Re:Re: ATM Aplanatic 4-mirror Exit Pupils

["Dwight K. Elvey" <dwightk.elvey@amd.com>]

>X-Original-From: kwhitefire@juno.com
>    
>  
>Hi Kevin
> I've not done and math on your design but there
>is one thing you need to check. You need to look
>at exit pupil for each of the surfaces. I had what
>I though was a real nice design, when I just figured
>focal lengths. Once I analyzed exit pupils, I found
>that my eye needed to be someplace inside of the
>telescope. Exit pupil changes when you place other
>optical elements in the light path. You don't want
>to make Gallileo's mistake.
>Dwight
>
>
>Now how do I do that?
>

>From previous post:

>
>Of course, I'm always the theorist.  This is what I have:
>
>This design features 4 mirrors on-axis.  The field curvature is in excess of 
250 miles with excellent construction and polishing techniques.  There are no 
exotic curves, though the primary does have a huge perforation.  Field of view 
is .25 degrees half-angle.
>
>All preliminary tracing done using Dave Stevick's Spotplot, Kevspot version, 
which allows the operator to choose paraboloids as +1 or -1.  I used -1 in these 
numbers to determine the figures.
>
>The data:
>Primary Mirror:
>D = 13.2 inches
>roc = 82.5 inches
>b = -.8305
>
>Secondary Mirror:
>D = 3.25 inches
>roc = -17 inches
>b = -.0148
>
>Tertiary mirror:
>D = 7.75 inches
>roc = 50 inches
>b = -.0949
>
>Quaternary mirror is a flat placed for convenient viewing between primary and 
tertiary mirrors.
>
>Primary to secondary distance = 32 inches
>Secondary to tertiary distance = 64 inches
>Tertiary to quaternary distance = 26 inches
>Quaternary to focal point = 3.35 inches

Hi Kevin
 I drug out my calculator and here is what I have.
I first placed things in line so that I could visualize
things like I was looking through a set of lenses.
This modeling works fine except for the location
of the final mirror needs to be shown at a hole
at the location in front of the focus and as a solid
blocking piece, in front of the tertiary. I didn't
do any vignetting math on this mirror but it looks
like it will be comparable to the hole in the primary.
 First thing I did was to check all of the math
for the focal points of images. These all checked.
 Now, lets look at exit pupil effects. The primary's
image through the secondary will be someplace between
the primary and the secondary ( since we're modeling
things as lenses, there is no confusion as to who
sees what image. This is why I like remodeling as
lenses, rather than mirrors). The secondary has a
focal length of -8.5 inches. Figuring where the image
would be as seen from the tertiary side, it is at
about 11.6 inches in front of the secondary. We can
now remove the original primary and secondary and
replace these with the new image, as though it were
the primary. Now, the tertiary sees a primary that
is 76 (64+11.6) inches away and is 4.77 inches in diameter.
 The tertiary lens images this new effective primary
at about 37.25 inches behind the tertiary. The
diameter of this image is about 2.34 inches. If one
places an eyepiece at focus, you get all kinds of
vignetting of the primary by the field stop until
the field stop gets to at least 1.84 inches in
diameter. It gets worse before it reaches your eyes.
Most eyepieces are not designed to except a diverging
objective image. The exit pupil through an eyepiece
will never come to focus and will continue to
expand. At least this is what my math shows.
 So, as you can see, you won't be able to make
an effective telescope for visual but it may still
be OK for photo.
 If someone else will check my math, it would be nice.
Dwight