ATM 1st mirror goal - overcorrected

[Steve Lee <SL@AAOCBN1.AAO.GOV.AU>]

> I'm grinding my first mirror, a six inch, f/4.5 that I plan to figure 
> to complement a Lumicon 48mm aperture coma corrector.  According to 
> Lumicon's literature they recommend 20-25% overcorrection.  The 
> question I have is:

> How does this degree of overcorrection apply to knife edge test 
> readings?  Do I simply increase the expected knife edge travel for 
> the same R of C parabola by 20-25%?

I believe that the knife-edge formula is

delta = b(r**2/R) + (r**4/2R**3)

where delta is the knife-edge movement for the zone in question
      r     is the radius if the zone
      R     is the radius of curvature of the mirror
and   b     is the "deformation coefficient" which is the eccentricity
            squared
(for a fixed light and moving slit.)

But it depends on exactly what they mean (which is you're question).
If they've supplied the desired eccentricity then just plug it into
the above formula, but they could have already done this and mean that
you just do 1.25(r**2/R).

> And then Mel asked...
> Your note that Lumicon's literature recommends overcorrection for their
> coma corrector caught me by surprise.  I don't see how deepening the
> center of the mirror is going to change coma.  The comatic tail is
> formed from light coming from the far side of the mirror, not only the
> mirror center.

The reason for the overcorrection is to correct the spherical aberration
that the coma corrector supplies.  It is the nature of the Ross corrector
that to reduce the coma you end up introducing spherical aberration - if
you are using a paraboloid.  It turns out that making wide field correctors
is much easier and better if you have a hyperboloid primary.

I guess that Lumicon went for the best correction of coma and ignored
the slight spherical aberration that it introduced (and told the purchaser
what to do if they wanted to leave the lens in place always).  You
wouldn't notice the spherical aberration at low power, but at high power
it would be apparent.

You might know that Takahashi have a range of fast Newtonians with
in-built coma correctors intended for wide-field photography.  Their
advertisements note that the primary mirror is a hyperboloid.

Steven Lee
URL:        http://www.aao.gov.au/local/www/sl/
e-mail      SL@aaocbn.aao.gov.au