Re: [ATM] Secondary Cage Sizing?

["Lawrence Sayre" <lsayre@neo.rr.com>]

On Sat, 17 Apr 2004 20:49:58 -0700, MATTHEW SIMMONS <msimmonsmcse@msn.com>  
wrote:

> So I have a design conundrum here....My specs are as follows:
>
> 13.1" f4.5
> 2.6" (?)
> .25" focuser board
> 1.55" Moonlite Crayford +.25" racked out
>
> So, according to K&B, my secondary cage should be ~13.75" and my  
> illuminated FOV for a 2" ep sizes the secondary at just over 2.6" So far  
> so good. However, NEWT says that I will vignette the 75% ray at front  
> aperture. If I fool with the numbers in NEWT to prevent any vignetting,  
> it will take a 14.75" secondary cage. However, when I run those numbers  
> through the K&B equations, my fully illuminated FOV requires a 2.73"  
> secondary.
>
> So, should I care more about not undersizing the secondary or vignetting  
> the 75% ray at the front aperture? Which is worse for the overall  
> performance of the scope?
>
>
>
> Matt Simmons
>

To avoid all possible vignetting at the front cage ring, just make sure  
that your cage ID is at least the dia. of your mirror plus the field stop  
diameter of the widest field stop eyepiece you ever plan to use in the  
scope.  For a totally maximized example:

13.1" = 332.74 mm aperture
46 mm = widest possible field stop for any 2" eyepiece
332.74 + 46 = 378.74 mm
378.74/25.4 = 14.91" ID rings for the secondary mirror cage

Using 9.505" as diagonal to the focal plain distance (based on a cage ID  
of 14.91"), the excellent Mel Bartels Diagonal Calculator  
( http://members.efn.org/~mbartels/tm/diagonal.htm ) suggests that a 2.6"  
diameter secondary mirror will just ever so slightly vignette the  
outermost 10% FOV visually for a 46mm field stop eyepiece.  A drop-off of  
up to 70% illumination at the extreme field edge is considered "visually"  
imperceptible, and the "Diagonal Calculator" gives 68% illumination at the  
outermost edge here.  The 31mm Nagler has only a 42mm field stop, and the  
Wide Scan III maxes out at 44mm.  The only known eyepieces with 46mm field  
stops are 40mm or more in focal length, so in the real world you (assuming  
you are an average person) will not visually be able to perceive any drop  
off at all (of more than 70%) in edge of field illumination with any  
eyepiece available for actual use with your F/4.5 scope.  You can go to  
14.75" for the upper cage ID if the 31mm Nagler is to be considered, so  
NEWT is right on the money here.

The only thing that happens if the cage rings are designed at 13.75" as  
K&B suggest is that effectively you will loose about 1.1 inches of  
aperture with your absolutely widest TFOV (largest field stop) eyepiece.   
13.75" minus 1.73" (44mm field stop dia.) equals an aperture of 12.02  
inches.  The effect here will not be visible as edge of field vignetting  
(as it would be if you went much smaller than 2.6" for your secondary  
mirror), but only as a waste of (bought and paid for) aperture.  However,  
any other of your likely eyepieces in your collection will be 100% fine  
with a 13.75" cage ID, as they will not loose aperture due to their far  
smaller field stops.

It's always a matter of compromise in the end.  Since most viewing will be  
done with your smaller FL eyepieces, going with K&B for cage ID isn't a  
bad choice overall when weight and size savings (and balance factors) are  
considered.  However, K&B uses the same old simple and incorrect formula  
for deriving the 2.73" secondary mirror here that most books use.  The  
simple book formula always gives you a slightly larger secondary mirror  
than is truly necessary.  Mel Bartels Diagonal Calculator uses the far  
more complex true formula (that being the same formula that the program  
SEC.EXE uses, as well documented in an old Astronomy Magazine article), so  
it is to be trusted over K&B, etc...

Lawrence Sayre
-- 
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My philosophy, in essence, is the concept of man as
a moral being, with his own happiness as the moral
purpose of his life, with productive achievement as
his noblest activity, and reason as his only absolute.

Ayn Rand (in the appendix to 'Atlas Shrugged')
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