From: "Dwight K. Elvey" 
To: atm{at}shore.net
Reply-To: "Dwight K. Elvey" 


>From: "Mike space" 
>
>
>Hi Everyone,
>
>I have a question I can't seem to find an answer to:
>
>Here goes, Is the aperture stop of the end of the tube what limits the
F.O.V.or
is it the f ratio of the primary. My question is if you have the same focal
length primary and one tube you cut in half and shoot it out the side of
the telescope (forget about diagonal size) will the F.O.V. double.
>
>Thanks Mike
>

Hi Mike
 The field of view has two forms. One is the true field of view.
This is the angle of the sky that one sees. The other is call apparent
field of view. This is the angle seen by the eye. Surprisingly, both of
these are effectively limited by the design of the eyepiece.
 The focal length of the primary determines the angle of sky
that can be visible at the eyepiece. This is simple geometry. Say the
opening of the eyepiece ( field stop ) is one inch. Now lets say that your
telescope has a focal length of 5 feet ( 60 inches ):

  2*arcsin((1/2)/60)= 0.95 degrees ( the 2's are there to make
                                      right triangles for trig )

from the above, you can see that the true field of view is determined by
the size of the eyepiece's field stop and the focal length of the primary (
no mention yet of f-ratio ).
 This of course assumes that there is nothing else blocking
the light. Now, lets look at the effects of the tube itself. One can see
that a light ray coming from the edge of the tube to the edge of the mirror
might be less then 0.95 degrees. Still, if one looks at all of the light
rays from the star coming in parallel to each other, most make it to the
primary, and only a small crescent shape near the edge gets cut off. From
the eyepiece, we see this effects the brightness of the star near the edge
of the field of view. This dimming of the edges is called vignetting. This
can also happen from the secondary size as well.
 As one can see from the above example, that the angle of the star
light path would have to be quite far off to the side before it completely
cut of the light from the star reaching the eyepiece. Lets say that our
mirror was a 6 inch and the tube was an 8 inch tube. As an example, we'll
say that the tube extended 66 inches from the front of the mirror ( a
practical value ). The light would have to be at an angle of:

 arctan((6+1)/66)= 6.05 degrees.

 Without going into the limiting factor of the secondary, this
would require an eyepiece with a field stop of 6.3 inches in diameter
before there was a problem of this blocking all the light. This is not very
practical. Even 2 inch eyepieces cost a bunch, not to mention that the
secondary to get this much light to the eyepiece would block most of the
entire primary.
 Now, lets look at this f-ratio thing. Why do you hear that
lower f-ratios are used for wide field of views. This is simply because
lower f-ratios have shorter focal lengths. They don't magnify the sky as
much before entering the eyepiece. This means that for a particular field
stop, a same sized mirror will have the more field of view with a lower
f-ratio mirror. It will also have less magnification but the apparent field
of view will remain the same ( only controlled by the eyepiece).
 For any given telescope, the way to get more true field of
view and more apparent field of view at the same time is to buy an eyepiece
that is designed to have a larger field stop and a larger apparent field of
view ( $$$ ). I wish there was an easier way.
Dwight

--- BBBS/NT v4.00 MP