical system, degrades as the focal
ratio becomes smaller (as the light cone becomes wider).  So for a
particular eyepiece and observer there is a smallest focal ratio
which produces an acceptably sharp view.

So an eyepiece might be said to have a performance limited focal
ratio.  This is a real consideration.  Most old eyepiece designs only
perform acceptably at f/10 or f/15 and above.  Even old wide angle
designs, like the Erfle, only work well at higher focal ratios.
Plossls work pretty well to f/6 or so. The main problem with
eyepieces at low focal ratios is astigmatism in the eyepiece (which
worsens as you get farther from the center of the field). The Nagler
eyepiece was the first eyepiece to correct the astigmatism
sufficiently so that wide light cones (down to f/3.5 or so) and wide
field of view (82 degrees) produce very sharp views.

Makes a lot of difference.
Too bad manufacturers do not specify this or any other eyepiece
f-number. 
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One thing that can make 2" better than 1.25" (everything else being
equal) is that a 2" focuser tube allows a wider light cone to enter
the focuser without vignetting.  Assuming, of course, that you are
using a focuser design which places the eyepiece at one end of a
tube. But this is more of a focuser issue than an eyepiece issue. A
3" focuser is even better!

Makes some difference.
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Chuck