From: chaloux@mandolin.mitre.org (Dave Chaloux)
Newsgroups: sci.astro
Subject: Re: Purchasing a portable telescope
Date: 17 Dec 92 17:37:19 GMT
Reply-To: chaloux@mandolin.mitre.org (Dave Chaloux)
Organization: The MITRE Corporation, McLean, Va

Doug McDonald writes:

>(Dave Chaloux) writes:


>>Some thoughts about off axis masks: I find it interesting that Mike has >>mentioned
>>using a 3" off axis mask to help. If a mirror is a figure of revolution with
>>a 1/2 mirror masking the mirror it is still 1/2 wave. Maximum Longitudinal and
>>transverse aberrations will be just as bad.


>Those last two statements may be true .. or they may be false, totally false.

>If the mirror has a smooth surface, but has spherical aberration,
>and is 1/n wave full aperture, it will be 1/(4*n) wave at half aperture.
>The same is true for pure third order astigmatism.

>If. in the other hand, it has narrow zonal aberrations and **no**
>third order spherical or astigmatism, then indeed stopping down will still
>leave a 1/n wave mirror 1/n wave.

>Doug McDonald

I hate to get into a squabble with a professional optician, especially since
there is the "remote" chance I am wrong.

I believe I understand what Doug is talking about and I think we are talking
Apples and Oranges. Specifically, what he says is true if you mask the
aperture down on Axis. In otherwords, the center of the mask matches the
center of the mirror. I specified that the mask was off axis and in this
case I am pretty sure that masking does not cut down the error in the
way he says. Trying to draw an ASCII diagram, if the mirror is a figure of
revolution your typical mirror might look like this.

    /-------------\          /--------------\
  /                 \       /                \
/                     \   /                   \
------------------------+----------------------- Prefect surface.


In the diagram the + marks the center of revolution. The peaks represent
the wavefront error at any particular distance across the mirror given the
center of curvature constant that minimizes the maximum wavefront error.
The way these particular diagrams are usually drawn this mirror is
overcorrected.

Now if you have a mask that is on axis you might expect that you would
simply chop off the diagram at the proper points and measure the
wavefront errors remaining. THIS DOESN'T WORK and I agree completely
with Doug on this point. Explaining why diagramatically is difficult but
the bottom line reason is that the center of curvature constant that
was used before is no longer the most appropriate constant. (These
constants can be thought of in terms of moving the focus slightly in
or out.)

Specifically, if you meet the conditions Doug sites, you will have a
much better mirror than you would expect from the diagram.

However, if you have your mask off axis, then the best center of curvature
constant remains the same. (By Off Axis I mean cut the above diagram in
half at the center of revolution). Because of this the total wavefront
error remains the same.

Now this actually gets complicated for a number of reasons.

1) In reality you have a central obstruction in the system. When you go
off axis you avoid the central obstruction. This leads to some gain. I would
point out that when using the mirror on axis you also have a central obstruction
and this means your best center of curvature is slightly different as well.
However the small gain you get from this on axis is more than made up for
by the bad affects of the central obstruction scattering light because of
diffraction affects.

2) When using the off axis mask, as pointed out by me previously, the
proportion of light coming from different parts of the mirror changes. This
means that the optimum way to focus the mirror is in fact somewhat different.
By focusing the mirror slightly different you actually get a worse total
wavefront error but since the proportion of light coming from the outer edge
is smaller, you get a better image.

----------------------------------------------------------------------------

My overall conclusion to this is likely to be somewhat controversial. In
my opinion, On Axis masks can be superior to Off Axis masks depending on the
size of the mirror, the kind of error, and the size of the central obstruction.
Doug has previously argued that a mirror with a central obstruction that is
perfect is as good as a perfect unobstructed system of size
Mirror_Rad - Obstruction_Rad/2. Because masking on axis has the positive
affects that Doug mentioned a large gain in wavefront error can sometimes be
gotten at a relatively small penalty in central obstruction.

I think this result should be better known in the amateur community. One
further benefit of masking on axis is that your sensitivity to collimation
errors is decreased where masking off axis I don't think (but I would love
to know if I am wrong) this is the case.

Doug, I would love to know how much of the above I have gotten dead wrong
as this entire area is very interesting to me both from a theoretical and
practical point of view.

Thanks: Dave

BTW Doug: I have been using the simple little program you wrote to get
pictorial images of the diffraction pattern of a mirror. A very simple
change to the program lets you get PGM files directly without going
through the converted. (Simple meaning writing three lines to the
beginning of the file as a header).
Newsgroups: sci.astro,sci.physics