Re: ATM Herschelian, was (no subject)

[glheiner@pacbell.net]

James O'Malley wrote:
> 
> On Thu, 19 Aug 1999 glheiner@pacbell.net wrote:
> 
> > No, I don't think that's quite right. A spherical 8" needs to be
> > about f/9.0 (sez Couder via Tex) to be diff limited ON axis. Also
> > from Couder,
> > minimum f/length for a spherical mirror of diameter D to stay diff
> > limited is f^3 = 88.6D^4 (units in inches). Let's say your scope
> > is "almost Herchelian" & has 1/2 it's secondary in the field. Now
> > you would consider your 8" as a cylinder cut out of a 16", so
> >
> 
> You don't need to consider it a portion of a 16", a sphere is a sphere is
> a sphere.

The reason for considering a section of a 16" is because the Couder
formula above assumes on-axis operation. To use it to apply to an off-
axis situation requires using a section of a mirror of sufficient size
to simulate on-axis. You can't just tilt a curved mirror & expect
aberrations to not get worse- it's why we stick a secondary smack in
the middle of the primary's field, the exact place we'd really like NOT
to have to put it.  Even the "perfect" shape of a paraboloid, optically
perfect on-axis, turns garbage less than 2 degrees away in the sizes
of primarys we're interested in.  To actually get the focal field
clear of the incoming light & have a little room for a focuser & the
side of your head in the above example would require a section from
about
a 20" primary. Now the minimum f/l is a bit over 20 feet, and that
minimum
length is required for diff limited performance whether you use the
entire
20" or mask off an 8" chunk near the edge.

> >...
>...
> > If that 16 is an f/4 paraboloid, cutting out your 8" section
> > gives you an 8" f/8 that has the coma of an f/4,  still has
> > 1/2 the secondary in the field, & was such a total $!#@& to figure
> > you gave it up after your 40th figuring attempt & went Newt :)
> >
> This needs to be ray-traced. You bring up a good point but I am not sure a
> sphere has these problems. It does seem to me that you would need an
> oversized primary and an aperture mask to make the primary appear circular
> that far off-axis. 

Raytracing will basically confirm it, tho overall aberrations may be
slightly
reduced by monkeying with the focus or tilt of the eyepiece at the
expense of center-of-field performance, due to the now-non-symetrical
pattern of coma & astigmatism.  Yes, to keep the primary looking 
circular would require either a mask or a slightly elliptical primary.
But at the angles we're talking about, say 3 to 6 degrees, it can pretty
much be ignored.

> Say a 10" F/8 primary, an 8" aperture mask 3 inches off
> axis and tilted, an eyepiece 3 inches off-axis in the other direction with
> the opposite tilt.

If you draw this geometry out, the aperture mask won't make much
difference
because your head is still in the way. Now, you COULD tilt the primary
a couple of degrees just enough to be collecting from a field adjacent
to but clear
of your head. The resulting image will make it clear as to why
secondaries are
tolerated, and raytracing will confirm it. The results are exactly the
same
as those of a Newt's whose primary is grossly mis-collimated. aperture
mask
or not.

> The reason I think this is true is that if you look at the way a Schimdt
> camera handles off-axis rays through its small corrector, I think that we
> have the same situation here.

..or more like tilting a lensless Schmidt, ie moving the aperature mask
up to the center of curvature? Same rules & limitations on minimum F/L
as
above still apply. I'd guess adding the mask @ COC may allow a little
relaxation over the f/30 minimum on our 8", but not much. Don't really
know for sure offhand.

> You could leave the whole 16", make two 8" apertures in a single mask, and
> have a binocular Herschelian. It would be easier than matching two
> mirrors. (I'm getting out of hand now....)

You still have only one focal point & would need a bino adapter- might
as well lose the mask.

> jim

Gary
PS- Welcome to optics, where first-glance common sense is the biggest
hazard.
BTDT, & still doing it :)